dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 3,595 | left_eq_midpoint_iff | Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_comm</a>, <a>midpoint_eq_left_iff</a>] | R : Type u_1
V : Type u_2
V' : Type u_3
P : Type u_4
P' : Type u_5
inst✝⁷ : Ring R
inst✝⁶ : Invertible 2
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module R V
inst✝³ : AddTorsor V P
inst✝² : AddCommGroup V'
inst✝¹ : Module R V'
inst✝ : AddTorsor V' P'
x✝ y✝ z x y : P
⊢ x = midpoint R x y ↔ x = y | ((:c Iff) ((:c Eq) (:fv _uniq.106447) (:fv _uniq.108443) ((:c midpoint) (:fv _uniq.106438) (:fv _uniq.106441) (:fv _uniq.106447) (:fv _uniq.106453) (:fv _uniq.107005) (:fv _uniq.107008) (:fv _uniq.107550) (:fv _uniq.107636) (:fv _uniq.108443) (:fv _uniq.108444))) ((:c Eq) (:fv _uniq.106447) (:fv _uniq.108443) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"V'","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"P'","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.106438))"},{"name":"inst✝⁶","sexp":"((:c Invertible) (:fv _uniq.106438... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:app (:c midpoint) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.106438","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.106441","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6950,"sourceStart":6948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6952,"sourceStart":6951,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"eq_comm","source_end":6959,"source_start":6952,"syntax_kind":"ident"},{"source":"midpoint_eq_left_iff","source_end":6981,"source_start":6961,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.106438","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.106441","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 51 | 2 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b183671b36f5b206baefdd21b3471adb6febc4a1ef9f2b974699cfa56dacbbce | 6fbb87b2c0178091ccc76dcbe8cb9cc5b0806001962ceb1ac399267d4e6a2f0a | bd6f66ff558faa2df2049a15120872be646919b69545c3750791a84b2a62c74e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,596 | Function.not_injective_iff | Mathlib/Logic/Function/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Function.Injective</a>, <a>Classical.not_forall</a>, <a>exists_prop</a>] | α : Sort u_1
β : Sort u_2
γ : Sort u_3
f : α → β
⊢ ¬Injective f ↔ ∃ a b, f a = f b ∧ a ≠ b | ((:c Iff) ((:c Not) ((:c Function.Injective) (:fv _uniq.2364) (:fv _uniq.2367) (:fv _uniq.2374))) ((:c Exists) (:fv _uniq.2364) (:lambda a (:fv _uniq.2364) ((:c Exists) (:fv _uniq.2364) (:lambda b (:fv _uniq.2364) ((:c And) ((:c Eq) (:fv _uniq.2367) ((:fv _uniq.2374) 1) ((:fv _uniq.2374) 0)) ((:c Ne) (:fv _uniq.2364) 1... | [{"name":"α","sexp":"(:sort u_1)"},{"name":"β","sexp":"(:sort u_2)"},{"name":"γ","sexp":"(:sort u_3)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.2364) (:fv _uniq.2367))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Function.Injective) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV3)))))) (:arg :explicit 1 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2364","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2367","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4218,"sourceStart":4214,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4223,"sourceStart":4219,"tag":"atom"}],"kind":"nu... | [] | [{"source":"Injective","source_end":4234,"source_start":4225,"syntax_kind":"ident"},{"source":"not_forall","source_end":4246,"source_start":4236,"syntax_kind":"ident"},{"source":"exists_prop","source_end":4259,"source_start":4248,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2364","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2367","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 41 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e8636e85d65e4e9fed216cab4fdac02dfa15a6a338789ed47355b0420673a37 | c9ba59fdce55dc55b09133fa494ff59e612350bb32a8b4f3455f2542467a9697 | 5b10dc1eaaf7e26f28543a64ad9b63fd01f9c1ab0046b54256feb83ac01a927b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,597 | Finset.sup'_union | Mathlib/Data/Finset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>or_imp</a>, <a>forall_and</a>] | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝¹ : SemilatticeSup α
s : Finset β
H : s.Nonempty
f✝ : β → α
inst✝ : DecidableEq β
s₁ s₂ : Finset β
h₁ : s₁.Nonempty
h₂ : s₂.Nonempty
f : β → α
a : α
