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cat-searcher/leandojo-benchmark-4-random | test | 3,696 | MvPowerSeries.inv_eq_zero | Mathlib/RingTheory/MvPowerSeries/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical rw [<a>MvPowerSeries.coeff_inv</a>] split_ifs <;> simp only [h, <a>map_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>GroupWithZero.inv_zero</a>, <a>neg_zero</a>] | σ : Type u_1
R : Type u_2
k : Type u_3
inst✝ : Field k
φ : MvPowerSeries σ k
h : (constantCoeff σ k) φ = 0
n : σ →₀ ℕ
⊢ (coeff k n) φ⁻¹ = (coeff k n) 0 | ((:c Eq) (:fv _uniq.56254) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.56254) (:fv _uniq.56254) ((:c DivisionSemiring.toSemiring) (:fv _uniq.56254) ((:c Semifield.toDivisionSemiring) (:fv _uniq.56254) ((:c Field.toSemifield) (:fv _uniq.56254) (:fv _uniq.56257)))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.56254) ((... | [{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"k","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.56254))"},{"name":"φ","sexp":"((:c MvPowerSeries) (:fv _uniq.56248) (:fv _uniq.56254))"},{"name":"h","sexp":"((:c Eq) (:fv _uniq.56254) ((:c DFunLike.co... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":7822,"sourceStart":7813,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":7831,"sourceStart":7829,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"... | [] | [{"source":"coeff_inv","source_end":7842,"source_start":7833,"syntax_kind":"ident"},{"source":"h","source_end":7884,"source_start":7883,"syntax_kind":"ident"},{"source":"map_zero","source_end":7894,"source_start":7886,"syntax_kind":"ident"},{"source":"zero_mul","source_end":7904,"source_start":7896,"syntax_kind":"ident... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 40 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dde8e82eb08ed46021e81969e30910d6d096f7d047b827fd19ccfd8a274055cc | cb3c5df1a5b729ac4febc00a4c11f19a06f39c363531b93c21a391f06900d968 | b24c3948b2892085a35ba261764da0dc42946b5f60bee1018517b4d0b27ec29c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,697 | MvPowerSeries.inv_eq_zero | Mathlib/RingTheory/MvPowerSeries/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MvPowerSeries.coeff_inv</a>] | σ : Type u_1
R : Type u_2
k : Type u_3
inst✝ : Field k
φ : MvPowerSeries σ k
h : (constantCoeff σ k) φ = 0
n : σ →₀ ℕ
⊢ (coeff k n) φ⁻¹ = (coeff k n) 0 | σ : Type u_1
R : Type u_2
k : Type u_3
inst✝ : Field k
φ : MvPowerSeries σ k
h : (constantCoeff σ k) φ = 0
n : σ →₀ ℕ
⊢ (if n = 0 then ((constantCoeff σ k) φ)⁻¹
else
-((constantCoeff σ k) φ)⁻¹ * ∑ x ∈ antidiagonal n, if x.2 < n then (coeff k x.1) φ * (coeff k x.2) φ⁻¹ else 0) =
(coeff k n) 0 | ((:c Eq) (:fv _uniq.56254) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.56254) (:fv _uniq.56254) ((:c DivisionSemiring.toSemiring) (:fv _uniq.56254) ((:c Semifield.toDivisionSemiring) (:fv _uniq.56254) ((:c Field.toSemifield) (:fv _uniq.56254) (:fv _uniq.56257)))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.56254) ((... | [{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"k","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.56254))"},{"name":"φ","sexp":"((:c MvPowerSeries) (:fv _uniq.56248) (:fv _uniq.56254))"},{"name":"h","sexp":"((:c Eq) (:fv _uniq.56254) ((:c DFunLike.co... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":7831,"sourceStart":7829,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7833,"sourceStart":7832,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MvPowerSeries.coeff_... | [] | [{"source":"coeff_inv","source_end":7842,"source_start":7833,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 40 | 12 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8fbc9b30a2c6175c2fc88caecf4a64a8a02c0868b824128daf05b09f62d76aec | cb3c5df1a5b729ac4febc00a4c11f19a06f39c363531b93c21a391f06900d968 | 44f52189c7e1681efa121091322d5070927960cf8401cd1715642ade879925ad | 179e159997c51a7e778f4c123cab612aab2ab73bef7b144d5fbd2de07e72bae8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,698 | MvPowerSeries.inv_eq_zero | Mathlib/RingTheory/MvPowerSeries/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs <;> simp only [h, <a>map_zero</a>, <a>MulZeroClass.zero_mul</a>, <a>GroupWithZero.inv_zero</a>, <a>neg_zero</a>] | σ : Type u_1
R : Type u_2
k : Type u_3
inst✝ : Field k
φ : MvPowerSeries σ k
h : (constantCoeff σ k) φ = 0
n : σ →₀ ℕ
⊢ (if n = 0 then ((constantCoeff σ k) φ)⁻¹
else
-((constantCoeff σ k) φ)⁻¹ * ∑ x ∈ antidiagonal n, if x.2 < n then (coeff k x.1) φ * (coeff k x.2) φ⁻¹ else 0) =
(coeff k n) 0 | ((:c Eq) (:fv _uniq.56254) ((:c ite) (:fv _uniq.56254) ((:c Eq) ((:c Finsupp) (:fv _uniq.56248) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero))) (:fv _uniq.56797) ((:c OfNat.ofNat) ((:c Finsupp) (:fv _uniq.56248) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.... | [{"name":"σ","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"k","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.56254))"},{"name":"φ","sexp":"((:c MvPowerSeries) (:fv _uniq.56248) (:fv _uniq.56254))"},{"name":"h","sexp":"((:c Eq) (:fv _uniq.56254) ((:c DFunLike.co... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c ite) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Nat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"source":"split_ifs","sourceEnd":7859,"sourceStart":7850,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.splitIfs","source":"split_ifs","sourceEnd":7859,"sourceStart":7850,"tag":"node"},{"sourc... | [] | [{"source":"h","source_end":7884,"source_start":7883,"syntax_kind":"ident"},{"source":"map_zero","source_end":7894,"source_start":7886,"syntax_kind":"ident"},{"source":"zero_mul","source_end":7904,"source_start":7896,"syntax_kind":"ident"},{"source":"inv_zero","source_end":7914,"source_start":7906,"syntax_kind":"ident"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56248","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56251","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 40 | 15 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b9451373e05a7a4b18a72f2e903b1b05dc3b9ffcf6d72572535327619f9fe76 | 179e159997c51a7e778f4c123cab612aab2ab73bef7b144d5fbd2de07e72bae8 | 4053bbe7d8a2dcfeed1f0200d3ebb8c3a4351518bef3c7da488e1a935867ca23 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,699 | Polynomial.degree_C_mul_X_pow_le | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.C_mul_X_pow_eq_monomial</a>] | R : Type u
S : Type v
a✝ b c d : R
n✝ m : ℕ
inst✝ : Semiring R
p q r : R[X]
n : ℕ
a : R
⊢ (C a * X ^ n).degree ≤ ↑n | R : Type u
S : Type v
a✝ b c d : R
n✝ m : ℕ
inst✝ : Semiring R
p q r : R[X]
n : ℕ
a : R
⊢ ((monomial n) a).degree ≤ ↑n | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.33448) (:fv _uniq.33465) ((:c HMul.hMul) ((... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a✝","sexp":"(:fv _uniq.33448)"},{"name":"b","sexp":"(:fv _uniq.33448)"},{"name":"c","sexp":"(:fv _uniq.33448)"},{"name":"d","sexp":"(:fv _uniq.33448)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","se... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33448","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33450","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":12563,"sourceStart":12561,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12565,"sourceStart":12564,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.C_mul... | [] | [{"source":"C_mul_X_pow_eq_monomial","source_end":12588,"source_start":12565,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33448","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33450","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 114 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf163181c59e5ba9f4f72337edaa0e0c9d5dddb344bdc024c280e74a43c80d6d | 57718fae4a68538edeeb8977c8e060dce5eb470927b998c69b50133894160150 | dffc05b8564a577a6de543f2143656400078349e54a85136d142afa8320b3f72 | dcd1be976af1a51d97bd54f362156a4d6b3859d198052fc98b3cb17013029e7c |
cat-searcher/leandojo-benchmark-4-random | test | 3,700 | Polynomial.degree_C_mul_X_pow_le | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Polynomial.degree_monomial_le</a> | R : Type u
S : Type v
a✝ b c d : R
n✝ m : ℕ
inst✝ : Semiring R
p q r : R[X]
n : ℕ
a : R
⊢ ((monomial n) a).degree ≤ ↑n | ((:c LE.le) ((:c WithBot) (:c Nat)) ((:c Preorder.toLE) ((:c WithBot) (:c Nat)) ((:c WithBot.preorder) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))))) ((:c Polynomial.degree) (:fv _uniq.33448) (:fv _uniq.33465) ((:c DFunLike.coe)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a✝","sexp":"(:fv _uniq.33448)"},{"name":"b","sexp":"(:fv _uniq.33448)"},{"name":"c","sexp":"(:fv _uniq.33448)"},{"name":"d","sexp":"(:fv _uniq.33448)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","se... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat))))))) (:arg :explicit 2 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33448","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33450","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":12597,"sourceStart":12592,"tag":"atom"},{"name":"Polynomial.degree_monomial_le","semanticRole":"global","source":"degree_monomial_le","sourceEnd":12616,"sourceStart":12598,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply degree_monomial_le","sourceEnd":12... | [] | [{"source":"degree_monomial_le","source_end":12616,"source_start":12598,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33448","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33450","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 114 | 7 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a18e4d7d9da06434c7923b26fdf4f39708f3593ca102f0d445f40f7a1a607d9 | dcd1be976af1a51d97bd54f362156a4d6b3859d198052fc98b3cb17013029e7c | b5ad45d7b4c84cd72c8d4ed5eeca4c8f286b70dea2107c55e8ceb1c7ebaaf7a3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,701 | Submodule.le_one_toAddSubmonoid | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x ⟨n, rfl⟩ | ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ 1 ≤ toAddSubmonoid 1 | case intro
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n✝ : A
n : ℕ
⊢ (Nat.castAddMonoidHom A) n ∈ toAddSubmonoid 1 | ((:c LE.le) ((:c AddSubmonoid) (:fv _uniq.6547) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.6547) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.6547) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.6547) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.6547) ((:c Semiring.toNonAssocSemiring) (:fv _un... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.6542))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.6547))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.6542) (:fv _uniq.6547) (:fv _uniq.654... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6540","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6542","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"rintro","sourceEnd":3021,"sourceStart":3015,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":3023,"sourceStart":3022,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":3023,"sourceStart":3022,"tag":"... | [{"role":"fresh_name","source":"n","source_end":3028,"source_start":3027,"syntax_kind":"ident"}] | [{"source":"⟨n, rfl⟩","source_end":3036,"source_start":3024,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6540","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6542","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 22 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0f3408a7239d01c039805a582ae0ccd0d679ab3915b3cf022fffe40c55371ff | 89b31d858c8055ea957211aad68abbd93087f9f4b18f0035889fbaec8c3c1dcf | d96d970d48a0df310b670fd661d0120a54936b4d953adc4d4a0df7ce9566b9cb | 0dcd591189a34f8cd2d7791282b5ae9c00b212213d169e2f5b6888e738dedf03 |
cat-searcher/leandojo-benchmark-4-random | test | 3,702 | Submodule.le_one_toAddSubmonoid | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨n, <a>map_natCast</a> (<a>algebraMap</a> R A) n⟩ | case intro
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n✝ : A
n : ℕ
⊢ (Nat.castAddMonoidHom A) n ∈ toAddSubmonoid 1 | ((:c Membership.mem) (:fv _uniq.6547) ((:c AddSubmonoid) (:fv _uniq.6547) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.6547) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.6547) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.6547) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.6547) ((:c Semiring.to... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.6542))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.6547))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.6542) (:fv _uniq.6547) (:fv _uniq.654... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6540","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6542","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"source":"exact","sourceEnd":3044,"sourceStart":3039,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":3048,"sourceStart":3045,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"n","sourceEnd":3049,"sourceStart":3048,"tag":"identifier"},{"source":",","sourceEnd":3050,"source... | [] | [{"source":"⟨n, map_natCast (algebraMap R A) n⟩","source_end":3084,"source_start":3045,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6540","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6542","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 22 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 413f9f854df413e8066d6cc40e5cea4b848e774870d833f8daf7f4abe41d3d75 | 0dcd591189a34f8cd2d7791282b5ae9c00b212213d169e2f5b6888e738dedf03 | ea22b95c76b6d9de783aa996d1cda6f51caf948f478beade65d333a638ffcbb8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,703 | Finpartition.part_surjOn | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨x, hx⟩ := P.nonempty_of_mem_parts hp | α : Type u_1
inst✝ : DecidableEq α
s t u : Finset α
P : Finpartition s
a : α
p : Finset α
hp : p ∈ ↑P.parts
⊢ p ∈ P.part '' ↑s | case intro
α : Type u_1
inst✝ : DecidableEq α
s t u : Finset α
P : Finpartition s
a : α
p : Finset α
hp : p ∈ ↑P.parts
x : α
hx : x ∈ p
⊢ p ∈ P.part '' ↑s | ((:c Membership.mem) ((:c Finset) (:fv _uniq.77429)) ((:c Set) ((:c Finset) (:fv _uniq.77429))) ((:c Set.instMembership) ((:c Finset) (:fv _uniq.77429))) (:fv _uniq.77844) ((:c Set.image) (:fv _uniq.77429) ((:c Finset) (:fv _uniq.77429)) ((:c Finpartition.part) (:fv _uniq.77429) (:fv _uniq.77436) (:fv _uniq.77441) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.77429))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"P","sexp":"((:c Finpartition) ((:c Finset) (:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"obtain","sourceEnd":19610,"sourceStart":19604,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":19614,"sourceStart":19611,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEn... | [] | [{"source":"P.nonempty_of_mem_parts hp","source_end":19652,"source_start":19626,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, hx⟩","source_end":19622,"source_start":19611,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 111 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa33980a4bb6d8ef4fae89eb84ac6e629e50c5d043dbf1e66f3f25ed0b46dc9c | cab57ac184b112aa19dafd853ede2689d40b2566c0ba3decbac1ea0dc80ad34f | 230eaa31f029ebc816dce891e90ba4fc44dcfbfc1a00f1a038646bccd3f0f3e3 | 0850af480c74023b3642756187a3af9f31cc10009d0416ee23b0a2da05b617e8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,704 | Finpartition.part_surjOn | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hx' := <a>Finset.mem_of_subset</a> (P.le hp) hx | case intro
α : Type u_1
inst✝ : DecidableEq α
s t u : Finset α
P : Finpartition s
a : α
p : Finset α
hp : p ∈ ↑P.parts
x : α
hx : x ∈ p
⊢ p ∈ P.part '' ↑s | case intro
α : Type u_1
inst✝ : DecidableEq α
s t u : Finset α
P : Finpartition s
a : α
p : Finset α
hp : p ∈ ↑P.parts
x : α
hx : x ∈ p
hx' : x ∈ s
⊢ p ∈ P.part '' ↑s | ((:c Membership.mem) ((:c Finset) (:fv _uniq.77429)) ((:c Set) ((:c Finset) (:fv _uniq.77429))) ((:c Set.instMembership) ((:c Finset) (:fv _uniq.77429))) (:fv _uniq.77844) ((:c Set.image) (:fv _uniq.77429) ((:c Finset) (:fv _uniq.77429)) ((:c Finpartition.part) (:fv _uniq.77429) (:fv _uniq.77436) (:fv _uniq.77441) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.77429))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"P","sexp":"((:c Finpartition) ((:c Finset) (:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"have","sourceEnd":19659,"sourceStart":19655,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx'","sourceEnd":19663,"sourceStart":19660,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hx'","sourceEnd":19663,"sourceStart":19660,"tag":"n... | [] | [{"source":"mem_of_subset (P.le hp) hx","source_end":19693,"source_start":19667,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 111 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 02baa5769635515ffb2f6c21661f076dcb7ab0458286dcfa20e18856cc01d4c5 | 0850af480c74023b3642756187a3af9f31cc10009d0416ee23b0a2da05b617e8 | a6746aaf6bbcea2914c07384c6e1d3aae4ef7f9b2103097cc09fcd18f98b34fc | 2660c483e96686b6606363569d5827e21aa6268893ba0858bf008d56feb0a43b |
cat-searcher/leandojo-benchmark-4-random | test | 3,705 | Finpartition.part_surjOn | Mathlib/Order/Partition/Finpartition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use x, hx', (P.existsUnique_mem hx').<a>ExistsUnique.unique</a> ⟨P.part_mem hx', P.mem_part hx'⟩ ⟨hp, hx⟩ | case intro
α : Type u_1
inst✝ : DecidableEq α
s t u : Finset α
P : Finpartition s
a : α
p : Finset α
hp : p ∈ ↑P.parts
x : α
hx : x ∈ p
hx' : x ∈ s