⊢ (s₁ ∪ s₂).sup' ⋯ f ≤ a ↔ s₁.sup' h₁ f ⊔ s₂.sup' h₂ f ≤ a | ((:c Iff) ((:c LE.le) (:fv _uniq.207876) ((:c Preorder.toLE) (:fv _uniq.207876) ((:c PartialOrder.toPreorder) (:fv _uniq.207876) ((:c SemilatticeSup.toPartialOrder) (:fv _uniq.207876) (:fv _uniq.207891)))) ((:c Finset.sup') (:fv _uniq.207876) (:fv _uniq.207879) (:fv _uniq.207891) ((:c Union.union) ((:c Finset) (:fv _un... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝¹","sexp":"((:c SemilatticeSup) (:fv _uniq.207876))"},{"name":"s"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Finset.sup') (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semilat... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.207873","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.207876","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":35310,"sourceStart":35306,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"or_imp","source_end":35318,"source_start":35312,"syntax_kind":"ident"},{"source":"forall_and","source_end":35330,"source_start":35320,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.207873","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.207876","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 306 | 2 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5a35d88b40ba8146b24aa41acd66503a8ce5459506ffe548d26d1373ae3e2fe | ac3a2b1fa0677f6c4937add4579f799df3702f5a647d256fb6a001419884b9c3 | 558b319171fd1e757436ec070309c60dabebf68baf77115f54b91787561a176e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,598 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases m.eq_zero_or_pos with (rfl | hm) | p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
n m : ℕ
hmn : m ≤ n
h : Irreducible (cyclotomic (p ^ n) R)
⊢ Irreducible (cyclotomic (p ^ m) R) | case inl
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ
h : Irreducible (cyclotomic (p ^ n) R)
hmn : 0 ≤ n
⊢ Irreducible (cyclotomic (p ^ 0) R)
case inr
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
n m : ℕ
hmn : m ≤ n
h : Irreducible (cyclotomic (p ^ n) R)... | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"rcases","sourceEnd":5579,"sourceStart":5573,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.eq_zero_or_pos","semanticRole":"global","source":"m.eq_zero_or_pos","sourceEnd":5596,"sourceStart":5580,"tag":"identifier"}],"kind":"Lean.Parser... | [] | [{"source":"m.eq_zero_or_pos","source_end":5596,"source_start":5580,"syntax_kind":"ident"},{"source":"(rfl | hm)","source_end":5612,"source_start":5602,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7c8793920fae94e8e321d0348ef79e7d17b411cd505a6ae5f344499b876f446 | da7e783367bddd9bfc6ea8151da5bb718509cfc9293882ac3e676aa196048d58 | e3bb06fe6935526288d5921ad3c431a5a4c67ea9749f965fea970dbebacc52e8 | e384f14e023a4a72b31640c881ffbcc9ce7b87b27bc41e70f2834f6d341fb6f2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,599 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨k, rfl⟩ := <a>Nat.exists_eq_add_of_le</a> hmn | case inr
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
n m : ℕ
hmn : m ≤ n
h : Irreducible (cyclotomic (p ^ n) R)
hm : m > 0
⊢ Irreducible (cyclotomic (p ^ m) R) | case inr.intro
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hmn : m ≤ m + k
h : Irreducible (cyclotomic (p ^ (m + k)) R)
⊢ Irreducible (cyclotomic (p ^ m) R) | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"obtain","sourceEnd":5666,"sourceStart":5660,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5670,"sourceStart":5667,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":5... | [] | [{"source":"Nat.exists_eq_add_of_le hmn","source_end":5710,"source_start":5683,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨k, rfl⟩","source_end":5679,"source_start":5667,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 10 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c8c8b8268529bd42882bfbdddf7bf0f76e7ac827d149db902cd7ff4b92936254 | fedadcfc3d410c2348170705328da54e4629efc3eca6778ba2e5641d974f714b | f84eaa9db6480f95bb9ae51d0d64c8f71004d54f16f9aa1beddb69a76ef469f6 | 2941dcbecaed22ce0ed223167cbfc2dbc388c2069d15f635d5f866306661df0f |
cat-searcher/leandojo-benchmark-4-random | test | 3,600 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' k with k hk | case inr.intro
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hmn : m ≤ m + k
h : Irreducible (cyclotomic (p ^ (m + k)) R)
⊢ Irreducible (cyclotomic (p ^ m) R) | case inr.intro.zero
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
hmn : m ≤ m + 0
h : Irreducible (cyclotomic (p ^ (m + 0)) R)
⊢ Irreducible (cyclotomic (p ^ m) R)
case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > ... | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"induction'","sourceEnd":5723,"sourceStart":5713,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"k","sourceEnd":5725,"sourceStart":5724,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"k","source_end":5725,"source_start":5724,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 11 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48517a97087f8e57616ca0f28ca1c6ce0e676ba75227ac69131a7249a9dccbb8 | 2941dcbecaed22ce0ed223167cbfc2dbc388c2069d15f635d5f866306661df0f | bdd90a9f67761af6ddd88c7f71b638d76e05afffcce7177d70e7841529535423 | fd1d977a20cd1994953933f254ccd4dd3ac9b4a8aee8168c586c1f60bf808cd5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,601 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : m + k ≠ 0 := (<a>add_pos_of_pos_of_nonneg</a> hm k.zero_le).<a>LT.lt.ne'</a> | case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible (cyclotomic (p ^ (m + (k + 1))) R)
⊢ Irreducible (cyclotomic (p ^ m) ... | case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible (cyclotomic (p ^ (m + (k + 1))) R)