⊢ p ∈ P.part '' ↑s | ((:c Membership.mem) ((:c Finset) (:fv _uniq.77429)) ((:c Set) ((:c Finset) (:fv _uniq.77429))) ((:c Set.instMembership) ((:c Finset) (:fv _uniq.77429))) (:fv _uniq.77844) ((:c Set.image) (:fv _uniq.77429) ((:c Finset) (:fv _uniq.77429)) ((:c Finpartition.part) (:fv _uniq.77429) (:fv _uniq.77436) (:fv _uniq.77441) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.77429))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"u","sexp":"((:c Finset) (:fv _uniq.77429))"},{"name":"P","sexp":"((:c Finpartition) ((:c Finset) (:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"use","sourceEnd":19699,"sourceStart":19696,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"x","sourceEnd":19701,"sourceStart":19700,"tag":"identifier"},{"... | [] | [{"source":"x","source_end":19701,"source_start":19700,"syntax_kind":"ident"},{"source":"hx'","source_end":19706,"source_start":19703,"syntax_kind":"ident"},{"source":"(P.existsUnique_mem hx').unique ⟨P.part_mem hx', P.mem_part hx'⟩ ⟨hp, hx⟩","source_end":19789,"source_start":19708,"syntax_kind":"Lean.Parser.Term.app"}... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77429","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.77436","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 111 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7a74fbcb8e018455c2fbc922241d2ef21b196df6cd577a20b0cab5f2ea3d161 | 2660c483e96686b6606363569d5827e21aa6268893ba0858bf008d56feb0a43b | fce270573577cdc0a9db686cfa7e22ef1eb44d3289ae10f0f5294cc379213bd0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,706 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext : 1 | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ uniformSpace α β =
UniformSpace.comap (⇑ofFun ∘ (fun ... | case h
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) = 𝓤 (α →ᵤ β) | ((:c Eq) ((:c UniformSpace) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552))) ((:c UniformFun.uniformSpace) (:fv _uniq.22549) (:fv _uniq.22552) (:fv _uniq.22576)) ((:c Inf.inf) ((:c UniformSpace) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552))) ((:c instInfUniformSpace) ((:c UniformFun) (:fv _uniq.22549) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c UniformSpace) (:arg :explicit 0 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))) (:arg :explicit 1 (:app (:c UniformFun.uniformSpace) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Unif... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":29399,"sourceStart":29396,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":":","sourceEnd":29401,"sourceStart":29400,"tag":"atom"},{"children":[{"source":"1","sourceEnd":29403,"sourceStart":29402,"tag":"atom"}],"kind":"num","source":"1"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce53c88f6d554cf8d023f0935f192edc065190a9ce1d1353fdac5dc835310ac4 | 37b203deb5b29a4d8541e090a57be6d3ad133d3a1c06ebb07159754c8cf7ed43 | a4ea0d095b23c377b445886e241cfd6658b6349e43c999fdf92c3aa35594219b | 49edf2361ceb21a595d432f69cfd1f08af3195151c425fbc9fa02a1a83b47ee4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,707 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>le_antisymm</a> (<a>le_inf</a> ?_ ?_) ?_ | case h
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) = 𝓤 (α →ᵤ β) | case h.refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) ≤ 𝓤 (α →ᵤ β)
case h.refine_2... | ((:c Eq) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c uniformity) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun.uniformSpace) (:fv _uniq.22549) (:fv _uniq.22552) (:fv _uniq.22576))) ((:c uniformity) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))))) (:arg :explicit 1 (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":29412,"sourceStart":29406,"tag":"atom"},{"children":[{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":29424,"sourceStart":29413,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":29426,"sourceStart":29425,"tag":"atom"},{"ch... | [] | [{"source":"le_antisymm (le_inf ?_ ?_) ?_","source_end":29442,"source_start":29413,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 5 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2c8ad575c8c9362b77952a4be858167a3b412ca1b243a2e321549082a46d7a7 | 49edf2361ceb21a595d432f69cfd1f08af3195151c425fbc9fa02a1a83b47ee4 | 3fb84b63d2ace253b594b209fb072c3ff9b5fd137cc2254da1eec663b0596e6c | 8953f77556d056dde1fa10c6178e12d085c8ec5fe91d3996c36ab4b7fd58c7d3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,708 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact tendsto_iff_comap.mp <a>UniformFun.precomp_uniformContinuous</a> | case h.refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) ≤ 𝓤 (α →ᵤ β) | ((:c LE.le) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c Preorder.toLE) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c PartialOrder.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))))) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":29453,"sourceStart":29448,"tag":"atom"},{"children":[{"source":"tendsto_iff_comap.mp","sourceEnd":29474,"sourceStart":29454,"tag":"identifier"},{"children":[{"name":"UniformFun.precomp_uniformContinuous","semanticRole":"global","source":"... | [] | [{"source":"tendsto_iff_comap.mp UniformFun.precomp_uniformContinuous","source_end":29511,"source_start":29454,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 8 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ac6aa3076043adcf23024839bb728224598e8953eb0e523c6b7a409a6cbf4bc5 | ceecb63c60f829c5120cd4a11edeee262e191948b51fb30b0d6829a9cfe5ebbf | d89cb80b01c028b55a16e2921b657e3594af0dbd63cffd576b92be8c25f64cb5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,709 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact tendsto_iff_comap.mp <a>UniformFun.precomp_uniformContinuous</a> | case h.refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) ≤ 𝓤 (α →ᵤ β) | ((:c LE.le) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c Preorder.toLE) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c PartialOrder.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))))) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":29522,"sourceStart":29517,"tag":"atom"},{"children":[{"source":"tendsto_iff_comap.mp","sourceEnd":29543,"sourceStart":29523,"tag":"identifier"},{"children":[{"name":"UniformFun.precomp_uniformContinuous","semanticRole":"global","source":"... | [] | [{"source":"tendsto_iff_comap.mp UniformFun.precomp_uniformContinuous","source_end":29580,"source_start":29523,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 13 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb84ad6b972bb4b8b8206b9b86ee02f671a76d5e616fe1984b7282abbeb1f889 | b3f74f2bee2dbef93f044cdb13b91a645449b65a41e1412ddd61634f4d0105c9 | d89cb80b01c028b55a16e2921b657e3594af0dbd63cffd576b92be8c25f64cb5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,710 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>UniformFun.hasBasis_uniformity</a> δ₁ β |>.<a>Filter.HasBasis.comap</a> _).<a>Filter.HasBasis.inf</a> (<a>UniformFun.hasBasis_uniformity</a> δ₂ β |>.<a>Filter.HasBasis.comap</a> _) |>.<a>Filter.HasBasis.le_basis_iff</a> (<a>UniformFun.hasBasis_uniformity</a> α β) |>.<a>Iff.mpr</a> fun U hU ↦ ⟨⟨U, U⟩, ⟨hU, hU... | case h.refine_3
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
⊢ 𝓤 (α →ᵤ β) ≤ 𝓤 (α →ᵤ β) | case h.refine_3
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x✝¹ : α
p : Filter ι
g✝ : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
U : Set (β × β)
hU : U ∈ 𝓤 β
x✝ : (α →ᵤ... | ((:c LE.le) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c Preorder.toLE) ((:c Filter) ((:c Prod) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)) ((:c UniformFun) (:fv _uniq.22549) (:fv _uniq.22552)))) ((:c PartialOrder.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:app (:c UniformFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))))) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":29592,"sourceStart":29586,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":29600,"sourceStart":29599,"tag":"atom"},{"children":[{"children":[{"name":"UniformFun.hasBasis_uniformity","semanticRole":"global","source":"Unif... | [] | [{"source":"(UniformFun.hasBasis_uniformity δ₁ β |>.comap _).inf\n (UniformFun.hasBasis_uniformity δ₂ β |>.comap _)\n |>.le_basis_iff (UniformFun.hasBasis_uniformity α β) |>.mpr fun U hU ↦\n ⟨⟨U, U⟩, ⟨hU, hU⟩, fun ⟨f, g⟩ hfg x ↦ ?_⟩","source_end":29865,"source_start":29599,"syntax_kind":"Lean.Parser.... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 20 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9be9d735c6a2a43dcbc89dc9c89a29726c34a0a7d6e82d3fdf2c9f5aa00757bf | 43fd23e790e2ce7ae16ccefc02fff7ac1a87f9e375b442dd438fddacfa7baa20 | eec523c0d548096bb97bb46130862b5b14dd86b0d8f4f6530dbf4d2882154013 | 70c4d6103ab21316f2af54d8755e981ee3a2c5c680563a33b5e5b598138152bc |
cat-searcher/leandojo-benchmark-4-random | test | 3,711 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h_cover.ge <| <a>Set.mem_univ</a> x with (⟨y, rfl⟩|⟨y, rfl⟩) | case h.refine_3
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x✝¹ : α
p : Filter ι
g✝ : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
U : Set (β × β)
hU : U ∈ 𝓤 β
x✝ : (α →ᵤ... | case h.refine_3.inl.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g✝ : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
U : Set (β × β)
hU : U ∈ 𝓤 β
x✝... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552)) ((:c Set) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Prod.mk) (:fv _uniq.22552) (:fv _uniq.22552) ((:c DFunLike.coe) ((:c Equiv) ((:c UniformFun) (:fv _uniq.22549) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x✝¹","sexp":"(:fv _uniq.22549)"},{"name":"p","s... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":29876,"sourceStart":29870,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"h_cover.ge","sourceEnd":29887,"sourceStart":29877,"tag":"identifier"},{"source":"<|","sourceEnd":29890,"sourceStart":29888,"tag":"a... | [] | [{"source":"h_cover.ge <| mem_univ x","source_end":29901,"source_start":29877,"syntax_kind":"«term_<|_»"},{"source":"(⟨y, rfl⟩|⟨y, rfl⟩)","source_end":29934,"source_start":29907,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 21 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d421eefd909fbdfb1355c6c18a3f0cef2c88fcfbedf0163b8a18640ca8ffd711 | 70c4d6103ab21316f2af54d8755e981ee3a2c5c680563a33b5e5b598138152bc | 5c6ca7c34006caf13ad62a181adddc44abddb99725b45298b9c34cecd9292b8b | 9b8cdfdaf42ce047c037caed654893eae61e977b1fa9d479f2b79a9a5e95ffc6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,712 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hfg.1 y | case h.refine_3.inl.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g✝ : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
U : Set (β × β)
hU : U ∈ 𝓤 β
x✝... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552)) ((:c Set) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Prod.mk) (:fv _uniq.22552) (:fv _uniq.22552) ((:c DFunLike.coe) ((:c Equiv) ((:c UniformFun) (:fv _uniq.22549) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":29947,"sourceStart":29942,"tag":"atom"},{"children":[{"children":[{"contextIndex":23,"semanticRole":"local","source":"hfg","sourceEnd":29951,"sourceStart":29948,"tag":"identifier"},{"source":".","sourceEnd":29952,"sourceStart":29951,"tag"... | [] | [{"source":"hfg.1 y","source_end":29955,"source_start":29948,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 24 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27b107e6dbc60deddec55ef34300f5ac2475db1c3d77b13594d06ff427d571e7 | f98abf6bc329a1ee057acb5ef1e8695c7ea93d4ba09a25a46972cd9d8f878413 | 8da69b76be2676effe3d6f68a08555aef2bf45d6dbc0c9621538941aeedcd6dd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,713 | UniformFun.uniformSpace_eq_inf_precomp_of_cover | Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hfg.2 y | case h.refine_3.inr.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
s s' : Set α
x : α
p : Filter ι
g✝ : ι → α
inst✝¹ : UniformSpace β
δ : ι → Type u_5
inst✝ : (i : ι) → UniformSpace (δ i)
δ₁ : Type u_6
δ₂ : Type u_7
φ₁ : δ₁ → α
φ₂ : δ₂ → α
h_cover : range φ₁ ∪ range φ₂ = univ
U : Set (β × β)
hU : U ∈ 𝓤 β
x✝... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552)) ((:c Set) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.22552) (:fv _uniq.22552))) ((:c Prod.mk) (:fv _uniq.22552) (:fv _uniq.22552) ((:c DFunLike.coe) ((:c Equiv) ((:c UniformFun) (:fv _uniq.22549) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"s'","sexp":"((:c Set) (:fv _uniq.22549))"},{"name":"x","sexp":"(:fv _uniq.22549)"},{"name":"p","sex... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":29968,"sourceStart":29963,"tag":"atom"},{"children":[{"children":[{"contextIndex":23,"semanticRole":"local","source":"hfg","sourceEnd":29972,"sourceStart":29969,"tag":"identifier"},{"source":".","sourceEnd":29973,"sourceStart":29972,"tag"... | [] | [{"source":"hfg.2 y","source_end":29976,"source_start":29969,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22549","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.22552","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 97 | 29 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cb113711db5ecf18d438616e21816393d0480bc86ba9315d67f6ff2b115c70f | b861c952b59a68ee7ef4f00d45d0387e039a17fbca8e66ab6190343750dbb09c | 0a64accb052fd0ba41d58929ff87642160585142c269b7f0a3b4c90584210023 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,714 | InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>neg_eq_zero</a>, ← <a>inner_neg_right</a>] at h | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x y : V
h : ⟪x, y⟫_ℝ = 0
⊢ angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x y : V
h : ⟪x, -y⟫_ℝ = 0
⊢ angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) | ((:c Eq) (:c Real) ((:c InnerProductGeometry.angle) (:fv _uniq.70736) (:fv _uniq.70739) (:fv _uniq.70752) (:fv _uniq.71650) ((:c HSub.hSub) (:fv _uniq.70736) (:fv _uniq.70736) (:fv _uniq.70736) ((:c instHSub) (:fv _uniq.70736) ((:c SubNegMonoid.toSub) (:fv _uniq.70736) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.70736) ((... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.70736))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.70736) (:c Real.RCLike) (:fv _uniq.70739))"},{"name":"x","sexp":"(:fv _uniq.70736)"},{"name":"y","sexp":"(:fv _uniq.70736)"},{"name":"h","s... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c InnerProductGeometry.angle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70736","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.70739","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"rw","sourceEnd":12935,"sourceStart":12933,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12937,"sourceStart":12936,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":12940,"sourceSt... | [] | [{"source":"neg_eq_zero","source_end":12952,"source_start":12941,"syntax_kind":"ident"},{"source":"h","source_end":12979,"source_start":12978,"syntax_kind":"ident"},{"source":"inner_neg_right","source_end":12973,"source_start":12958,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70736","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.70739","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 46 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62df44837a308c2442c2c6624e4028d21179ff19a8710e0d40101d0156094a18 | 06967c109356fbb5156801f30890a2134cb42e997395f6487a79453d0d8ef30e | c8cc136c6a703d0bac123f73d01c3bbf162a881d9aef84e4464046208d4ac90b | dddfe25eae4594309113abe0539f7d7b31eae98daaec74930d79f18e225a7bd1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,715 | InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero | Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_eq_add_neg</a>, <a>InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero</a> h] | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x y : V
h : ⟪x, -y⟫_ℝ = 0
⊢ angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) | ((:c Eq) (:c Real) ((:c InnerProductGeometry.angle) (:fv _uniq.70736) (:fv _uniq.70739) (:fv _uniq.70752) (:fv _uniq.71650) ((:c HSub.hSub) (:fv _uniq.70736) (:fv _uniq.70736) (:fv _uniq.70736) ((:c instHSub) (:fv _uniq.70736) ((:c SubNegMonoid.toSub) (:fv _uniq.70736) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.70736) ((... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.70736))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.70736) (:c Real.RCLike) (:fv _uniq.70739))"},{"name":"x","sexp":"(:fv _uniq.70736)"},{"name":"y","sexp":"(:fv _uniq.70736)"},{"name":"h","s... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c InnerProductGeometry.angle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70736","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.70739","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"rw","sourceEnd":12984,"sourceStart":12982,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12986,"sourceStart":12985,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sub_eq_add_neg",... | [] | [{"source":"sub_eq_add_neg","source_end":13000,"source_start":12986,"syntax_kind":"ident"},{"source":"angle_add_eq_arccos_of_inner_eq_zero h","source_end":13040,"source_start":13002,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.70736","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.70739","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 46 | 8 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50e8a6ea692ba072db4b7f5eb01d1d5b977d415e2ec620a91d60a5097232774a | dddfe25eae4594309113abe0539f7d7b31eae98daaec74930d79f18e225a7bd1 | 8b25002674424a8ae76c776ed4fff6b8b528321add4d291338ea4a550889b115 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,716 | CategoryTheory.Abelian.exact_iff_exact_coimage_π | Mathlib/CategoryTheory/Abelian/Exact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_lhs => rw [← <a>CategoryTheory.Abelian.coimage.fac</a> g] | C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
inst✝ : Abelian C
X Y Z : C
f : X ⟶ Y
g : Y ⟶ Z