this : m + k ≠ 0
⊢ Irreducible (cy... | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"have","sourceEnd":5761,"sourceStart":5757,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5762,"sourceStart":5762,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5762,"sourceStart":5762,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"m + k ≠ 0","source_end":5775,"source_start":5764,"syntax_kind":"«term_≠_»"},{"source":"(add_pos_of_pos_of_nonneg hm k.zero_le).ne'","source_end":5822,"source_start":5779,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 17 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e12f3b9be0a171c187b1eaa0de114e41406781846af0da67ab6b7e4ab958a53 | 7f535d62efcbcdb97de24c10a3108f8f45683949e72333ee71c75c2259d4c114 | 2602e2daee1429a54580006bcb1ec5bf7fe09676ba7ac2a8642c04fc135afd59 | f754b806f7047183b8e47fe3a8da308cd88bb9b58c67dc540c13c250aee09765 |
cat-searcher/leandojo-benchmark-4-random | test | 3,602 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.add_succ</a>, <a>pow_succ</a>, ← <a>Polynomial.cyclotomic_expand_eq_cyclotomic</a> hp <| <a>dvd_pow_self</a> p this] at h | case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible (cyclotomic (p ^ (m + (k + 1))) R)
this : m + k ≠ 0
⊢ Irreducible (cy... | case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible ((expand R p) (cyclotomic (p ^ (m + k)) R))
this : m + k ≠ 0
⊢ Irredu... | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"rw","sourceEnd":5827,"sourceStart":5825,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5829,"sourceStart":5828,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.add_succ","seman... | [] | [{"source":"Nat.add_succ","source_end":5841,"source_start":5829,"syntax_kind":"ident"},{"source":"h","source_end":5920,"source_start":5919,"syntax_kind":"ident"},{"source":"pow_succ","source_end":5851,"source_start":5843,"syntax_kind":"ident"},{"source":"cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this","sourc... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 18 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 41c9bdd80cb10a6c3389d8a7b6747a248134e578c9937469864fb7c3781e3087 | f754b806f7047183b8e47fe3a8da308cd88bb9b58c67dc540c13c250aee09765 | b53aef55ff49dc5f1f3db5131621936ba0ea11d57dbb09a85f9a3c5c513f45b8 | 97f4c5e3615eed17c2598a06e92dda9041f13c26c73c65ca0fc632321d258474 |
cat-searcher/leandojo-benchmark-4-random | test | 3,603 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hk (by omega) (<a>Polynomial.of_irreducible_expand</a> hp.ne_zero h) | case inr.intro.succ
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible ((expand R p) (cyclotomic (p ^ (m + k)) R))
this : m + k ≠ 0
⊢ Irredu... | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"source":"exact","sourceEnd":5928,"sourceStart":5923,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"hk","sourceEnd":5931,"sourceStart":5929,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":5933,"sourceStart":5932,"tag":"atom"},{"children":[{"source":"b... | [] | [{"source":"hk (by omega) (of_irreducible_expand hp.ne_zero h)","source_end":5979,"source_start":5929,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 23 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e7a65b962b38481cb180302e90edb95d7fc6312b3e98575ec34c782f930fe0ec | 97f4c5e3615eed17c2598a06e92dda9041f13c26c73c65ca0fc632321d258474 | 2b2df9afa7261ec3bf06ce6726b2f36089a0f6fa7aa4dc7b53c04ad3033a55e7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,604 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>Polynomial.irreducible_X_sub_C</a> (1 : R) | case inl
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
n : ℕ
h : Irreducible (cyclotomic (p ^ n) R)
hmn : 0 ≤ n
⊢ Irreducible (cyclotomic (p ^ 0) R) | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5623,"sourceStart":5618,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"irreducible_X_sub_C (1 : R)","source_end":5657,"source_start":5630,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 7 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 435699ae0607ffbcfca18ea06ff7d87c3706279d4b83337756a2886041eed1ed | 7ad05038449262bb542afaf3f850cf93527c27b1c6fe96844ccb7c14c7796257 | 1f3338749e0950d6ed979e6a65fcc39c23cab1e9af9cca6301d478dd13768701 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,605 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using h | case inr.intro.zero
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
hmn : m ≤ m + 0
h : Irreducible (cyclotomic (p ^ (m + 0)) R)
⊢ Irreducible (cyclotomic (p ^ m) R) | ((:c Irreducible) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ((:c MonoidWithZero.toMonoid) ((:c Polynomial) (:fv _uniq.20801) ((:c Ring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toRing) (:fv _uniq.20801) (:fv _uniq.20802)))) ... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c Irreducible) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5746,"sourceStart":5741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"h","source_end":5754,"source_start":5753,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 14 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e0cd91a6c65063cf5044148aed4666e137c4e6d843a9c94d606b6c767d4180e0 | b0cd8018bce4e5cdc9f7714c6022afecf155e3dd9f8465a750e588a151eba054 | 13dcd7fec2d6a08b4136e7d3cde44729710b940c2bfede2f5f86c973c3d8a2ee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,606 | Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝¹ : CommRing R
inst✝ : IsDomain R
m : ℕ
hm : m > 0
k : ℕ
hk : m ≤ m + k → Irreducible (cyclotomic (p ^ (m + k)) R) → Irreducible (cyclotomic (p ^ m) R)
hmn : m ≤ m + (k + 1)
h : Irreducible ((expand R p) (cyclotomic (p ^ (m + k)) R))
this : m + k ≠ 0
⊢ m ≤ m + k | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.20805) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.20805) (:fv _uniq.23384))) | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.20799))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.20801))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.20801) ((:c CommSemiring.toSemiring) (:fv _uniq.20801) ((:c CommRing.toCommSemi... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV6)) (:arg :explicit 3 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instan... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1))... | {"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":5941,"sourceStart":5936,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":5941,"sourceStart":5936,"tag":"node"}],"kind":"null","source":"omega","sourceEnd"... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20799","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20800","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 7 | 26 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7828b09814491c381d14b3f46f6f10a5c13e2e590a1d8780a497ce944d3f11e | af09ed67d720ec61acc37e060712a442e82bfcaa0ef71638d1eaf35eed2413a8 | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,607 | SignType.nonneg_iff_ne_neg_one | Mathlib/Data/Sign.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases a <;> decide | a : SignType
⊢ 0 ≤ a ↔ a ≠ -1 | ((:c Iff) ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.instZero))) (:fv _uniq.28602)) ((:c Ne) (:c SignType) (:fv _uniq.28602) ((:c Neg.neg) (:c SignType) (:c SignType.instNeg) ((:c OfNat.ofNat) (:c SignType) (:lit 1) ((:c One.toO... | [{"name":"a","sexp":"(:c SignType)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c SignType)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c SignType))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c O... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28602","is_instance":false,"is_let":false,"name":"a","sexp":"(:c SignType)"}] | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":4986,"sourceStart":4981,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":1,"semanticRole":"local","source":"a","sourceEnd":4988,"sourceStart":4987,"tag":"identifie... | [] | [{"source":"a","source_end":4988,"source_start":4987,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28602","is_instance":false,"is_let":false,"user_name":"a"}] | 37 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2efad7e63d5b4476c9ebe3f888756d38992e8ff8e04969dbb6de45277a81b398 | d073fa2a2ecf4cd8667ce2b91b352b5db67c796010fdc28ef4a43b81f02722f6 | 083dd6d9748a6d1a8724ea8415eebb55e35fa3dabb6b58d8bb0d0d3d64b34190 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,608 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
⊢ cs.length w = 1 ↔ ∃ i, w = cs.simple i | case mp
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
⊢ cs.length w = 1 → ∃ i, w = cs.simple i
case mpr
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
⊢ (∃ i, w = cs.simple i) → cs.length w = 1 | ((:c Iff) ((:c Eq) (:c Nat) ((:c CoxeterSystem.length) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) (:fv _uniq.35940)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) (:... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c CoxeterSystem.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit 3) (:arg :explicit 4 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"constructor","sourceEnd":6264,"sourceStart":6253,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":6264,"sourceStart":6253,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e0d80bc96c6bce7fa7b28a2aea8d4ada1bafc9394ae87c2f4babdccd817cf32 | 8b07b75e6deabac16f2ef362c30fcfedb5fb1ced24f5a52329d831ad1ccbe7af | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 831b1ccdb414579c43c5c6c38636862387de12ef8d7bdb29748a2740fdfa8ab3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,609 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | case mp
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
⊢ cs.length w = 1 → ∃ i, w = cs.simple i | case mp
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
h : cs.length w = 1
⊢ ∃ i, w = cs.simple i | (:forall _ ((:c Eq) (:c Nat) ((:c CoxeterSystem.length) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) (:fv _uniq.35940)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) (... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c CoxeterSystem.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV4)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":6275,"sourceStart":6270,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":6277,"sourceStart":6276,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":6277,"sourceStart":6276,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"h","source_end":6277,"source_start":6276,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 9 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6bf4e46fe34c7821ba4ad2d7139f4d0925e8abba244de08296ddf7f1572b7865 | 575d53392cc7b31c8528f6a65eb87d90add7b036c1e1666a42ff0d58e8bae6ce | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | 456f4300c3be61af8b983efa60ca08d15efd0b41a8b2ad043884e8f7313a678b |
cat-searcher/leandojo-benchmark-4-random | test | 3,610 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases cs.exists_reduced_word w with ⟨ω, hω, rfl⟩ | case mp
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
h : cs.length w = 1
⊢ ∃ i, w = cs.simple i | case mp.intro.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
ω : List B
h : cs.length (cs.wordProd ω) = 1
hω : ω.length = cs.length (cs.wordProd ω)
⊢ ∃ i, cs.wordProd ω = cs.simple i | ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) (:fv _uniq.35940) ((:c CoxeterSystem.simple) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) 0)))) | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c CoxeterSystem.simple) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":6288,"sourceStart":6282,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"cs.exists_reduced_word","sourceEnd":6311,"sourceStart":6289,"tag":"identifier"},{"children":[{"contextIndex":6,"semanticRole":"local"... | [] | [{"source":"cs.exists_reduced_word w","source_end":6313,"source_start":6289,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨ω, hω, rfl⟩","source_end":6337,"source_start":6319,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 10 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 170306ff0703676f1ecde5c36a0f009df7d33172165599f6e97bbb07d4f62410 | 456f4300c3be61af8b983efa60ca08d15efd0b41a8b2ad043884e8f7313a678b | 69ce40b8c97f80a203ab36fa62fe61831f3b00ff429013d68fd33cd4d611b726 | fe384d4293d4cba2a7888cb6f52e42fdf95db8c83977f808a1463d1ddc8b0581 |
cat-searcher/leandojo-benchmark-4-random | test | 3,611 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases List.length_eq_one.mp (hω.trans h) with ⟨i, rfl⟩ | case mp.intro.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
ω : List B
h : cs.length (cs.wordProd ω) = 1
hω : ω.length = cs.length (cs.wordProd ω)
⊢ ∃ i, cs.wordProd ω = cs.simple i | case mp.intro.intro.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
i : B
h : cs.length (cs.wordProd [i]) = 1
hω : [i].length = cs.length (cs.wordProd [i])
⊢ ∃ i_1, cs.wordProd [i] = cs.simple i_1 | ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) ((:c CoxeterSystem.wordProd) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) (:fv _uniq.35995)) ((:c CoxeterSystem.simple) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.358... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c CoxeterSystem.wordProd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Group) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":6348,"sourceStart":6342,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"List.length_eq_one.mp","sourceEnd":6370,"sourceStart":6349,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":63... | [] | [{"source":"List.length_eq_one.mp (hω.trans h)","source_end":6384,"source_start":6349,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨i, rfl⟩","source_end":6402,"source_start":6390,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 11 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8fb6b74e8ff3a471475eb2ec62fdf789b29f809495ead66658affd81f88600ea | fe384d4293d4cba2a7888cb6f52e42fdf95db8c83977f808a1463d1ddc8b0581 | 7ca2110a7f31f36d30e402a023f82b6fb954ebff42507ae1be0c90f2bf2fc93c | eac06b99ad7ec152e373616a5bd2e03a756aba1129309facd152aa988886bed3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,612 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨i, cs.wordProd_singleton i⟩ | case mp.intro.intro.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
i : B
h : cs.length (cs.wordProd [i]) = 1
hω : [i].length = cs.length (cs.wordProd [i])