⊢ Exact f g ↔ Exact f (coimage.π g) | C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
inst✝ : Abelian C
X Y Z : C
f : X ⟶ Y
g : Y ⟶ Z
⊢ Exact f (coimage.π g ≫ Abelian.factorThruCoimage g) ↔ Exact f (coimage.π g) | ((:c Iff) ((:c CategoryTheory.Exact) (:fv _uniq.100340) (:fv _uniq.100343) ((:c CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations) (:fv _uniq.100340) (:fv _uniq.100343) ((:c CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations) (:fv _uniq.100340) (:fv _uniq.100343) (:fv _uniq.100358))) ((:c Categor... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.100340))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Abelian) (:fv _uniq.100340) (:fv _uniq.100343))"},{"name":"X","sexp":"(:fv _uniq.100340)"},{"name":"Y","sexp":"(:fv _uniq.100340)"},{"name":"Z","sexp":"(:fv _u... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.Exact) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Limits.HasImages) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100340","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100343","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"conv_lhs","sourceEnd":12044,"sourceStart":12036,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":12047,"sourceStart":12045,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou... | [] | [{"source":"Abelian.coimage.fac g","source_end":12077,"source_start":12056,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100340","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100343","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 49 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1917a0a7a30d50cc48f9c7e44ea29c12818eee37a02a572661ff31fc8d5b768b | 6ed9a185b9af590fd717362b1f4434f81cb2b87f4b9534071d751c5c7328b01f | a4b81623cb26b67bef8a9eb587141151a7c62f39cdbf8049efd64077105e11f6 | 673a0bf77f2f0e7a2930937956a8493e57e06f0e99a51c1461a7253b00441290 |
cat-searcher/leandojo-benchmark-4-random | test | 3,717 | CategoryTheory.Abelian.exact_iff_exact_coimage_π | Mathlib/CategoryTheory/Abelian/Exact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>CategoryTheory.exact_comp_mono_iff</a>] | C : Type u₁
inst✝¹ : Category.{v₁, u₁} C
inst✝ : Abelian C
X Y Z : C
f : X ⟶ Y
g : Y ⟶ Z
⊢ Exact f (coimage.π g ≫ Abelian.factorThruCoimage g) ↔ Exact f (coimage.π g) | ((:c Iff) ((:c CategoryTheory.Exact) (:fv _uniq.100340) (:fv _uniq.100343) ((:c CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations) (:fv _uniq.100340) (:fv _uniq.100343) ((:c CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations) (:fv _uniq.100340) (:fv _uniq.100343) (:fv _uniq.100358))) ((:c Categor... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.100340))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Abelian) (:fv _uniq.100340) (:fv _uniq.100343))"},{"name":"X","sexp":"(:fv _uniq.100340)"},{"name":"Y","sexp":"(:fv _uniq.100340)"},{"name":"Z","sexp":"(:fv _u... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.Exact) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Limits.HasImages) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100340","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100343","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Catego... | {"children":[{"source":"rw","sourceEnd":12083,"sourceStart":12081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12085,"sourceStart":12084,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.e... | [] | [{"source":"exact_comp_mono_iff","source_end":12104,"source_start":12085,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100340","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100343","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 49 | 9 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79e2469a437edc3366349dcd56a37e709e8028cfb0fb5217b536824a331f9b75 | 673a0bf77f2f0e7a2930937956a8493e57e06f0e99a51c1461a7253b00441290 | 6c9652cd7ef07cf643d00ee8acb700b66dce241e226b1bd2386e5d1098810d9d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,718 | Matroid.comap_base_iff | Mathlib/Data/Matroid/Map.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matroid.basis_ground_iff</a>, <a>Matroid.comap_basis_iff</a>] | α : Type u_1
β : Type u_2
f : α → β
E I s : Set α
M : Matroid α
N : Matroid β
B : Set α
⊢ (N.comap f).Base B ↔ N.Basis (f '' B) (f '' (f ⁻¹' N.E)) ∧ InjOn f B ∧ B ⊆ f ⁻¹' N.E | α : Type u_1
β : Type u_2
f : α → β
E I s : Set α
M : Matroid α
N : Matroid β
B : Set α
⊢ N.Basis (f '' B) (f '' (N.comap f).E) ∧ InjOn f B ∧ B ⊆ (N.comap f).E ↔
N.Basis (f '' B) (f '' (f ⁻¹' N.E)) ∧ InjOn f B ∧ B ⊆ f ⁻¹' N.E | ((:c Iff) ((:c Matroid.Base) (:fv _uniq.18825) ((:c Matroid.comap) (:fv _uniq.18825) (:fv _uniq.18828) (:fv _uniq.18847) (:fv _uniq.18832)) (:fv _uniq.18941)) ((:c And) ((:c Matroid.Basis) (:fv _uniq.18828) (:fv _uniq.18847) ((:c Set.image) (:fv _uniq.18825) (:fv _uniq.18828) (:fv _uniq.18832) (:fv _uniq.18941)) ((:c S... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.18825) (:fv _uniq.18828))"},{"name":"E","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"M","sex... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Matroid.Base) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Matroid.comap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:fv FV2)))) (:arg :explicit 2 (:fv FV9)))) (:arg :explicit 1 (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18825","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18828","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":11263,"sourceStart":11261,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11265,"sourceStart":11264,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":11268,"sourceSt... | [] | [{"source":"basis_ground_iff","source_end":11285,"source_start":11269,"syntax_kind":"ident"},{"source":"comap_basis_iff","source_end":11302,"source_start":11287,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18825","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18828","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 14 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a82e9dc5f30542c5cc7cc6d6b30b48e3ab654ed9d94d06a4e8a8b64fc96e891d | 9fc42cac9528fd3603344707e95e6e9c71a52473bea7538eb91fbb5651063e6c | 7bd2351748a2c3da6f9168ad12d86e8b6d41bd73b817e7fa091a5b535ad066f0 | faf71d1b1da6801d426cd65314bd1c75c38a94d471c6a52debe08da299e61b31 |
cat-searcher/leandojo-benchmark-4-random | test | 3,719 | Matroid.comap_base_iff | Mathlib/Data/Matroid/Map.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
β : Type u_2
f : α → β
E I s : Set α
M : Matroid α
N : Matroid β
B : Set α
⊢ N.Basis (f '' B) (f '' (N.comap f).E) ∧ InjOn f B ∧ B ⊆ (N.comap f).E ↔
N.Basis (f '' B) (f '' (f ⁻¹' N.E)) ∧ InjOn f B ∧ B ⊆ f ⁻¹' N.E | ((:c Iff) ((:c And) ((:c Matroid.Basis) (:fv _uniq.18828) (:fv _uniq.18847) ((:c Set.image) (:fv _uniq.18825) (:fv _uniq.18828) (:fv _uniq.18832) (:fv _uniq.18941)) ((:c Set.image) (:fv _uniq.18825) (:fv _uniq.18828) (:fv _uniq.18832) ((:c Matroid.E) (:fv _uniq.18825) ((:c Matroid.comap) (:fv _uniq.18825) (:fv _uniq.18... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.18825) (:fv _uniq.18828))"},{"name":"E","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.18825))"},{"name":"M","sex... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Matroid.Basis) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)) (:arg :explicit 3 (:fv FV9))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18825","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18828","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":11308,"sourceStart":11305,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":11308,"sourceStart":11305,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18825","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18828","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 14 | 9 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | affdc130935d4fce0f2feaa39a29ec8404520b02fe17b40b58674f791dc02353 | faf71d1b1da6801d426cd65314bd1c75c38a94d471c6a52debe08da299e61b31 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,720 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MulAction.fixedBy_inv</a>] | α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
⊢ s ∈ fixedBy (Set α) g | α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
⊢ s ∈ fixedBy (Set α) g⁻¹ | ((:c Membership.mem) ((:c Set) (:fv _uniq.18707)) ((:c Set) ((:c Set) (:fv _uniq.18707))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.18707))) (:fv _uniq.19385) ((:c MulAction.fixedBy) (:fv _uniq.18710) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18713))) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5846,"sourceStart":5844,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5848,"sourceStart":5847,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5851,"sourceStart":... | [] | [{"source":"fixedBy_inv","source_end":5863,"source_start":5852,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f8a67db9170dfa58cb82ad13daa01524e301d14ecd088639b089fb994b8d3f9 | 31875d7addc1f87a6b1c17366631589ccab842c89c045fac77543760589c6fce | 28df746e8bd56890204ae37f1009eb414b5bf34f258bfee535c761048601dc6f | 01ca1e0a0325ea5c738fe19b3eff04f7cf77373a34379557397f5ec8518a1c29 |
cat-searcher/leandojo-benchmark-4-random | test | 3,721 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
⊢ s ∈ fixedBy (Set α) g⁻¹ | case h
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
⊢ x ∈ g⁻¹ • s ↔ x ∈ s | ((:c Membership.mem) ((:c Set) (:fv _uniq.18707)) ((:c Set) ((:c Set) (:fv _uniq.18707))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.18707))) (:fv _uniq.19385) ((:c MulAction.fixedBy) (:fv _uniq.18710) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18713))) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"ext","sourceEnd":5870,"sourceStart":5867,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":5872,"sourceStart":5871,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":5872,"sourceStart":5871,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":5872,"source_start":5871,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8e4989eb88fc05abdabe1c70bb56f9a6926132c48e35ef6490a96274cf94b66 | 01ca1e0a0325ea5c738fe19b3eff04f7cf77373a34379557397f5ec8518a1c29 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 9779e5b011f13add86003392b2363151aad81c3b920a8ecb136b237c5fc9aae0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,722 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_inv_smul_set_iff</a>] | case h
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
⊢ x ∈ g⁻¹ • s ↔ x ∈ s | case h
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
⊢ g • x ∈ s ↔ x ∈ s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.18707) ((:c Set) (:fv _uniq.18707)) ((:c Set.instMembership) (:fv _uniq.18707)) (:fv _uniq.19444) ((:c HSMul.hSMul) (:fv _uniq.18710) ((:c Set) (:fv _uniq.18707)) ((:c Set) (:fv _uniq.18707)) ((:c instHSMul) (:fv _uniq.18710) ((:c Set) (:fv _uniq.18707)) ((:c MulAction.toSMul) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5877,"sourceStart":5875,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5879,"sourceStart":5878,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_inv_smul_set... | [] | [{"source":"Set.mem_inv_smul_set_iff","source_end":5903,"source_start":5879,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b299796e708db630f8fdcaa390745f9db3d4efeb199348f51b331e24b80f243 | 9779e5b011f13add86003392b2363151aad81c3b920a8ecb136b237c5fc9aae0 | fffff4efcab2bad7dc381a7858cf5fae21a43feac2e6a2964c034d019ee22662 | 7ec294e1a3ad2baf13fa5a7dd5a5d137ec5a62eb704dca3a525d50e3d961f4ef |
cat-searcher/leandojo-benchmark-4-random | test | 3,723 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun gxs => ?xs, fun xs => (s_ss_fixedBy xs).<a>Eq.symm</a> ▸ xs⟩ | case h
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
⊢ g • x ∈ s ↔ x ∈ s | case xs
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
gxs : g • x ∈ s
⊢ x ∈ s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.18707) ((:c Set) (:fv _uniq.18707)) ((:c Set.instMembership) (:fv _uniq.18707)) ((:c HSMul.hSMul) (:fv _uniq.18710) (:fv _uniq.18707) (:fv _uniq.18707) ((:c instHSMul) (:fv _uniq.18710) (:fv _uniq.18707) ((:c MulAction.toSMul) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMono... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":5913,"sourceStart":5907,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5917,"sourceStart":5914,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":5920,"sourceStart":5917,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"gx... | [] | [{"source":"⟨fun gxs => ?xs, fun xs => (s_ss_fixedBy xs).symm ▸ xs⟩","source_end":5975,"source_start":5914,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 11 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9796b209b128a150993810e6b076e2a31b8d4e2005e35501ed8c1815f3069f7e | 7ec294e1a3ad2baf13fa5a7dd5a5d137ec5a62eb704dca3a525d50e3d961f4ef | fcfdd807e7938054b4223a7f65f93810e54d46f6658f0733fa8385c2ac27cd95 | 68cca52add3d6d10234e61e9adf5e0926c088c788f474ca7230a4d1de2815993 |
cat-searcher/leandojo-benchmark-4-random | test | 3,724 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MulAction.fixedBy_inv</a>] at s_ss_fixedBy | case xs
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g
x : α
gxs : g • x ∈ s
⊢ x ∈ s | case xs
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g⁻¹
x : α
gxs : g • x ∈ s
⊢ x ∈ s | ((:c Membership.mem) (:fv _uniq.18707) ((:c Set) (:fv _uniq.18707)) ((:c Set.instMembership) (:fv _uniq.18707)) (:fv _uniq.19444) (:fv _uniq.19385)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV11)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":5980,"sourceStart":5978,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5982,"sourceStart":5981,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5985,"sourceStart":... | [] | [{"source":"fixedBy_inv","source_end":5997,"source_start":5986,"syntax_kind":"ident"},{"source":"s_ss_fixedBy","source_end":6014,"source_start":6002,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 12 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 00143df7f19a5fcd1e854ca1e9600a72fb387b14e28e931e684b33dd43027c3f | 68cca52add3d6d10234e61e9adf5e0926c088c788f474ca7230a4d1de2815993 | 2b5567fdf875d9e974db6126e475185857a4fc68ffbe9d0def8bed4a86be5736 | 237e8dbf448ec494942cc24db06a2050d8314a0583d753f08e191d4727c253fe |
cat-searcher/leandojo-benchmark-4-random | test | 3,725 | MulAction.set_mem_fixedBy_of_subset_fixedBy | Mathlib/GroupTheory/GroupAction/FixedPoints.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← s_ss_fixedBy gxs, <a>inv_smul_smul</a>] at gxs | case xs
α : Type u_1
G : Type u_2
inst✝³ : Group G
inst✝² : MulAction G α
M : Type u_3
inst✝¹ : Monoid M
inst✝ : MulAction M α
s : Set α
g : G
s_ss_fixedBy : s ⊆ fixedBy α g⁻¹
x : α
gxs : g • x ∈ s
⊢ x ∈ s | ((:c Membership.mem) (:fv _uniq.18707) ((:c Set) (:fv _uniq.18707)) ((:c Set.instMembership) (:fv _uniq.18707)) (:fv _uniq.19688) (:fv _uniq.19385)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.18710))"},{"name":"inst✝²","sexp":"((:c MulAction) (:fv _uniq.18710) (:fv _uniq.18707) ((:c DivInvMonoid.toMonoid) (:fv _uniq.18710) ((:c Group.toDivInvMonoid) (:fv _uniq.18710) (:fv _uniq.18... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV11)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rwa","sourceEnd":6020,"sourceStart":6017,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6022,"sourceStart":6021,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6025,"sourceStart":6022,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"gxs","source_end":6065,"source_start":6062,"syntax_kind":"ident"},{"source":"s_ss_fixedBy gxs","source_end":6042,"source_start":6026,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inv_smul_smul","source_end":6057,"source_start":6044,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18707","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18710","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 20 | 15 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79a13d7d3f09aaefa5520ad8674a613bfac269bb9e40355c9b4447a1ec96ad6a | 237e8dbf448ec494942cc24db06a2050d8314a0583d753f08e191d4727c253fe | a732cf1c78b4fd568e3cd4df2ab8efb5cc31d84579700e9a7a0166d525131dcd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,726 | Matrix.BlockTriangular.det_fintype | Mathlib/LinearAlgebra/Matrix/Block.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine h.det.trans (<a>Finset.prod_subset</a> (<a>Finset.subset_univ</a> _) fun a _ ha => ?_) | α : Type u_1
β : Type u_2
m : Type u_3
n : Type u_4
o : Type u_5
m' : α → Type u_6
n' : α → Type u_7
R : Type v
inst✝⁷ : CommRing R
M N : Matrix m m R
b : m → α
inst✝⁶ : DecidableEq m
inst✝⁵ : Fintype m
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq α
inst✝¹ : Fintype α
inst✝ : LinearOrder α
h : M.Block... | α : Type u_1
β : Type u_2
m : Type u_3
n : Type u_4
o : Type u_5
m' : α → Type u_6
n' : α → Type u_7
R : Type v
inst✝⁷ : CommRing R
M N : Matrix m m R
b : m → α
inst✝⁶ : DecidableEq m
inst✝⁵ : Fintype m
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq α
inst✝¹ : Fintype α
inst✝ : LinearOrder α
h : M.Block... | ((:c Eq) (:fv _uniq.57310) ((:c Matrix.det) (:fv _uniq.57292) (:fv _uniq.57334) (:fv _uniq.57339) (:fv _uniq.57310) (:fv _uniq.57313) (:fv _uniq.57318)) ((:c Finset.prod) (:fv _uniq.57286) (:fv _uniq.57310) ((:c CommRing.toCommMonoid) (:fv _uniq.57310) (:fv _uniq.57313)) ((:c Finset.univ) (:fv _uniq.57286) (:fv _uniq.5... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"o","sexp":"(:sort (+ u_5 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.57286) (:sort (+ u_6 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.57286... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit-type 3 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":10778,"sourceStart":10772,"tag":"atom"},{"children":[{"source":"h.det.trans","sourceEnd":10790,"sourceStart":10779,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":10792,"sourceStart":10791,"tag":"atom"},{"children":[{"name":"Finset.prod_subset","semant... | [] | [{"source":"h.det.trans (prod_subset (subset_univ _) fun a _ ha => ?_)","source_end":10837,"source_start":10779,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 65 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11ec5e4a17a4e132df14411367ff9e4cd6b67eb055e39e77049fda22635f1865 | bfa2eb65f5ac863694b9f79e5f30d03a5b3be35998685dc4000f0b48a84e91f2 | 4d3aa4cde9da2a81d88877f38813725167b317840d8377aef8bd37c80d22bcae | dd8bf7107b50279bb7ea62d72a5b0ee77cf010fe75c1282753adf97d65d8c011 |
cat-searcher/leandojo-benchmark-4-random | test | 3,727 | Matrix.BlockTriangular.det_fintype | Mathlib/LinearAlgebra/Matrix/Block.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>IsEmpty</a> { i // b i = a } := ⟨fun i => ha <| <a>Finset.mem_image</a>.2 ⟨i, <a>Finset.mem_univ</a> _, i.2⟩⟩ | α : Type u_1
β : Type u_2
m : Type u_3
n : Type u_4
o : Type u_5
m' : α → Type u_6
n' : α → Type u_7
R : Type v
inst✝⁷ : CommRing R
M N : Matrix m m R
b : m → α
inst✝⁶ : DecidableEq m
inst✝⁵ : Fintype m
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq α
inst✝¹ : Fintype α
inst✝ : LinearOrder α
h : M.Block... | α : Type u_1
β : Type u_2
m : Type u_3
n : Type u_4
o : Type u_5
m' : α → Type u_6
n' : α → Type u_7
R : Type v
inst✝⁷ : CommRing R
M N : Matrix m m R
b : m → α
inst✝⁶ : DecidableEq m
inst✝⁵ : Fintype m
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq α
inst✝¹ : Fintype α
inst✝ : LinearOrder α
h : M.Block... | ((:c Eq) (:fv _uniq.57310) ((:c Matrix.det) ((:c Subtype) (:fv _uniq.57292) (:lambda a (:fv _uniq.57292) ((:c Eq) (:fv _uniq.57286) ((:fv _uniq.57327) 0) (:fv _uniq.59256)))) (:lambda a ((:c Subtype) (:fv _uniq.57292) (:lambda a (:fv _uniq.57292) ((:c Eq) (:fv _uniq.57286) ((:fv _uniq.57327) 0) (:fv _uniq.59256)))) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"o","sexp":"(:sort (+ u_5 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.57286) (:sort (+ u_6 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.57286... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 0))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":10844,"sourceStart":10840,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10845,"sourceStart":10845,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10845,"sourceStart":10845,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"IsEmpty { i // b i = a }","source_end":10871,"source_start":10847,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨fun i => ha <| mem_image.2 ⟨i, mem_univ _, i.2⟩⟩","source_end":10932,"source_start":10875,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 65 | 5 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f14b663675af7f63edb1ea58d3d6b996e8440f1d95d5a1b48bb2b3e5aac9da1f | dd8bf7107b50279bb7ea62d72a5b0ee77cf010fe75c1282753adf97d65d8c011 | 0d76e063cb84b0e22413696163524d1445d10376d2442fc6d841e6a5fe28f02a | d4ed52e8ade5579c014858caeeef146a85b61c075d6db757ba1766125f84b6f9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,728 | Matrix.BlockTriangular.det_fintype | Mathlib/LinearAlgebra/Matrix/Block.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Matrix.det_isEmpty</a> | α : Type u_1
β : Type u_2
m : Type u_3
n : Type u_4
o : Type u_5
m' : α → Type u_6
n' : α → Type u_7
R : Type v
inst✝⁷ : CommRing R
M N : Matrix m m R
b : m → α
inst✝⁶ : DecidableEq m
inst✝⁵ : Fintype m
inst✝⁴ : DecidableEq n
inst✝³ : Fintype n
inst✝² : DecidableEq α
inst✝¹ : Fintype α
inst✝ : LinearOrder α
h : M.Block... | ((:c Eq) (:fv _uniq.57310) ((:c Matrix.det) ((:c Subtype) (:fv _uniq.57292) (:lambda a (:fv _uniq.57292) ((:c Eq) (:fv _uniq.57286) ((:fv _uniq.57327) 0) (:fv _uniq.59256)))) (:lambda a ((:c Subtype) (:fv _uniq.57292) (:lambda a (:fv _uniq.57292) ((:c Eq) (:fv _uniq.57286) ((:fv _uniq.57327) 0) (:fv _uniq.59256)))) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"(:sort (+ u_3 1))"},{"name":"n","sexp":"(:sort (+ u_4 1))"},{"name":"o","sexp":"(:sort (+ u_5 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.57286) (:sort (+ u_6 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.57286... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 0))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":10940,"sourceStart":10935,"tag":"atom"},{"name":"Matrix.det_isEmpty","semanticRole":"global","source":"det_isEmpty","sourceEnd":10952,"sourceStart":10941,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact det_isEmpty","sourceEnd":10952,"sourceStart":10935,"... | [] | [{"source":"det_isEmpty","source_end":10952,"source_start":10941,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57286","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.57289","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 65 | 6 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0028150c894d11dfed13a6c571ec299a207bc6e2aad4ce3a6f13695d814eeeaf | d4ed52e8ade5579c014858caeeef146a85b61c075d6db757ba1766125f84b6f9 | 6b8e1541606c372f51d5dace73e48da7e3742a8d051bc419c76af3def9313af7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,729 | DirectSum.equivCongrLeft_apply | Mathlib/Algebra/DirectSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>DFinsupp.comapDomain'_apply</a> _ h.right_inv _ _ | ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝¹ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝ : AddCommMonoid γ
κ : Type u_1
h : ι ≃ κ
f : ⨁ (i : ι), β i
k : κ
⊢ ((equivCongrLeft h) f) k = f (h.symm k) | ((:c Eq) ((:fv _uniq.111203) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.111219) (:fv _uniq.111190)) (:fv _uniq.111219) (:lambda _ (:fv _uniq.111219) (:fv _uniq.111190)) ((:c Equiv.instFunLike) (:fv _uniq.111219) (:fv _uniq.111190)) ((:c Equiv.symm) (:fv _uniq.111190) (:fv _uniq.111219) (:fv _uniq.111577)) (:fv _uniq.111... | [{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"dec_ι","sexp":"((:c DecidableEq) (:fv _uniq.111190))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.111190) (:sort (+ w 1)))"},{"name":"inst✝¹","sexp":"(:forall i (:fv _uniq.111190) ((:c AddCommMonoid) ((:fv _uniq.111203) 0)))"},{"name":"γ","sexp":"(:sort (+ u₁ 1))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV2) (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Equiv) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV6)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.111190","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.111197","is_instance":true,"is_let":false,"name":"dec_ι","sexp":"(:app (:c DecidableEq) (:arg :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":11215,"sourceStart":11210,"tag":"atom"},{"children":[{"name":"DFinsupp.comapDomain'_apply","semanticRole":"global","source":"DFinsupp.comapDomain'_apply","sourceEnd":11243,"sourceStart":11216,"tag":"identifier"},{"children":[{"children":[... | [] | [{"source":"DFinsupp.comapDomain'_apply _ h.right_inv _ _","source_end":11261,"source_start":11216,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.111190","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.111197","is_instance":true,"is_let":false,"user_name":"dec_ι"},{"binder_role":":implicit","context_index":2,"inter... | 92 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8323e82ae50768ccb94976e1c264a9b0403897d9349251cf0faccc4b07bfcd89 | fefcad227d3514bba47d4288baf0a989adf459e4cf9a5d7fae48aca1f9292e9a | 7d4640e63fa21bd94a9a5744ed87ad75fe621813be7f8b64bfa4734ed785e7e2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,730 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let g := <a>GeneralizedContinuedFraction.of</a> v | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
⊢ ∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
⊢ ∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr | (:forall ifp_n ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:forall _ ((:c Eq) ((:c Option) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711))) ((:c GeneralizedContinuedFraction.IntFractPair.stream) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716) (:fv _uniq.2718)... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:forall ifp_n :implicit (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Gene... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":5114,"sourceStart":5111,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"g","sourceEnd":5116,"sourceStart":5115,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"sou... | [] | [{"source":"of v","source_end":5124,"source_start":5120,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 61e67bd28202cad47ca2f0a5d36df2d3872acc4cb42b54f0b6370e99b9d60e6a | dfc7d70ac836675b00d8f9325d780f44e4514b2349346ff0f6ea775e45742367 | a8ec5fcc596c6f9192642341953e164a00b98afef053b0d297a588076553e616 | a81eee17d3f0e128339115aaede6f6b0236b70e6d7de9cff2c3caaaa638761e9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,731 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' n with n IH | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
⊢ ∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
⊢ ∀ {ifp_n : IntFractPair K},
IntFractPair.stream v 0 = some ifp_n →
v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) ifp_n.fr
case succ
K : Type u_1
inst... | (:forall ifp_n ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:forall _ ((:c Eq) ((:c Option) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711))) ((:c GeneralizedContinuedFraction.IntFractPair.stream) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716) (:fv _uniq.2718)... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:forall ifp_n :implicit (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Gene... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"induction'","sourceEnd":5137,"sourceStart":5127,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":3,"semanticRole":"local","source":"n","sourceEnd":5139,"sourceStart":5138,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"n","source_end":5139,"source_start":5138,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcb3a03da7835c6091b7fe6e0c978e7a64094a0b5a31e68deaca6e2c095f095c | a81eee17d3f0e128339115aaede6f6b0236b70e6d7de9cff2c3caaaa638761e9 | b20639682fd3d1d8c9daeba241ba23f700098b0a3baf4bbd0b56715a5124c4b0 | f191073935802dab5d4b82a83c64b0cf57cc258112e53057d28f3c79c265f69d |
cat-searcher/leandojo-benchmark-4-random | test | 3,732 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ifp_zero stream_zero_eq | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
⊢ ∀ {ifp_n : IntFractPair K},
IntFractPair.stream v 0 = some ifp_n →
v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) ifp_n.fr | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) ifp_zero.fr | (:forall ifp_n ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:forall _ ((:c Eq) ((:c Option) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711))) ((:c GeneralizedContinuedFraction.IntFractPair.stream) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716) ((:c OfNat.ofNat... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:forall ifp_n :implicit (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Gene... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"intro","sourceEnd":5160,"sourceStart":5155,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ifp_zero","sourceEnd":5169,"sourceStart":5161,"tag":"identifier"},{"semanticRole":"scoped_local","source":"stream_zero_eq","sourceEnd":5184,"sourceStart":5170,"tag":"identifier"}],"kind... | [{"role":"fresh_name","source":"ifp_zero","source_end":5169,"source_start":5161,"syntax_kind":"ident"},{"role":"fresh_name","source":"stream_zero_eq\n -- Nat.zero","source_end":5184,"source_start":5170,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 10 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e68e82059ca597275ce6bc55d60794bf966fd9c6f56111f72f2c405b69b011b0 | 9e08bf6ba621f558e8a24aa8d3a3080d3dd3911607f149a1ac8689528d2b6faa | 04175a20323bb226b61258ee44c637e6bce83f41e5932e81c8049ea50cbab998 | 893d0ad57739fd89613121fb1f0e120d31f225e49c99fdc7c6549ca3f6e24946 |
cat-searcher/leandojo-benchmark-4-random | test | 3,733 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>GeneralizedContinuedFraction.IntFractPair.of</a> v = ifp_zero := by have : <a>GeneralizedContinuedFraction.IntFractPair.stream</a> v 0 = <a>Option.some</a> (<a>GeneralizedContinuedFraction.IntFractPair.of</a> v) := <a>rfl</a> simpa only [<a>Nat.zero_eq</a>, this, Option.some.injEq] using stream_zero_eq | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) ifp_zero.fr | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
this : IntFractPair.of v = ifp_zero
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 ... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":5209,"sourceStart":5205,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5210,"sourceStart":5210,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5210,"sourceStart":5210,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"IntFractPair.of v = ifp_zero","source_end":5240,"source_start":5212,"syntax_kind":"«term_=_»"},{"source":"IntFractPair.stream v 0 = some (IntFractPair.of v)","source_end":5310,"source_start":5260,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":5317,"source_start":5314,"syntax_kind":"ident"},{"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 11 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0388fb657b4556a30c33fde965490da42283f97d640878ba7aa3a479efbfe2a1 | 893d0ad57739fd89613121fb1f0e120d31f225e49c99fdc7c6549ca3f6e24946 | 2ff9104d6a30f83a9b7f0875725bbe978003caa72413fc00fb1a4933df4720a7 | cee3c017634e0df11bfb1bab7f83cf4e49ae40ddbe70606f59393197ad913fed |
cat-searcher/leandojo-benchmark-4-random | test | 3,734 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases this | case zero
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
this : IntFractPair.of v = ifp_zero
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 ... | case zero.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) (IntFractPair.of v).fr | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"cases","sourceEnd":5404,"sourceStart":5399,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"this","sourceEnd":5409,"sourceStart":5405,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"this","source_end":5409,"source_start":5405,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 15 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff09af43e9a9b2b879b1f6b59c9852e7e6f859986b437096a97dce8162131650 | cee3c017634e0df11bfb1bab7f83cf4e49ae40ddbe70606f59393197ad913fed | a7a143fbe87a86d904dbf239a0096e0c1df53c4f9aefa4568c95e8e97069604f | 149c1db25596cac3220c5e0c08196daa5567de25bc25adc59a7a141de8781618 |
cat-searcher/leandojo-benchmark-4-random | test | 3,735 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>Decidable.em</a> (<a>Int.fract</a> v = 0) with fract_eq_zero fract_ne_zero | case zero.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) (IntFractPair.of v).fr | case zero.refl.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) (Int... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"cases'","sourceEnd":5420,"sourceStart":5414,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Decidable.em","semanticRole":"global","source":"Decidable.em","sourceEnd":5433,"sourceStart":5421,"tag":"identifier"},{"children":[{"ch... | [] | [{"source":"Decidable.em (Int.fract v = 0)","source_end":5451,"source_start":5421,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 16 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 476434088dc90d94bf55bb3a84b50396e234e08132e7955fa204a605a8c5aff6 | 149c1db25596cac3220c5e0c08196daa5567de25bc25adc59a7a141de8781618 | 071f290d5acfab873ef2e9bfbee29b9f56b90ba7637d089f8d4ac48391926980 | 1c2925ad22be8a9e8001e529db3a9ce83717eef147d142b88d6305be8901b188 |
cat-searcher/leandojo-benchmark-4-random | test | 3,736 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>GeneralizedContinuedFraction.IntFractPair.stream</a> v 0 = <a>Option.some</a> (<a>GeneralizedContinuedFraction.IntFractPair.of</a> v) := <a>rfl</a> | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
⊢ IntFractPair.of v = ifp_zero | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
this : IntFractPair.stream v 0 = some (IntFractPair.of v)
⊢ IntFractPair.of v = ifp_zero | ((:c Eq) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716)) (:fv _uniq.2913)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.of) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":5257,"sourceStart":5253,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5258,"sourceStart":5258,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5258,"sourceStart":5258,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"IntFractPair.stream v 0 = some (IntFractPair.of v)","source_end":5310,"source_start":5260,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":5317,"source_start":5314,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 13 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 75bbb9a3bc53669e0449e6526ced44d19cdb4c387d6f2afbf93779b057c062b5 | ba1bdc7203734fdd2bdde9da13b699fd73838776ad14efb399aa9f2b8ae82da8 | 256ff7b2f410a7efe60ce4f7ab6adab3b69b394a602b9b6b6f47be10a4b67733 | 7f2d31a2142e8969f5d317e6778989e9bd82feba42c19030281f899cd064fb27 |
cat-searcher/leandojo-benchmark-4-random | test | 3,737 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Nat.zero_eq</a>, this, Option.some.injEq] using stream_zero_eq | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
ifp_zero : IntFractPair K
stream_zero_eq : IntFractPair.stream v 0 = some ifp_zero
this : IntFractPair.stream v 0 = some (IntFractPair.of v)
⊢ IntFractPair.of v = ifp_zero | ((:c Eq) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716)) (:fv _uniq.2913)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.of) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"simpa","sourceEnd":5329,"sourceStart":5324,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"Nat.zero_eq","source_end":5347,"source_start":5336,"syntax_kind":"ident"},{"source":"this","source_end":5353,"source_start":5349,"syntax_kind":"ident"},{"source":"Option.some.injEq","source_end":5372,"source_start":5355,"syntax_kind":"ident"},{"source":"stream_zero_eq","source_end":5394,"source_start":5380,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 14 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2f3b671a5e11b6e6b9757cc59f2deadf0fc701f6609fbb477f7dc0385490bea | 7f2d31a2142e8969f5d317e6778989e9bd82feba42c19030281f899cd064fb27 | 7c642bf28b947c3cc78a9e8cc86789b57fd56824265020a4267344b67c703279 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,739 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc v = <a>Int.fract</a> v + ⌊v⌋ := by rw [<a>Int.fract_add_floor</a>] _ = ⌊v⌋ := by simp [fract_eq_zero] | case zero.refl.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
⊢ v = ↑⌊v⌋ | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c Int.cast) (:fv _uniq.2711) ((:c Ring.toIntCast) (:fv _uniq.2711) ((:c StrictOrderedRing.toRing) (:fv _uniq.2711) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrderedField.toLinearO... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Int.cast) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c IntCast) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Int.floor) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"calc","sourceEnd":5852,"sourceStart":5848,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":2,"semanticRole":"local","source":"v","sourceEnd":5862,"sourceStart":5861,"tag":"identifier"},{"source":"=","sourceEnd":5864,"sourceStart":5863,"tag":"atom"},{"children":[{"children":[{... | [] | [{"source":"v = Int.fract v + ⌊v⌋","source_end":5886,"source_start":5861,"syntax_kind":"«term_=_»"},{"source":"Int.fract_add_floor","source_end":5916,"source_start":5897,"syntax_kind":"ident"},{"source":"_","source_end":5927,"source_start":5926,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"⌊v⌋","source_end":5937,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 30 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c7d75983845ec31ce4422fbc6d43daf1e1fa7872fd4efa95c222c16a9db0b03 | efb1b39ccb2cbf20b6d6d5aa674b35a66599d1e0d92d9b894a86a8d75f416152 | 8c2071a7ba2c4ee7d8dd0a27fe2bdf6f3c062b02acf39aec055bb5c1269ab954 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,740 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [<a>GeneralizedContinuedFraction.nextContinuants</a>, <a>GeneralizedContinuedFraction.nextNumerator</a>, <a>GeneralizedContinuedFraction.nextDenominator</a>, <a>GeneralizedContinuedFraction.compExactValue</a>] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
this : v = ↑⌊v⌋
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) (IntFra... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
this : v = ↑⌊v⌋
⊢ v = if (IntFractPair.of v).fr = 0 then ↑⌊v⌋ else ↑⌊v⌋ + (IntFractPair.of v).fr | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"field_simp","sourceEnd":5675,"sourceStart":5665,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":5677,"sourceStart... | [] | [{"source":"nextContinuants","source_end":5692,"source_start":5677,"syntax_kind":"ident"},{"source":"nextNumerator","source_end":5707,"source_start":5694,"syntax_kind":"ident"},{"source":"nextDenominator","source_end":5724,"source_start":5709,"syntax_kind":"ident"},{"source":"compExactValue","source_end":5740,"source_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 24 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c9d9f3bd14bab1d3589c31e8c4474d4c605c0a315db9165827d340b41948a6f | bdb8f9bf02477ad9457c262d2c2e21b1c0ecf8c90863dfecd7ceec5dfa50a95b | c3a4d2b6d78b0c438ee8930c5b02f2a41b20a79b1ea1388dcb9d964e02007c53 | 3fda36bdef60f9f4e5fd688dfcc0bd9d46da105e2d9bc3ffd8bf4f99a882861d |
cat-searcher/leandojo-benchmark-4-random | test | 3,741 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : (<a>GeneralizedContinuedFraction.IntFractPair.of</a> v).<a>GeneralizedContinuedFraction.IntFractPair.fr</a> = <a>Int.fract</a> v := <a>rfl</a> | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
this : v = ↑⌊v⌋
⊢ v = if (IntFractPair.of v).fr = 0 then ↑⌊v⌋ else ↑⌊v⌋ + (IntFractPair.of v).fr | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
this✝ : v = ↑⌊v⌋
this : (IntFractPair.of v).fr = Int.fract v
⊢ v = if (IntFractPair.of v).fr = 0 then ... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c ite) (:fv _uniq.2711) ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716))) ((:c OfNat.ofNat) (:fv _uniq.2711) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.fr) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":5754,"sourceStart":5750,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5755,"sourceStart":5755,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5755,"sourceStart":5755,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"(IntFractPair.of v).fr = Int.fract v","source_end":5793,"source_start":5757,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":5800,"source_start":5797,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 25 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff45e573f973634acebd49f373765c7d0ce5ce35253048a0a25603ddf899b88d | 3fda36bdef60f9f4e5fd688dfcc0bd9d46da105e2d9bc3ffd8bf4f99a882861d | eca851649f68794d8372e562f14ce3079bb0fdd6e20927427ce2053cd1bdcb35 | 28a54d515526b2f72a79a7065a37c966d57c57b3b932296c8425975d13666719 |
cat-searcher/leandojo-benchmark-4-random | test | 3,742 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [this, <a>if_pos</a> fract_eq_zero] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
this✝ : v = ↑⌊v⌋
this : (IntFractPair.of v).fr = Int.fract v
⊢ v = if (IntFractPair.of v).fr = 0 then ... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c ite) (:fv _uniq.2711) ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716))) ((:c OfNat.ofNat) (:fv _uniq.2711) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.fr) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rwa","sourceEnd":5812,"sourceStart":5809,"tag":"atom"},{"children":[{"source":"[","sourceEnd":5814,"sourceStart":5813,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"this","sourceEnd":5818,"sourceS... | [] | [{"source":"this","source_end":5818,"source_start":5814,"syntax_kind":"ident"},{"source":"if_pos fract_eq_zero","source_end":5840,"source_start":5820,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 26 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59a7f35a46506ee9ad984a2ac3394dcd026f6f29eea2532f4bf2e767f996ec03 | 28a54d515526b2f72a79a7065a37c966d57c57b3b932296c8425975d13666719 | 9fb87c2a25d46f72b51d1faec5d05358be25d932655c4a35a5b454a819f24329 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,743 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Int.fract_add_floor</a>] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
⊢ v = Int.fract v + ↑⌊v⌋ | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) (... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5895,"sourceStart":5893,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5897,"sourceStart":5896,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Int.fract_add_floor","source_end":5916,"source_start":5897,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 33 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 498167798ea3993fd81a71322def25133cba03e171d1b0930ad6e3c32e6025e7 | b81af0e3c7d621c89a3428220ec66e3e72713246f0ad74c5150833483acfa6ef | 5768c9fe0da7d15cb51630c3005b73d2d2c7c96a20b467a597059f75af23b373 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,744 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [fract_eq_zero] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_eq_zero : Int.fract v = 0
⊢ Int.fract v + ↑⌊v⌋ = ↑⌊v⌋ | ((:c Eq) (:fv _uniq.2711) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) ((:c NonUnitalNonA... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5948,"sourceStart":5944,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"fract_eq_zero","source_end":5963,"source_start":5950,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 40 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f976fe5fe0b492e187aa35d3880cc0622ffc7028a6fc7562dea2061be8ac60e7 | f9c468df70af2c837c9717d771e2ef3cc97ca661980683554939203972ea3713 | 95f12a9f4040b721dc7d276c199647357909767aca5d318784ae3b3ec4f77906 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,745 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [<a>GeneralizedContinuedFraction.continuantsAux</a>, <a>GeneralizedContinuedFraction.nextContinuants</a>, <a>GeneralizedContinuedFraction.nextNumerator</a>, <a>GeneralizedContinuedFraction.nextDenominator</a>, <a>GeneralizedContinuedFraction.of_h_eq_floor</a>, <a>GeneralizedContinuedFraction.compExactValue</... | case zero.refl.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_ne_zero : ¬Int.fract v = 0
⊢ v = compExactValue ((of v).continuantsAux 0) ((of v).continuantsAux (0 + 1)) (In... | case zero.refl.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_ne_zero : ¬Int.fract v = 0
⊢ v = if (IntFractPair.of v).fr = 0 then ↑⌊v⌋ else ↑⌊v⌋ + (IntFractPair.of v).fr | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"field_simp","sourceEnd":6077,"sourceStart":6067,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":6079,"sourceStart... | [] | [{"source":"continuantsAux","source_end":6093,"source_start":6079,"syntax_kind":"ident"},{"source":"nextContinuants","source_end":6110,"source_start":6095,"syntax_kind":"ident"},{"source":"nextNumerator","source_end":6125,"source_start":6112,"syntax_kind":"ident"},{"source":"nextDenominator","source_end":6142,"source_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 47 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8a9e3991222c73030aaa298c976f7dd42fee5d4f65f3490934e929fbbf40415 | 9488b7ab91fb3f60c26acc2eb1d11b6c1c7778855a80f21f8ba04a54f47092bc | c089c42afb92c84734cb9e7aa049b96ffb8eea0677d5b6cbe890a4310b5841f1 | c7fe36092d28ecc4d9bb7115617174126cfa63b835672e70cfc0ee90743554f8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,746 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : (<a>GeneralizedContinuedFraction.IntFractPair.of</a> v).<a>GeneralizedContinuedFraction.IntFractPair.fr</a> = <a>Int.fract</a> v := <a>rfl</a> | case zero.refl.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_ne_zero : ¬Int.fract v = 0
⊢ v = if (IntFractPair.of v).fr = 0 then ↑⌊v⌋ else ↑⌊v⌋ + (IntFractPair.of v).fr | case zero.refl.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_ne_zero : ¬Int.fract v = 0
this : (IntFractPair.of v).fr = Int.fract v
⊢ v = if (IntFractPair.of v).fr = 0 th... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c ite) (:fv _uniq.2711) ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716))) ((:c OfNat.ofNat) (:fv _uniq.2711) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.fr) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":6255,"sourceStart":6251,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":6256,"sourceStart":6256,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6256,"sourceStart":6256,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"(IntFractPair.of v).fr = Int.fract v","source_end":6294,"source_start":6258,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":6301,"source_start":6298,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 48 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0437eb50c1dc8ee7032173e5317c820886d0d2dd423a3c3362e0ff9bf04c8b48 | c7fe36092d28ecc4d9bb7115617174126cfa63b835672e70cfc0ee90743554f8 | eca851649f68794d8372e562f14ce3079bb0fdd6e20927427ce2053cd1bdcb35 | f2d785db2d35beae4771d5df22befad17a23f7faf678112884459bbc7e16080d |
cat-searcher/leandojo-benchmark-4-random | test | 3,747 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this, <a>if_neg</a> fract_ne_zero, <a>Int.floor_add_fract</a>] | case zero.refl.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
stream_zero_eq : IntFractPair.stream v 0 = some (IntFractPair.of v)
fract_ne_zero : ¬Int.fract v = 0
this : (IntFractPair.of v).fr = Int.fract v
⊢ v = if (IntFractPair.of v).fr = 0 th... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c ite) (:fv _uniq.2711) ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.IntFractPair.of) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716))) ((:c OfNat.ofNat) (:fv _uniq.2711) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrdere... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c ite) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.IntFractPair.fr) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rw","sourceEnd":6310,"sourceStart":6308,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6312,"sourceStart":6311,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRo... | [] | [{"source":"this","source_end":6316,"source_start":6312,"syntax_kind":"ident"},{"source":"if_neg fract_ne_zero","source_end":6338,"source_start":6318,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Int.floor_add_fract","source_end":6359,"source_start":6340,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 49 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 107ddc768bd7eb872b364acb4368d610b7fb0a686f65b2c91e6af18cbd8be655 | f2d785db2d35beae4771d5df22befad17a23f7faf678112884459bbc7e16080d | f4b80a377c2ab882814311758802675514c8323291a512af38e8e34340c13234 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,748 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ifp_succ_n succ_nth_stream_eq | case succ
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr
⊢ ∀ {ifp_n : In... | case succ
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr
ifp_succ_n : In... | (:forall ifp_n ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:forall _ ((:c Eq) ((:c Option) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711))) ((:c GeneralizedContinuedFraction.IntFractPair.stream) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.2736) (:fv _uniq.2716) ((:c HAdd.hAdd) ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:forall ifp_n :implicit (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Gene... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"intro","sourceEnd":6371,"sourceStart":6366,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ifp_succ_n","sourceEnd":6382,"sourceStart":6372,"tag":"identifier"},{"semanticRole":"scoped_local","source":"succ_nth_stream_eq","sourceEnd":6401,"sourceStart":6383,"tag":"identifier"}]... | [{"role":"fresh_name","source":"ifp_succ_n","source_end":6382,"source_start":6372,"syntax_kind":"ident"},{"role":"fresh_name","source":"succ_nth_stream_eq\n -- Nat.succ","source_end":6401,"source_start":6383,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 58 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a23a9a1f2ecd6ab22cd941b90cf9c4e884fa27a8bf75a2cfa2793644a66d344a | f8b854f9c7d1fb7706bd1a7fcdd1105d497998b2b6cf30bafc230e9f31bbc081 | 46840cedadbd17ba785a8a62ff08884b5529c09fcf492a237b869f9046b643a5 | b70897d28567627f38bd76ff56553a1bccc21361b9125bc0ead8a937b736bb3c |
cat-searcher/leandojo-benchmark-4-random | test | 3,749 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨ifp_n, nth_stream_eq, nth_fract_ne_zero, -⟩ : ∃ ifp_n, <a>GeneralizedContinuedFraction.IntFractPair.stream</a> v n = <a>Option.some</a> ifp_n ∧ ifp_n.fr ≠ 0 ∧ <a>GeneralizedContinuedFraction.IntFractPair.of</a> ifp_n.fr⁻¹ = ifp_succ_n := <a>GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_eq_some_iff</... | case succ
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.fr
ifp_succ_n : In... | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"obtain","sourceEnd":6428,"sourceStart":6422,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6432,"sourceStart":6429,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ifp_n","sourceEn... | [] | [{"source":"∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧\n ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n","source_end":6607,"source_start":6486,"syntax_kind":"«term∃_,_»"},{"source":"IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq\n -- introduce some notation","source_end":6678,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 59 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9a5f752d003a1d8b1e3f00f44afbfd94802c6b6ab02ed76bd325ff89eff7248 | b70897d28567627f38bd76ff56553a1bccc21361b9125bc0ead8a937b736bb3c | b702c6a9143f2600f1581c1e2d80d0aff0fb281b8327e6330a805c7f2e05a9a2 | d2a4d318ac141ccb951fab09f7ab8f032143e7c48e191aac2c20792e3f25fb7d |
cat-searcher/leandojo-benchmark-4-random | test | 3,750 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let conts := g.continuantsAux (n + 2) | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.... | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":6717,"sourceStart":6714,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"conts","sourceEnd":6723,"sourceStart":6718,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{... | [] | [{"source":"g.continuantsAux (n + 2)","source_end":6751,"source_start":6727,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 60 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de24fc2e4ed1f5e6c6de64d73da4cedc518c97a755bad0ee932fce270aabcb9f | d2a4d318ac141ccb951fab09f7ab8f032143e7c48e191aac2c20792e3f25fb7d | e02c738d41afca3adb416017b5114e3da2c7b5a05e5dabd3caddd87711379458 | 5213af5956afbcb53752dc1828d79088ef8e5b3616a3921c020357b497177225 |
cat-searcher/leandojo-benchmark-4-random | test | 3,751 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | set pconts := g.continuantsAux (n + 1) with pconts_eq | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
IH :
∀ {ifp_n : IntFractPair K},
IntFractPair.stream v n = some ifp_n →
v = compExactValue ((of v).continuantsAux n) ((of v).continuantsAux (n + 1)) ifp_n.... | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c Generali... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c GeneralizedCon... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"set","sourceEnd":6759,"sourceStart":6756,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"pconts","sourceEnd":6766,"sourceStart":6760,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":":=... | [] | [{"source":"g.continuantsAux (n + 1)","source_end":6794,"source_start":6770,"syntax_kind":"Lean.Parser.Term.app"},{"source":"pconts","source_end":6766,"source_start":6760,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 61 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59d98c7e32208fccbe22555f07d5ecb76e677d2e9a795fa28399626f2b96d958 | 5213af5956afbcb53752dc1828d79088ef8e5b3616a3921c020357b497177225 | fe00e5fc6f27a21ba147b7e4c377c6f6f6e6f81aeb320c8e6f96efe0ddedd028 | 5a92ee1dfbef687af971173e7108cb1afb38997ca927f25b329c338a968237aa |
cat-searcher/leandojo-benchmark-4-random | test | 3,752 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | set ppconts := g.continuantsAux n with ppconts_eq | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ... | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"set","sourceEnd":6817,"sourceStart":6814,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"ppconts","sourceEnd":6825,"sourceStart":6818,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":":... | [] | [{"source":"g.continuantsAux n","source_end":6847,"source_start":6829,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ppconts","source_end":6825,"source_start":6818,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 62 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8cabda0dfcc98ff261955ed2d4f6bb314ffc60cd6b273ba3fb1724aa2f229ac | 5a92ee1dfbef687af971173e7108cb1afb38997ca927f25b329c338a968237aa | 059819a4198406af038e48b5ccefaffdb55769f7eefd35c06ff5afccc7f1df7e | 1c89a2e3d19f07f1c2b3d34f672b7c00487ec60a7075f12b471581455196d805 |
cat-searcher/leandojo-benchmark-4-random | test | 3,753 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>Decidable.em</a> (ifp_succ_n.fr = 0) with ifp_succ_n_fr_eq_zero ifp_succ_n_fr_ne_zero | case succ.intro.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ... | case succ.intro.intro.intro.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"cases'","sourceEnd":6874,"sourceStart":6868,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Decidable.em","semanticRole":"global","source":"Decidable.em","sourceEnd":6887,"sourceStart":6875,"tag":"identifier"},{"children":[{"ch... | [] | [{"source":"Decidable.em (ifp_succ_n.fr = 0)","source_end":6907,"source_start":6875,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 63 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42c8f01c8bcf2181a272a98caea8c8bfcf0212d96ccc52ac3002b352597faf35 | 1c89a2e3d19f07f1c2b3d34f672b7c00487ec60a7075f12b471581455196d805 | 9c24b4438f7e451a5375fd80c70db4037442a617045e24369227418e8e8b2859 | 6a7612b5d99f6d9f609ead78057a2511f607bd88918f233305fea1c1811c1a7f |
cat-searcher/leandojo-benchmark-4-random | test | 3,754 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices v = conts.a / conts.b by simpa [<a>GeneralizedContinuedFraction.compExactValue</a>, ifp_succ_n_fr_eq_zero] | case succ.intro.intro.intro.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | case succ.intro.intro.intro.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"suffices","sourceEnd":6997,"sourceStart":6989,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":6998,"sourceStart":6998,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6998,"sourceStart":6998,"tag":"node"},{"children":[{"contextIndex":2,"semanticRole":"local","so... | [] | [{"source":"v = conts.a / conts.b","source_end":7019,"source_start":6998,"syntax_kind":"«term_=_»"},{"source":"compExactValue","source_end":7044,"source_start":7030,"syntax_kind":"ident"},{"source":"ifp_succ_n_fr_eq_zero","source_end":7067,"source_start":7046,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 68 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe3ca97c159cbf6b43d14b85026d0ba207363915366cabe87effaeb616842a05 | 4c5ce79f5a334acde66a61651567de9f68822372e41a27fd58f8931518e0b94a | e94117b465d2a4415c7b8421ef605f0e0d74b46b5ce92ca21355262b33e0a771 | b08f654d3751ac8daa8299d4dc10bc2c72f458efc8eb982efdcb454bf851cbfc |
cat-searcher/leandojo-benchmark-4-random | test | 3,755 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨ifp_n', nth_stream_eq', ifp_n_fract_inv_eq_floor⟩ : ∃ ifp_n, <a>GeneralizedContinuedFraction.IntFractPair.stream</a> v n = <a>Option.some</a> ifp_n ∧ ifp_n.fr⁻¹ = ⌊ifp_n.fr⁻¹⌋ := <a>GeneralizedContinuedFraction.IntFractPair.exists_succ_nth_stream_of_fr_zero</a> succ_nth_stream_eq ifp_succ_n_fr_eq_zero | case succ.intro.intro.intro.inl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | case succ.intro.intro.intro.inl.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.st... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"obtain","sourceEnd":7174,"sourceStart":7168,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7178,"sourceStart":7175,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ifp_n'","sourceE... | [] | [{"source":"∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧ ifp_n.fr⁻¹ = ⌊ifp_n.fr⁻¹⌋","source_end":7329,"source_start":7242,"syntax_kind":"«term∃_,_»"},{"source":"IntFractPair.exists_succ_nth_stream_of_fr_zero succ_nth_stream_eq ifp_succ_n_fr_eq_zero","source_end":7428,"source_start":7341,"syntax_kind":"Lean.Parser.Te... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 72 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b814fb6c89d051c2c517cf1442c7e3e8ab26813fad9df8438ec3e5a65eae220 | b08f654d3751ac8daa8299d4dc10bc2c72f458efc8eb982efdcb454bf851cbfc | 8a2df5d318f9c67250e0b9ee87d02d5750a8bc1d49e999106a1f0826dbde6f16 | e6743185913408653f5a249e12b966937280a2df6dba5f59578857c48540d286 |
cat-searcher/leandojo-benchmark-4-random | test | 3,756 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ifp_n' = ifp_n := by injection <a>Eq.trans</a> nth_stream_eq'.symm nth_stream_eq | case succ.intro.intro.intro.inl.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.st... | case succ.intro.intro.intro.inl.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.st... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":7439,"sourceStart":7435,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7440,"sourceStart":7440,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7440,"sourceStart":7440,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"ifp_n' = ifp_n","source_end":7456,"source_start":7442,"syntax_kind":"«term_=_»"},{"source":"Eq.trans nth_stream_eq'.symm nth_stream_eq","source_end":7515,"source_start":7473,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 73 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 56da8f161c75ac472b0a9a6d9afd6aaa786aa3464c59f5d4d30ffe177a68638b | e6743185913408653f5a249e12b966937280a2df6dba5f59578857c48540d286 | c69912e1be1787742666e9d01e5f28bbcf13827176528f67154d1e17d5d1bf80 | dedfea87db6a75a22fd7194eb2ca2eb2916f108033a01c8121a262b11730958c |
cat-searcher/leandojo-benchmark-4-random | test | 3,757 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases this | case succ.intro.intro.intro.inl.intro.intro
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.st... | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"cases","sourceEnd":7527,"sourceStart":7522,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":23,"semanticRole":"local","source":"this","sourceEnd":7532,"sourceStart":7528,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","so... | [] | [{"source":"this","source_end":7532,"source_start":7528,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 76 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aacd6409b0ef8906855d851522097038c4cc18dcbebb58264cec84ef57f0a360 | dedfea87db6a75a22fd7194eb2ca2eb2916f108033a01c8121a262b11730958c | a7a143fbe87a86d904dbf239a0096e0c1df53c4f9aefa4568c95e8e97069604f | 42782d7c999435604555f6a0a093f128f863e941e356408b2bce258012bfdbdb |
cat-searcher/leandojo-benchmark-4-random | test | 3,758 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have s_nth_eq : g.s.get? n = <a>Option.some</a> ⟨1, ⌊ifp_n.fr⁻¹⌋⟩ := <a>GeneralizedContinuedFraction.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero</a> nth_stream_eq nth_fract_ne_zero | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":7543,"sourceStart":7539,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s_nth_eq","sourceEnd":7552,"sourceStart":7544,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"s_nth_eq","sourceEnd":7552,"sourceStart":7544,"tag... | [] | [{"source":"g.s.get? n = some ⟨1, ⌊ifp_n.fr⁻¹⌋⟩","source_end":7601,"source_start":7555,"syntax_kind":"«term_=_»"},{"source":"get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero nth_stream_eq nth_fract_ne_zero","source_end":7699,"source_start":7613,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 77 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 551cfd299fd627c9ebf6c700d269067e8c177082decda3d972a6a544a70ee776 | 42782d7c999435604555f6a0a093f128f863e941e356408b2bce258012bfdbdb | 846506c649eab3710f01af1668b4f4950adb02c4664a7359103338bf2bf15bbf | ecb03889b8ca3ab75b00c7d3218ce6066496e8f59921df4b4775f7266aa6e06f |
cat-searcher/leandojo-benchmark-4-random | test | 3,759 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← ifp_n_fract_inv_eq_floor] at s_nth_eq | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rw","sourceEnd":7708,"sourceStart":7706,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7710,"sourceStart":7709,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7713,"sourceStart":... | [] | [{"source":"ifp_n_fract_inv_eq_floor","source_end":7738,"source_start":7714,"syntax_kind":"ident"},{"source":"s_nth_eq","source_end":7751,"source_start":7743,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 78 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4e455fa5a6373880700e187a4094574de699b6f16aa9e968c841d5d1cf21a37 | ecb03889b8ca3ab75b00c7d3218ce6066496e8f59921df4b4775f7266aa6e06f | 71169813925d677ede44480e9135942bca9bf59a34270f6f4e2ebc44ae511d2b | b9352c231f9874e89acc8ca3325adc441e77ef28314e59beb3bbd735d1e43f29 |
cat-searcher/leandojo-benchmark-4-random | test | 3,760 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices v = <a>GeneralizedContinuedFraction.compExactValue</a> ppconts pconts ifp_n.fr by simpa [conts, <a>GeneralizedContinuedFraction.continuantsAux</a>, s_nth_eq, <a>GeneralizedContinuedFraction.compExactValue</a>, nth_fract_ne_zero] using this | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"suffices","sourceEnd":7766,"sourceStart":7758,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":7767,"sourceStart":7767,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7767,"sourceStart":7767,"tag":"node"},{"children":[{"contextIndex":2,"semanticRole":"local","so... | [] | [{"source":"v = compExactValue ppconts pconts ifp_n.fr","source_end":7809,"source_start":7767,"syntax_kind":"«term_=_»"},{"source":"conts","source_end":7833,"source_start":7828,"syntax_kind":"ident"},{"source":"continuantsAux","source_end":7849,"source_start":7835,"syntax_kind":"ident"},{"source":"s_nth_eq","source_end... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 81 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a3b00ea67bed4dc20d038fc1e813b43febd75123fff3c4cbcde5fce6c578fda | b9352c231f9874e89acc8ca3325adc441e77ef28314e59beb3bbd735d1e43f29 | 1c7675af022956c03cd001b67275a1380c7525a93863c33db3f56cb8f25f0e2c | 5634a2f6f49d47f8bef1a3df96f32f785cc7a86b28bfbf00503acbe8040f4339 |
cat-searcher/leandojo-benchmark-4-random | test | 3,761 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact IH nth_stream_eq | case succ.intro.intro.intro.inl.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPa... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000)))) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV16)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"exact","sourceEnd":7918,"sourceStart":7913,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"IH","sourceEnd":7921,"sourceStart":7919,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"nth_stream_eq","sourceEnd":7935,"sourceStart":792... | [] | [{"source":"IH nth_stream_eq\n -- ifp_succ_n.fr ≠ 0","source_end":7935,"source_start":7919,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 85 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ea9b66df73a4f9cbe40efda19e611a5d1fbcd9a6c689a8718bedb0449a830ad | 5634a2f6f49d47f8bef1a3df96f32f785cc7a86b28bfbf00503acbe8040f4339 | d2f69a56c280ffa4a62e0e21a6a3fc077b893e3a5c7eb1f9dbd7244ea2dc375d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,762 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>GeneralizedContinuedFraction.compExactValue</a>, ifp_succ_n_fr_eq_zero] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":7028,"sourceStart":7023,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"compExactValue","source_end":7044,"source_start":7030,"syntax_kind":"ident"},{"source":"ifp_succ_n_fr_eq_zero","source_end":7067,"source_start":7046,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 69 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c88deaa42a6e73ed2ea8bfed6d8a8d464a1a93ac34f2043e1201f2413812b9a1 | 5a7703191c694df89f244ccbc7f3f1639119ad871534df8b74a7579c410c3f2b | b28aef190df2d8d019e85f396db7894e634316a392ddb77e2f9ebefc74936fda | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,763 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | injection <a>Eq.trans</a> nth_stream_eq'.symm nth_stream_eq | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:fv _uniq.17177) (:fv _uniq.16000)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV20)) (:arg :explicit 2 (:fv FV10))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"injection","sourceEnd":7472,"sourceStart":7463,"tag":"atom"},{"children":[{"name":"Eq.trans","semanticRole":"global","source":"Eq.trans","sourceEnd":7481,"sourceStart":7473,"tag":"identifier"},{"children":[{"name":"Eq.symm","semanticRole":"global","source":"nth_stream_eq'.symm","sourceEnd":7501,... | [] | [{"source":"Eq.trans nth_stream_eq'.symm nth_stream_eq","source_end":7515,"source_start":7473,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 75 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9da6dc324d238e847b681da1dee3c43105d20aa1bcad25e80eb3fdf9dd302657 | 440dc6a3f0ad23acab5409e1235722b90517da3f6d7bf1a6f264616e242f8e80 | 9fb0ddc82bb5ea8135785b6522bb41dabbcd448af74d044cf53b3efa96de49b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,764 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [conts, <a>GeneralizedContinuedFraction.continuantsAux</a>, s_nth_eq, <a>GeneralizedContinuedFraction.compExactValue</a>, nth_fract_ne_zero] using this | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c GeneralizedContinuedFraction.Pair.a) (:fv _uniq.2711) (:fv _uniq.16095)) ((:c GeneralizedContinuedFraction... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":7826,"sourceStart":7821,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"conts","source_end":7833,"source_start":7828,"syntax_kind":"ident"},{"source":"continuantsAux","source_end":7849,"source_start":7835,"syntax_kind":"ident"},{"source":"s_nth_eq","source_end":7859,"source_start":7851,"syntax_kind":"ident"},{"source":"compExactValue","source_end":7875,"source_start":7861,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 82 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68d39e317c96deba281908003a8976f2a67ba2d411cca21605e1747e85495081 | 1ff0749fb515bee09db9bfcc7fdd21563b518a8c6dcf8221096270b521a33719 | 7eaf611b6ac3a551b7a08ebbb1ded24daa902a76269d5793871ee6663c356e4e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,765 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices <a>GeneralizedContinuedFraction.compExactValue</a> ppconts pconts ifp_n.fr = <a>GeneralizedContinuedFraction.compExactValue</a> pconts conts ifp_succ_n.fr by have : v = <a>GeneralizedContinuedFraction.compExactValue</a> ppconts pconts ifp_n.fr := IH nth_stream_eq conv_lhs => rw [this] assumption | case succ.intro.intro.intro.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | case succ.intro.intro.intro.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"suffices","sourceEnd":8043,"sourceStart":8035,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":8052,"sourceStart":8052,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8052,"sourceStart":8052,"tag":"node"},{"children":[{"children":[{"name":"GeneralizedContinuedFr... | [] | [{"source":"compExactValue ppconts pconts ifp_n.fr = compExactValue pconts conts ifp_succ_n.fr","source_end":8134,"source_start":8052,"syntax_kind":"«term_=_»"},{"source":"v = compExactValue ppconts pconts ifp_n.fr","source_end":8195,"source_start":8153,"syntax_kind":"«term_=_»"},{"source":"IH nth_stream_eq","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 90 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee7c60babc8d89d7b9185bc4dc0526326f20c80aee0d58bf83da5ea1f104ef81 | e4b37e86985eae87fbeccfe1fa0b827710db7734de56ffb1bb6044f0963ee7e9 | 0aae8e56247ce814f1be76a56b74c309af90ad038a5fcc8c1212d2e82fc3408d | df0abd2bf88291084b90ba94cce6db5ab8fed208ba102edbdebf5fb34bf57583 |
cat-searcher/leandojo-benchmark-4-random | test | 3,766 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨ifp_n', nth_stream_eq', ifp_n_fract_ne_zero, ⟨refl⟩⟩ : ∃ ifp_n, <a>GeneralizedContinuedFraction.IntFractPair.stream</a> v n = <a>Option.some</a> ifp_n ∧ ifp_n.fr ≠ 0 ∧ <a>GeneralizedContinuedFraction.IntFractPair.of</a> ifp_n.fr⁻¹ = ifp_succ_n := <a>GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_eq_s... | case succ.intro.intro.intro.inr
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = s... | case succ.intro.intro.intro.inr.intro.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuants... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV16)) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"obtain","sourceEnd":8338,"sourceStart":8332,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":8342,"sourceStart":8339,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ifp_n'","sourceE... | [] | [{"source":"∃ ifp_n, IntFractPair.stream v n = some ifp_n ∧\n ifp_n.fr ≠ 0 ∧ IntFractPair.of ifp_n.fr⁻¹ = ifp_succ_n","source_end":8534,"source_start":8411,"syntax_kind":"«term∃_,_»"},{"source":"IntFractPair.succ_nth_stream_eq_some_iff.1 succ_nth_stream_eq","source_end":8607,"source_start":8546,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 100 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7f9c4624ca236faa45ac29e2eed03280992b27ab52f86e9ddb6e039b62e433ec | df0abd2bf88291084b90ba94cce6db5ab8fed208ba102edbdebf5fb34bf57583 | 66509ad4a596b5a5f58d5fbace5d0fca0c6fdb3877b1d5e4d7912b67b3282a20 | 550318cc166dca9384ba939bc5ce756cedd281cd3003c62d602d4c921797027a |
cat-searcher/leandojo-benchmark-4-random | test | 3,767 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ifp_n' = ifp_n := by injection <a>Eq.trans</a> nth_stream_eq'.symm nth_stream_eq | case succ.intro.intro.intro.inr.intro.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuants... | case succ.intro.intro.intro.inr.intro.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuants... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":8618,"sourceStart":8614,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8619,"sourceStart":8619,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8619,"sourceStart":8619,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"ifp_n' = ifp_n","source_end":8635,"source_start":8621,"syntax_kind":"«term_=_»"},{"source":"Eq.trans nth_stream_eq'.symm nth_stream_eq","source_end":8694,"source_start":8652,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 101 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6d4b4916238b2f3667ec1263ba76f633ad1222c7bbb5f864d3a22323ed41985 | 550318cc166dca9384ba939bc5ce756cedd281cd3003c62d602d4c921797027a | c69912e1be1787742666e9d01e5f28bbcf13827176528f67154d1e17d5d1bf80 | 74c9ac6e7577ec1aacf2f7f9226fde1fdbe8316fe83b2f0696edeb30a8db8c66 |
cat-searcher/leandojo-benchmark-4-random | test | 3,768 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases this | case succ.intro.intro.intro.inr.intro.intro.intro.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuants... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"cases","sourceEnd":8706,"sourceStart":8701,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":22,"semanticRole":"local","source":"this","sourceEnd":8711,"sourceStart":8707,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","so... | [] | [{"source":"this\n -- get the correspondence between ifp_n and g.s.nth n","source_end":8711,"source_start":8707,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 104 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ca5096785fb0f34885540447bfd55587e02d402e0d2371ccaee23d5350ae7c9 | 74c9ac6e7577ec1aacf2f7f9226fde1fdbe8316fe83b2f0696edeb30a8db8c66 | a7a143fbe87a86d904dbf239a0096e0c1df53c4f9aefa4568c95e8e97069604f | 6dd4d8cb4520e09b4ecb4c3e166c14699d197b5942f783b9d4e3a366ab5ca84e |
cat-searcher/leandojo-benchmark-4-random | test | 3,769 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have s_nth_eq : g.s.get? n = <a>Option.some</a> ⟨1, (⌊ifp_n.fr⁻¹⌋ : K)⟩ := <a>GeneralizedContinuedFraction.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero</a> nth_stream_eq ifp_n_fract_ne_zero | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":8782,"sourceStart":8778,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s_nth_eq","sourceEnd":8791,"sourceStart":8783,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"s_nth_eq","sourceEnd":8791,"sourceStart":8783,"tag... | [] | [{"source":"g.s.get? n = some ⟨1, (⌊ifp_n.fr⁻¹⌋ : K)⟩","source_end":8846,"source_start":8794,"syntax_kind":"«term_=_»"},{"source":"get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero nth_stream_eq ifp_n_fract_ne_zero\n -- the claim now follows by unfolding the definitions and tedious calculations\n -- some... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 105 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1aa404402b72c02651012f8bbb98285132ac49d7978730f34bf30ebc017c745b | 6dd4d8cb4520e09b4ecb4c3e166c14699d197b5942f783b9d4e3a366ab5ca84e | aee53aa829f36a49fb3f59da85fcbfa09972d962c2297a56c354ca6f31397302 | 13bdb06f801f5673139477ffedf1017861ca64b6622b8cf16e669774f852e1c1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,770 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ppA := ppconts.a | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":9074,"sourceStart":9071,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"ppA","sourceEnd":9078,"sourceStart":9075,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"s... | [] | [{"source":"ppconts.a","source_end":9091,"source_start":9082,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 106 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95690a0cb2044ee0040af878659efefb0022be524c12d1e591e369968c656c47 | 13bdb06f801f5673139477ffedf1017861ca64b6622b8cf16e669774f852e1c1 | dda892d511f40f4ed4831fa3d8df1b3c32d3b140ed4b071f89c701066556bc8d | dc5a37894850463460f77040c3dc1dc5233794899381a62a2417f080d2312a04 |
cat-searcher/leandojo-benchmark-4-random | test | 3,771 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ppB := ppconts.b | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":9101,"sourceStart":9098,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"ppB","sourceEnd":9105,"sourceStart":9102,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"s... | [] | [{"source":"ppconts.b","source_end":9118,"source_start":9109,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 107 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ab4ae12a8cb26b4cd75aa6840b34f5b3b4dbb0a52fe1ee6df0e4679686e2f5b | dc5a37894850463460f77040c3dc1dc5233794899381a62a2417f080d2312a04 | fd45921a9af5461fc956e88961720c8a2c0c8c8957aed158860300c804c7756f | 6d0bd18a6423520378a5fd6c468cebb45db8d924836f2be77e179c8859a172ff |
cat-searcher/leandojo-benchmark-4-random | test | 3,772 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let pA := pconts.a | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":9128,"sourceStart":9125,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"pA","sourceEnd":9131,"sourceStart":9129,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so... | [] | [{"source":"pconts.a","source_end":9143,"source_start":9135,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 108 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 082e8b4c1a7c648913dbfe39b9d1c5355b50ca46d1298c29ffed9ae1af6250a3 | 6d0bd18a6423520378a5fd6c468cebb45db8d924836f2be77e179c8859a172ff | 7e50243627124482643abd245f0d86e8ab19252c0ac2150c81baf9a8482d3801 | 2165138a5636187149dc0e2d1ea190320c7731fa47601fe6f2513864aabc3469 |
cat-searcher/leandojo-benchmark-4-random | test | 3,773 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let pB := pconts.b | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":9153,"sourceStart":9150,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"pB","sourceEnd":9156,"sourceStart":9154,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so... | [] | [{"source":"pconts.b","source_end":9168,"source_start":9160,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 109 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d828e16ea3fc23bec54ecf8d274e3ff1071e81da6120f6088a067bbd44b4bc9c | 2165138a5636187149dc0e2d1ea190320c7731fa47601fe6f2513864aabc3469 | 0b20962929e943536999ca9f9ad2fbb809097d4ef1ba6d96640944c37fb35c27 | 38a3bbe9117bae4d9c7699a5e1f5733ce4acf5249757114d00ac32c2eef2ce21 |
cat-searcher/leandojo-benchmark-4-random | test | 3,775 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rw","sourceEnd":9513,"sourceStart":9511,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9515,"sourceStart":9514,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":26,"semanticR... | [] | [{"source":"this","source_end":9519,"source_start":9515,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 114 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e29c7d574cf31694f363d6f7b5aa22de1cccf8ad8f49a6d7722dd0a304433b72 | c62f0cecee4daea0363efd91b10ab617d00d7867d48549b17b8e510dfdebfa36 | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | 83ab8d7381dc02c806fef8c7859fbee43022f251f7f1cb46d92058466aa1ba95 |
cat-searcher/leandojo-benchmark-4-random | test | 3,776 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have tmp_calc := <a>GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp</a> pA ppA ifp_succ_n_fr_ne_zero | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":9582,"sourceStart":9578,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"tmp_calc","sourceEnd":9591,"sourceStart":9583,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"tmp_calc","sourceEnd":9591,"sourceStart":9583,"tag... | [] | [{"source":"compExactValue_correctness_of_stream_eq_some_aux_comp pA ppA ifp_succ_n_fr_ne_zero","source_end":9685,"source_start":9603,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 117 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 031c37f1257f4ab8ee44c15f40565e4b0e68c99df0766d066e424f783fc024af | 83ab8d7381dc02c806fef8c7859fbee43022f251f7f1cb46d92058466aa1ba95 | ac85dac7c2694163e93ab0234698fdfb1b3c553539fa098aaeab975dff606421 | 1ce27046b059fff6c660c00d2de609a11a3b3c0c3edb3ec81483e255dddd1ae2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,777 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have tmp_calc' := <a>GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp</a> pB ppB ifp_succ_n_fr_ne_zero | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":9696,"sourceStart":9692,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"tmp_calc'","sourceEnd":9706,"sourceStart":9697,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"tmp_calc'","sourceEnd":9706,"sourceStart":9697,"t... | [] | [{"source":"compExactValue_correctness_of_stream_eq_some_aux_comp pB ppB ifp_succ_n_fr_ne_zero","source_end":9800,"source_start":9718,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 118 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1f2490a6d7c31e1c703741efb25186ef6603bdb596a72d719ac5a7dc85d6f36 | 1ce27046b059fff6c660c00d2de609a11a3b3c0c3edb3ec81483e255dddd1ae2 | cad2763119411249fe5ea29c76292c15a747044b7aaa742fc8b16090bd0e17e4 | 89929efa9fd805507e72c783624ddc9b0a179ea3055f5418c667f7bf0d8cb588 |
cat-searcher/leandojo-benchmark-4-random | test | 3,778 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let f := <a>Int.fract</a> (1 / ifp_n.fr) | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"let","sourceEnd":9810,"sourceStart":9807,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":9812,"sourceStart":9811,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"sou... | [] | [{"source":"Int.fract (1 / ifp_n.fr)","source_end":9840,"source_start":9816,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 119 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f36c974ef09a51e9ada129b813b8dddbc34d308cee43036b9b3eb6394bcc4051 | 89929efa9fd805507e72c783624ddc9b0a179ea3055f5418c667f7bf0d8cb588 | 90a3834b20d8e2dc8360ac74f438785116f08397964bf23f0fba7e281c06acb6 | a2d2389be3e48af1e1b9647bac7d559376562855849ec4bf24c39d56327e0fc1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,779 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have f_ne_zero : f ≠ 0 := by simpa [f] using ifp_succ_n_fr_ne_zero | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":9851,"sourceStart":9847,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"f_ne_zero","sourceEnd":9861,"sourceStart":9852,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"f_ne_zero","sourceEnd":9861,"sourceStart":9852,"t... | [] | [{"source":"f ≠ 0","source_end":9871,"source_start":9864,"syntax_kind":"«term_≠_»"},{"source":"f","source_end":9886,"source_start":9885,"syntax_kind":"ident"},{"source":"ifp_succ_n_fr_ne_zero","source_end":9915,"source_start":9894,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 120 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8bba3d145fd3e460a07d6e42007e5e6a7d763c66ff32f633c3d269d7290cf1a3 | a2d2389be3e48af1e1b9647bac7d559376562855849ec4bf24c39d56327e0fc1 | 9851a59a833c76e1156e944d1c662aedea37d886f67404e5da54d3880060097b | ee541844cf0343ffcdf4f8b9467a979073f65d00e38aad4799b9f92565912e3b |
cat-searcher/leandojo-benchmark-4-random | test | 3,780 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>inv_eq_one_div</a>] at tmp_calc tmp_calc' | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rw","sourceEnd":9924,"sourceStart":9922,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9926,"sourceStart":9925,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"inv_eq_one_div","sem... | [] | [{"source":"inv_eq_one_div","source_end":9940,"source_start":9926,"syntax_kind":"ident"},{"source":"tmp_calc","source_end":9953,"source_start":9945,"syntax_kind":"ident"},{"source":"tmp_calc'\n -- Porting note: the `tmp_calc`s need to be massaged, and some processing after `ac_rfl` done,\n -- because `field_s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 123 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a22028d834e55794fb802f4804de7d2ba19e35a958f468244d9843691019c1e9 | ee541844cf0343ffcdf4f8b9467a979073f65d00e38aad4799b9f92565912e3b | f2232e63828ca050d3ccef8d54354dbccd2b8df642b6771f7d23e39f375d84f8 | 3a05f634cde0789624bf740cc9224b5862c1502dafbc237c126a29735b56edcf |
cat-searcher/leandojo-benchmark-4-random | test | 3,781 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hA : (↑⌊1 / ifp_n.fr⌋ * pA + ppA) + pA * f = pA * (1 / ifp_n.fr) + ppA := by have := <a>congrFun</a> (<a>congrArg</a> <a>HMul.hMul</a> tmp_calc) f rwa [<a>right_distrib</a>, <a>div_mul_cancel₀</a> (h := f_ne_zero), <a>div_mul_cancel₀</a> (h := f_ne_zero)] at this | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":10124,"sourceStart":10120,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hA","sourceEnd":10127,"sourceStart":10125,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hA","sourceEnd":10127,"sourceStart":10125,"tag":"nod... | [] | [{"source":"(↑⌊1 / ifp_n.fr⌋ * pA + ppA) + pA * f = pA * (1 / ifp_n.fr) + ppA","source_end":10201,"source_start":10130,"syntax_kind":"«term_=_»"},{"source":"congrFun (congrArg HMul.hMul tmp_calc) f","source_end":10264,"source_start":10224,"syntax_kind":"Lean.Parser.Term.app"},{"source":"right_distrib","source_end":1029... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 126 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 889db9995644ef9a0aeea83e220b3fc57b3a16ad7cf6b2857ba92c509d73f77c | 3a05f634cde0789624bf740cc9224b5862c1502dafbc237c126a29735b56edcf | 6e9949fa51027941f6614b25f13f3815539acfbf0282df19f4c2119a36b623ed | 051d884b40c7dc6664aeccda85e80f378922d6e2eeff5781e2d632ee932351c4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,782 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hB : (↑⌊1 / ifp_n.fr⌋ * pB + ppB) + pB * f = pB * (1 / ifp_n.fr) + ppB := by have := <a>congrFun</a> (<a>congrArg</a> <a>HMul.hMul</a> tmp_calc') f rwa [<a>right_distrib</a>, <a>div_mul_cancel₀</a> (h := f_ne_zero), <a>div_mul_cancel₀</a> (h := f_ne_zero)] at this | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":10393,"sourceStart":10389,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hB","sourceEnd":10396,"sourceStart":10394,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hB","sourceEnd":10396,"sourceStart":10394,"tag":"nod... | [] | [{"source":"(↑⌊1 / ifp_n.fr⌋ * pB + ppB) + pB * f = pB * (1 / ifp_n.fr) + ppB","source_end":10470,"source_start":10399,"syntax_kind":"«term_=_»"},{"source":"congrFun (congrArg HMul.hMul tmp_calc') f","source_end":10534,"source_start":10493,"syntax_kind":"Lean.Parser.Term.app"},{"source":"right_distrib","source_end":105... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 134 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f1a918cd023baa89c69ffbb5923437e34626ae5de36d144a650502ac0ac94ad | 051d884b40c7dc6664aeccda85e80f378922d6e2eeff5781e2d632ee932351c4 | 1d19c7e8fd069cb72fb2f2534d377c87cfb5a8ef7efd827d740864b4ae8985e4 | e93b483d6a4ddbbdbe8fda9e675da177a6819d3d3f4cae8e834013e26f78dcb4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,783 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [conts, pconts, ppconts] | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"dsimp","sourceEnd":10760,"sourceStart":10755,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10765,"sourceStart":10761,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":10... | [] | [{"source":"conts","source_end":10772,"source_start":10767,"syntax_kind":"ident"},{"source":"pconts","source_end":10780,"source_start":10774,"syntax_kind":"ident"},{"source":"ppconts","source_end":10789,"source_start":10782,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 142 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3650717b5e6a8c6556113400e3200e1282c85f589bdde4a65e8306faa0cb42c | e93b483d6a4ddbbdbe8fda9e675da177a6819d3d3f4cae8e834013e26f78dcb4 | 8ce6e6d1571d48516dd95e41beae3bec3cece01f208f14dcce730a41adad7008 | 4cfff932109542dcbfa853ce2da365ffda8d3b9e5ae8c6b8e8cc7cc6fa83e0e0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,784 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [<a>GeneralizedContinuedFraction.compExactValue</a>, <a>GeneralizedContinuedFraction.continuantsAux_recurrence</a> s_nth_eq ppconts_eq pconts_eq, <a>GeneralizedContinuedFraction.nextContinuants</a>, <a>GeneralizedContinuedFraction.nextNumerator</a>, <a>GeneralizedContinuedFraction.nextDenominator</a>] | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c LinearOrderedField.toDiv) (:fv _uniq.2711) (:fv _uniq.2714))) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uni... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"field_simp","sourceEnd":10807,"sourceStart":10797,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":10809,"sourceSt... | [] | [{"source":"compExactValue","source_end":10823,"source_start":10809,"syntax_kind":"ident"},{"source":"continuantsAux_recurrence s_nth_eq ppconts_eq pconts_eq","source_end":10880,"source_start":10825,"syntax_kind":"Lean.Parser.Term.app"},{"source":"nextContinuants","source_end":10905,"source_start":10890,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 143 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3462383b7ca0d4dafffdd4814b7c6510056a9ad7d314e5434a80a957daff55de | 4cfff932109542dcbfa853ce2da365ffda8d3b9e5ae8c6b8e8cc7cc6fa83e0e0 | a7e095e1e7f381b6380db5adf210fc5057a8323d00435e8dafc3eb34ff60f950 | 5065e75cf61a1186ef445ed21e1cbb2908a8778589ce4e12d2fa5a442de4cbaa |
cat-searcher/leandojo-benchmark-4-random | test | 3,785 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hfr : (<a>GeneralizedContinuedFraction.IntFractPair.of</a> (1 / ifp_n.fr)).<a>GeneralizedContinuedFraction.IntFractPair.fr</a> = f := <a>rfl</a> | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c DivInvMonoid.toDiv) (:fv _uniq.2711) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.2711) ((:c DivisionCommMonoid.toDivisionMonoid) (:fv _uniq.2711) ((:c CommGroupWithZero.toDivisionCommMono... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":10949,"sourceStart":10945,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hfr","sourceEnd":10953,"sourceStart":10950,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hfr","sourceEnd":10953,"sourceStart":10950,"tag":"n... | [] | [{"source":"(IntFractPair.of (1 / ifp_n.fr)).fr = f","source_end":10995,"source_start":10956,"syntax_kind":"«term_=_»"},{"source":"rfl","source_end":11002,"source_start":10999,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 144 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c0dcfe0aa794370c7098d26d8a05d235338b1d3e574be7292041171d6cf3affb | 5065e75cf61a1186ef445ed21e1cbb2908a8778589ce4e12d2fa5a442de4cbaa | 3878203c4536112ccd070033daa217ca47163946c59fc335411dcaf277bbd624 | b6b854ba0bfdbb2824e8db62ac78380b8cc123e4c552a6ac0e920760c17e0eb9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,786 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>one_div</a>, <a>if_neg</a> _, ← <a>one_div</a>, hfr] | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | case succ.intro.intro.intro.inr.intro.intro.intro.refl.refl
K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.contin... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c DivInvMonoid.toDiv) (:fv _uniq.2711) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.2711) ((:c DivisionCommMonoid.toDivisionMonoid) (:fv _uniq.2711) ((:c CommGroupWithZero.toDivisionCommMono... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rw","sourceEnd":11011,"sourceStart":11009,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11013,"sourceStart":11012,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"one_div","semant... | [] | [{"source":"one_div","source_end":11020,"source_start":11013,"syntax_kind":"ident"},{"source":"if_neg _","source_end":11030,"source_start":11022,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_div","source_end":11043,"source_start":11036,"syntax_kind":"ident"},{"source":"hfr","source_end":11048,"source_start":1104... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 145 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a4ca2a0c32d6fc59ece9bf30a12863bd6df1bca83fa2aee666d0a8d0eb7ce5c | b6b854ba0bfdbb2824e8db62ac78380b8cc123e4c552a6ac0e920760c17e0eb9 | 9e8fc42bf04dbc366e0fdf49cbb721ebdb1dfec1b80871ed128d3c4acd47c58e | b39993db51e95d065930fff9aa46107efe8ad3611572af1cc36ad2ab644671aa |
cat-searcher/leandojo-benchmark-4-random | test | 3,787 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : v = <a>GeneralizedContinuedFraction.compExactValue</a> ppconts pconts ifp_n.fr := IH nth_stream_eq | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":8150,"sourceStart":8146,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":8151,"sourceStart":8151,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":8151,"sourceStart":8151,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"v = compExactValue ppconts pconts ifp_n.fr","source_end":8195,"source_start":8153,"syntax_kind":"«term_=_»"},{"source":"IH nth_stream_eq","source_end":8215,"source_start":8199,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 93 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5414f5a87f93f21da04787d235e728c907cf361e56da28fcfea765c041c83a2 | c8f038c1684a5da0b4890714db443852b9548636fa36cc2e797027b0a8fe8084 | 2db711d6915bb2ff51d2dc176b30281b3401eb80aa336acf3eee2446b4ab85a9 | d125ffe243ae97709ac2053d9129ccd83c189bf679c8c3104a73f146e1aa40b7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,788 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_lhs => rw [this] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) (:fv _uniq.2711) (:fv _uniq.2716) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.continuantsAux) (:fv _uniq.2711) ((:c Field.toDivisionRing) (:fv _uniq.2711) ((:c LinearOrderedField.toField) (:fv _uniq.2711) (:fv _uniq.271... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"conv_lhs","sourceEnd":8232,"sourceStart":8224,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":8235,"sourceStart":8233,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source"... | [] | [{"source":"this","source_end":8244,"source_start":8240,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 94 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b00eb0a4e19fbce0d6f71f4075087231edb0c8f6a51194e51ca39b843e0b98e | d125ffe243ae97709ac2053d9129ccd83c189bf679c8c3104a73f146e1aa40b7 | 1a5105bcb88521ef9bd82ce1ff94003724d3017e0f59b87687425e62582bd447 | 131d1d4c093aa54f8299fcdc40ed85e46385dfec6fd2004b39891516122a2f9e |
cat-searcher/leandojo-benchmark-4-random | test | 3,789 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_succ_n : IntFractPair K
succ_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : if... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV16)) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"assumption","sourceEnd":8264,"sourceStart":8254,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption\n -- get the correspondence between ifp_n and ifp_succ_n","sourceEnd":8264,"sourceStart":8254,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 99 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7a097ccbef55482a1210885c81a2579df93947c6f2e0e4be81cbb294e3f3275d | 131d1d4c093aa54f8299fcdc40ed85e46385dfec6fd2004b39891516122a2f9e | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,790 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | injection <a>Eq.trans</a> nth_stream_eq'.symm nth_stream_eq | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) ((:c GeneralizedContinuedFraction.IntFractPair) (:fv _uniq.2711)) (:fv _uniq.18193) (:fv _uniq.16000)) | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c GeneralizedContinuedFraction.IntFractPair) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:fv FV8))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"injection","sourceEnd":8651,"sourceStart":8642,"tag":"atom"},{"children":[{"name":"Eq.trans","semanticRole":"global","source":"Eq.trans","sourceEnd":8660,"sourceStart":8652,"tag":"identifier"},{"children":[{"name":"Eq.symm","semanticRole":"global","source":"nth_stream_eq'.symm","sourceEnd":8680,... | [] | [{"source":"Eq.trans nth_stream_eq'.symm nth_stream_eq","source_end":8694,"source_start":8652,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 103 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de68d73a496797ba7a2fe1fb48fb081cdc3d87deda45638288ad55a07e6a3c60 | 101854f08959585d636648c82f798e7dd216ce3383d259aba6c20d420bb24aff | 9fb0ddc82bb5ea8135785b6522bb41dabbcd448af74d044cf53b3efa96de49b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,791 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [ifp_n_fract_ne_zero, <a>GeneralizedContinuedFraction.compExactValue</a>, <a>GeneralizedContinuedFraction.nextContinuants</a>, <a>GeneralizedContinuedFraction.nextNumerator</a>, <a>GeneralizedContinuedFraction.nextDenominator</a>, ppA, ppB] | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c GeneralizedContinuedFraction.compExactValue) (:fv _uniq.2711) (:fv _uniq.2714) (:fv _uniq.16358) (:fv _uniq.16153) ((:c GeneralizedContinuedFraction.IntFractPair.fr) (:fv _uniq.2711) (:fv _uniq.16000))) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c GeneralizedContinuedFraction.compExactValue) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedField) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV12)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"field_simp","sourceEnd":9382,"sourceStart":9372,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":9384,"sourceStart... | [] | [{"source":"ifp_n_fract_ne_zero","source_end":9403,"source_start":9384,"syntax_kind":"ident"},{"source":"compExactValue","source_end":9419,"source_start":9405,"syntax_kind":"ident"},{"source":"nextContinuants","source_end":9436,"source_start":9421,"syntax_kind":"ident"},{"source":"nextNumerator","source_end":9451,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 112 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c434dfb5a5390baead675b49337b49d7721fe046728f326033c3c66f0e5a85bd | 8b8c05acf79d3dcac24ca0e8f1a456b519a03757670715df86b78dd606f0f967 | 4a0162fb96c30680d01ee8747fbb9875703a937183d53f4a6588e686d80a1505 | 28d3b10a303c42f15d813bc4f411a4efe9c0e6553c44e67ee0f182a50b23cf0b |
cat-searcher/leandojo-benchmark-4-random | test | 3,792 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ac_rfl | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c HDiv.hDiv) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHDiv) (:fv _uniq.2711) ((:c DivInvMonoid.toDiv) (:fv _uniq.2711) ((:c DivisionMonoid.toDivInvMonoid) (:fv _uniq.2711) ((:c DivisionCommMonoid.toDivisionMonoid) (:fv _uniq.2711) ((:c CommGroupWithZero.toDivisionCommMono... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"ac_rfl","sourceEnd":9504,"sourceStart":9498,"tag":"atom"}],"kind":"Lean.Parser.Tactic.acRfl","source":"ac_rfl","sourceEnd":9504,"sourceStart":9498,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 113 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67255391c2588f62853df6617391c06fe4863de7fccb3b15bd62aff2ebcaa185 | 28d3b10a303c42f15d813bc4f411a4efe9c0e6553c44e67ee0f182a50b23cf0b | 2dd78c9d090141d123f9af8735c699cf9192b0edec0d63080dd4083a3ed0b2a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,793 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [f] using ifp_succ_n_fr_ne_zero | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Ne) (:fv _uniq.2711) (:fv _uniq.58698) ((:c OfNat.ofNat) (:fv _uniq.2711) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.2711) ((:c CommMonoidWithZero.toZero) (:fv _uniq.2711) ((:c CommGroupWithZero.toCommMonoidWithZero) (:fv _uniq.2711) ((:c Semifield.toCommGroupWithZero) (:fv _uniq.2711) ((:c LinearOrderedSemifield.toS... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV29)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"simpa","sourceEnd":9883,"sourceStart":9878,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"f","source_end":9886,"source_start":9885,"syntax_kind":"ident"},{"source":"ifp_succ_n_fr_ne_zero","source_end":9915,"source_start":9894,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 122 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d0090707f20af80784bd3549e81301b09a409a2877f379588d5c53e9b1c7e05 | df8f08dbb9c343198ba83809230d222b18d8d649509f54ea3d0e5d55675af64c | 43c7a1233c2f0986a603d57945ed2d188d5d53d6c0386ace53102ea3db3f9b00 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,794 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>congrFun</a> (<a>congrArg</a> <a>HMul.hMul</a> tmp_calc) f | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) ((:c NonUnitalNonA... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":10220,"sourceStart":10216,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10221,"sourceStart":10221,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10221,"sourceStart":10221,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"congrFun (congrArg HMul.hMul tmp_calc) f","source_end":10264,"source_start":10224,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 128 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 81a9f4453a42528201314c1578cd218c4f91d782ca96a9e0dada405e6f85519e | 6dd2d8e37be14732623ad5498ebb1e82b5f5f1e29fe99e1192d9eb656ab87318 | 44e4eef573d35d1f5abd52679e1d23370f5eb2a67b7fc53cc706542e1b90964b | 80bdd5d1c4182233e017658ae7b4aa2499d2a1925b87e582fb8bddc3635366e2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,795 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>right_distrib</a>, <a>div_mul_cancel₀</a> (h := f_ne_zero), <a>div_mul_cancel₀</a> (h := f_ne_zero)] at this | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) ((:c NonUnitalNonA... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rwa","sourceEnd":10276,"sourceStart":10273,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10278,"sourceStart":10277,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"right_distrib","semanticRole":"global","source":"right_distrib","sourc... | [] | [{"source":"right_distrib","source_end":10291,"source_start":10278,"syntax_kind":"ident"},{"source":"this","source_end":10382,"source_start":10378,"syntax_kind":"ident"},{"source":"div_mul_cancel₀ (h := f_ne_zero)","source_end":10327,"source_start":10293,"syntax_kind":"Lean.Parser.Term.app"},{"source":"div_mul_cancel₀ ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 129 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54b14d78059d90fb98f518cd91b3d0ba2b56b88301f4bcbd3d38fa1ad8e07bfd | 80bdd5d1c4182233e017658ae7b4aa2499d2a1925b87e582fb8bddc3635366e2 | a502cebfb7dcfe6643bb578a3816833ade0e91b0810ca3da4a1383bd6ecfb6cb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,796 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>congrFun</a> (<a>congrArg</a> <a>HMul.hMul</a> tmp_calc') f | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) ((:c NonUnitalNonA... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"have","sourceEnd":10489,"sourceStart":10485,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10490,"sourceStart":10490,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10490,"sourceStart":10490,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"congrFun (congrArg HMul.hMul tmp_calc') f","source_end":10534,"source_start":10493,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 136 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d4f49a98fe2e08cc9e949714b128054d0f20b78d6677d6b3d97f83158d4c95e | 1b26e3157c28f53ea66665630c04ee264441cc8d33b3df7673f6221beee4719c | c3946e1df5c72dd0224d13d324e2e2c10493adce1b1d203abb69a5860c3614a7 | 2d845928cdc5e095cb4a1ba7557a3dc1f638969fc330ab44313e02c134e8ea6d |
cat-searcher/leandojo-benchmark-4-random | test | 3,797 | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some | Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>right_distrib</a>, <a>div_mul_cancel₀</a> (h := f_ne_zero), <a>div_mul_cancel₀</a> (h := f_ne_zero)] at this | K : Type u_1
inst✝¹ : LinearOrderedField K
v : K
n✝ : ℕ
inst✝ : FloorRing K
g : GeneralizedContinuedFraction K := of v
n : ℕ
ifp_n : IntFractPair K
nth_stream_eq : IntFractPair.stream v n = some ifp_n
nth_fract_ne_zero : ifp_n.fr ≠ 0
conts : Pair K := g.continuantsAux (n + 2)
pconts : Pair K := g.continuantsAux (n + 1)... | ((:c Eq) (:fv _uniq.2711) ((:c HAdd.hAdd) (:fv _uniq.2711) (:fv _uniq.2711) (:fv _uniq.2711) ((:c instHAdd) (:fv _uniq.2711) ((:c Distrib.toAdd) (:fv _uniq.2711) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.2711) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.2711) ((:c NonUnitalNonA... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.2711))"},{"name":"v","sexp":"(:fv _uniq.2711)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.2711) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.2711) ((:c LinearOrder... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:arg... | {"children":[{"source":"rwa","sourceEnd":10546,"sourceStart":10543,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10548,"sourceStart":10547,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"right_distrib","semanticRole":"global","source":"right_distrib","sourc... | [] | [{"source":"right_distrib","source_end":10561,"source_start":10548,"syntax_kind":"ident"},{"source":"this\n -- now unfold the recurrence one step and simplify both sides to arrive at the conclusion","source_end":10652,"source_start":10648,"syntax_kind":"ident"},{"source":"div_mul_cancel₀ (h := f_ne_zero)","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2711","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2714","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"internal... | 11 | 137 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a1f278698c5773489edc36eb79694df0236120e3fca343eea191ef368fe7f52 | 2d845928cdc5e095cb4a1ba7557a3dc1f638969fc330ab44313e02c134e8ea6d | a502cebfb7dcfe6643bb578a3816833ade0e91b0810ca3da4a1383bd6ecfb6cb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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