⊢ ∃ i_1, cs.wordProd [i] = cs.simple i_1 | ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) ((:c CoxeterSystem.wordProd) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) ((:c List.cons) (:fv _uniq.35845) (:fv _uniq.36099) ((:c List.nil) (:fv _uniq.35845)))) ((:c CoxeterSystem.simple)... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c CoxeterSystem.wordProd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Group) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":6412,"sourceStart":6407,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6416,"sourceStart":6413,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"i","sourceEnd":6417,"sourceStart":6416,"tag":"identifier"},{"source":",","sourceEnd":6418,"sourceS... | [] | [{"source":"⟨i, cs.wordProd_singleton i⟩","source_end":6445,"source_start":6413,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 12 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79da71ad9efc3edd9f26adb92e3494eae0d36690597fa1c0de4db2c4716a124e | eac06b99ad7ec152e373616a5bd2e03a756aba1129309facd152aa988886bed3 | 5546dbc76b4256d096c3e63b5eee01375dcbd6a2c6af188425bb5ea699303b82 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,613 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨i, rfl⟩ | case mpr
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
w : W
⊢ (∃ i, w = cs.simple i) → cs.length w = 1 | case mpr.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
i : B
⊢ cs.length (cs.simple i) = 1 | (:forall _ ((:c Exists) (:fv _uniq.35845) (:lambda i (:fv _uniq.35845) ((:c Eq) (:fv _uniq.35848) (:fv _uniq.35940) ((:c CoxeterSystem.simple) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) 0)))) ((:c Eq) (:c Nat) ((:c CoxeterSystem.length) (:fv _uniq.35845) (:fv _uniq.35848) ... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c CoxeterSystem.simple) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":6457,"sourceStart":6451,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6461,"sourceStart":6458,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":6462,"sourceSt... | [{"role":"fresh_name","source":"i","source_end":6462,"source_start":6461,"syntax_kind":"ident"}] | [{"source":"⟨i, rfl⟩","source_end":6470,"source_start":6458,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 17 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 38d7da843bc2d18d2c647a38344bc1267cc338395820ad56acdcc31d06153174 | 987fcfb6c002345c0956ff364641e2bb4647c9ae1248a0625ea446d23fc8bd56 | 7ce11d37335966409799f8126acc10468e66e360747b39fe4f2c87bfb1e9c154 | a77f4c9c3b9432932280efb9782fc7fab90fef09df12409c347cd69c357f7bef |
cat-searcher/leandojo-benchmark-4-random | test | 3,614 | CoxeterSystem.length_eq_one_iff | Mathlib/GroupTheory/Coxeter/Length.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact cs.length_simple i | case mpr.intro
B : Type u_1
W : Type u_2
inst✝ : Group W
M : CoxeterMatrix B
cs : CoxeterSystem M W
i : B
⊢ cs.length (cs.simple i) = 1 | ((:c Eq) (:c Nat) ((:c CoxeterSystem.length) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) ((:c CoxeterSystem.simple) (:fv _uniq.35845) (:fv _uniq.35848) (:fv _uniq.35851) (:fv _uniq.35854) (:fv _uniq.35866) (:fv _uniq.36162))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfN... | [{"name":"B","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.35848))"},{"name":"M","sexp":"((:c CoxeterMatrix) (:fv _uniq.35845))"},{"name":"cs","sexp":"((:c CoxeterSystem) (:fv _uniq.35845) (:fv _uniq.35854) (:fv _uniq.35848) (:fv _uniq.35851))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c CoxeterSystem.length) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV4)) (:arg :explicit 5 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"name":"W","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":6480,"sourceStart":6475,"tag":"atom"},{"children":[{"source":"cs.length_simple","sourceEnd":6497,"sourceStart":6481,"tag":"identifier"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"i","sourceEnd":6499,"sourceStart":6498,"tag":"identifier"}],"kind":"null","so... | [] | [{"source":"cs.length_simple i","source_end":6499,"source_start":6481,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.35845","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.35848","is_instance":false,"is_let":false,"user_name":"W"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 27 | 18 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e013a31df31fbc0a4b1d98291947a57704aac48c3ddc2c04821d407a99dba3b8 | a77f4c9c3b9432932280efb9782fc7fab90fef09df12409c347cd69c357f7bef | a1a27081308d150a60837014dda29e2c7bd3d0d91724f363766ac8748f767aa5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,615 | HahnSeries.single_coeff | Mathlib/RingTheory/HahnSeries/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h <;> simp [h] | Γ : Type u_1
R : Type u_2
inst✝¹ : PartialOrder Γ
inst✝ : Zero R
a b : Γ
r : R
⊢ ((single a) r).coeff b = if b = a then r else 0 | ((:c Eq) (:fv _uniq.9963) ((:c HahnSeries.coeff) (:fv _uniq.9960) (:fv _uniq.9963) (:fv _uniq.9966) (:fv _uniq.9969) ((:c DFunLike.coe) ((:c ZeroHom) (:fv _uniq.9963) ((:c HahnSeries) (:fv _uniq.9960) (:fv _uniq.9963) (:fv _uniq.9966) (:fv _uniq.9969)) (:fv _uniq.9969) ((:c HahnSeries.instZero) (:fv _uniq.9960) (:fv _u... | [{"name":"Γ","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c PartialOrder) (:fv _uniq.9960))"},{"name":"inst✝","sexp":"((:c Zero) (:fv _uniq.9963))"},{"name":"a","sexp":"(:fv _uniq.9960)"},{"name":"b","sexp":"(:fv _uniq.9960)"},{"name":"r","sexp":"(:fv _uniq.9963)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HahnSeries.coeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9960","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9963","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"split_ifs","sourceEnd":7453,"sourceStart":7444,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":7458,"sourceStart":7454,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceE... | [] | [{"source":"h","source_end":7472,"source_start":7471,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9960","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9963","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 50 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44c69f0fc98ffedb96dbdac195e519472485bcfde88b969b29076e05bab69842 | a94118180cb3ad075765456f4de068fcea692f4a293e5f7d42e3974fbd3e0f9b | 967de915a4bca2de7578bb7c1d71b707362e00ce57612b82ae6b17853f81e240 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,616 | Filter.EventuallyEq.mfderivWithin_eq | Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : <a>MDifferentiableWithinAt</a> I I' f s x | 𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝⁸ : Norme... | case pos
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.638975) (:fv _uniq.638975) ((:c DivisionSemiring.toSemiring) (:fv _uniq.638975) ((:c Semifield.toDivisionSemiring) (:fv _uniq.638975) ((:c Field.toSemifield) (:fv _uniq.638975) ((:c NormedField.toField) (:fv _uniq.638975) ((:c NontriviallyNormedField.toNormedField) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁵","sexp":"((:c NontriviallyNormedField) (:fv _uniq.638975))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.638981))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:fv _uniq.638975) (:fv _uniq.638981) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"name":"inst✝¹⁵","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"by_cases","sourceEnd":31357,"sourceStart":31349,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":31359,"sourceStart":31358,"tag":"identifier"},{"source":":","sourceEnd":31361,"sourceStart":31360,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd":31361,"sour... | [] | [{"source":"MDifferentiableWithinAt I I' f s x","source_end":31396,"source_start":31362,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"user_name":"inst✝¹⁵"},{"binder_role":":implicit","context_index":2,"in... | 195 | 4 | exact | true | 1 | 48 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc2dbe0a4ec8adfee70b69eae3a16d05cd6803eb45aac7a3b9ce81ab3ab4bcd4 | 69ae21a265b95fb07dfefd63a912d1fc18fc8e1a4c0c61f3e4786741861d0d0d | 80deca2a418294e7078d2d15dde41d1bfec570e1bb850ef5a46e1f6eb95d5096 | c5b31699379075207d732c089f10ca642ef2faa916bd283697c9a32a9c322828 |
cat-searcher/leandojo-benchmark-4-random | test | 3,617 | Filter.EventuallyEq.mfderivWithin_eq | Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (h.hasMFDerivWithinAt.congr_of_eventuallyEq hL hx).<a>HasMFDerivWithinAt.mfderivWithin</a> hs | case pos
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.638975) (:fv _uniq.638975) ((:c DivisionSemiring.toSemiring) (:fv _uniq.638975) ((:c Semifield.toDivisionSemiring) (:fv _uniq.638975) ((:c Field.toSemifield) (:fv _uniq.638975) ((:c NormedField.toField) (:fv _uniq.638975) ((:c NontriviallyNormedField.toNormedField) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁵","sexp":"((:c NontriviallyNormedField) (:fv _uniq.638975))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.638981))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:fv _uniq.638975) (:fv _uniq.638981) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"name":"inst✝¹⁵","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":31407,"sourceStart":31402,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":31409,"sourceStart":31408,"tag":"atom"},{"children":[{"source":"h.hasMFDerivWithinAt.congr_of_eventuallyEq","sourceEnd":31451,"source... | [] | [{"source":"(h.hasMFDerivWithinAt.congr_of_eventuallyEq hL hx).mfderivWithin hs","source_end":31475,"source_start":31408,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"user_name":"inst✝¹⁵"},{"binder_role":":implicit","context_index":2,"in... | 195 | 7 | exact | true | 1 | 49 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | edda893ca5f630daa3a4096454ad8c0e15c97b445b8d8003c3506e12d838d35e | 40b0b00e996879cd7448a2a6fbbf2acfb92d207fd7af9bf33e649d89567d6390 | 18a0fc56a18e1ec0963a690ba7fb1887a42cee7195c9a32cd49b7a65f9bb6058 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,618 | Filter.EventuallyEq.mfderivWithin_eq | Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>mfderivWithin</a> | case neg
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝... | case neg
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.638975) (:fv _uniq.638975) ((:c DivisionSemiring.toSemiring) (:fv _uniq.638975) ((:c Semifield.toDivisionSemiring) (:fv _uniq.638975) ((:c Field.toSemifield) (:fv _uniq.638975) ((:c NormedField.toField) (:fv _uniq.638975) ((:c NontriviallyNormedField.toNormedField) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁵","sexp":"((:c NontriviallyNormedField) (:fv _uniq.638975))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.638981))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:fv _uniq.638975) (:fv _uniq.638981) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"name":"inst✝¹⁵","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"unfold","sourceEnd":31487,"sourceStart":31481,"tag":"atom"},{"children":[{"name":"mfderivWithin","semanticRole":"global","source":"mfderivWithin","sourceEnd":31501,"sourceStart":31488,"tag":"identifier"}],"kind":"null","source":"mfderivWithin","sourceEnd":31501,"sourceStart":31488,"tag":"node"},... | [] | [{"source":"mfderivWithin","source_end":31501,"source_start":31488,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"user_name":"inst✝¹⁵"},{"binder_role":":implicit","context_index":2,"in... | 195 | 14 | exact | true | 1 | 49 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6429a0ac08a35e8638a05e5bec6c5b107046f45337e9c13026a4c53559bec10b | 3128ec8ebd2ab89045c7eb2fff35b92015c2491c4ea6d3b184553447f4a10ced | a9ff2801068d1b8b01378ecc695ed77a51ed0ce7b8899c9564f3a6f313e8353a | 417fee7db35e082003267815e9b6e78739aed7a7ecf05c91a2e56e4cb6aef1c4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,619 | Filter.EventuallyEq.mfderivWithin_eq | Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>if_neg</a> h, <a>if_neg</a>] | case neg
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
inst✝... | case neg.hnc
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
i... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.638975) (:fv _uniq.638975) ((:c DivisionSemiring.toSemiring) (:fv _uniq.638975) ((:c Semifield.toDivisionSemiring) (:fv _uniq.638975) ((:c Field.toSemifield) (:fv _uniq.638975) ((:c NormedField.toField) (:fv _uniq.638975) ((:c NontriviallyNormedField.toNormedField) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁵","sexp":"((:c NontriviallyNormedField) (:fv _uniq.638975))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.638981))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:fv _uniq.638975) (:fv _uniq.638981) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"name":"inst✝¹⁵","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rw","sourceEnd":31508,"sourceStart":31506,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31510,"sourceStart":31509,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"if_... | [] | [{"source":"if_neg h","source_end":31518,"source_start":31510,"syntax_kind":"Lean.Parser.Term.app"},{"source":"if_neg","source_end":31526,"source_start":31520,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"user_name":"inst✝¹⁵"},{"binder_role":":implicit","context_index":2,"in... | 195 | 15 | exact | true | 1 | 49 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7f006841f4db7c96bb3c11d64a8889fe350f10852521aec10a3c2e897c78337 | 417fee7db35e082003267815e9b6e78739aed7a7ecf05c91a2e56e4cb6aef1c4 | b21948b0078c12efee969b75f6f0faaa7c1160e6811a2a31e0bded97315a0a6e | e8eb2b89128e98c2a33173085349437fcae7db434e01aaa5b3d89cccd47d0d05 |
cat-searcher/leandojo-benchmark-4-random | test | 3,620 | Filter.EventuallyEq.mfderivWithin_eq | Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← hL.mdifferentiableWithinAt_iff I I' hx] | case neg.hnc
𝕜 : Type u_1
inst✝¹⁵ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹⁴ : NormedAddCommGroup E
inst✝¹³ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹² : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹¹ : TopologicalSpace M
inst✝¹⁰ : ChartedSpace H M
E' : Type u_5
inst✝⁹ : NormedAddCommGroup E'
i... | ((:c Not) ((:c MDifferentiableWithinAt) (:fv _uniq.638975) (:fv _uniq.638978) (:fv _uniq.638981) (:fv _uniq.638984) (:fv _uniq.639097) (:fv _uniq.639100) (:fv _uniq.639103) (:fv _uniq.639135) (:fv _uniq.639138) (:fv _uniq.639141) (:fv _uniq.639153) (:fv _uniq.639156) (:fv _uniq.639159) (:fv _uniq.639267) (:fv _uniq.639... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁵","sexp":"((:c NontriviallyNormedField) (:fv _uniq.638975))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.638981))"},{"name":"inst✝¹³","sexp":"((:c NormedSpace) (:fv _uniq.638975) (:fv _uniq.638981) ((:c ... | (:app (:c Not) (:arg :explicit 0 (:app (:c MDifferentiableWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"name":"inst✝¹⁵","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rwa","sourceEnd":31535,"sourceStart":31532,"tag":"atom"},{"children":[{"source":"[","sourceEnd":31537,"sourceStart":31536,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31540,"sourceStart":31537,"tag":"atom"}],"kind":"token.«← »","source"... | [] | [{"source":"hL.mdifferentiableWithinAt_iff I I' hx","source_end":31579,"source_start":31541,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.638975","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.638978","is_instance":true,"is_let":false,"user_name":"inst✝¹⁵"},{"binder_role":":implicit","context_index":2,"in... | 195 | 19 | exact | true | 1 | 49 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 784f259632ef3b12cdbc6251ff0bfe05876e289f4814db786a2747652921356f | e8eb2b89128e98c2a33173085349437fcae7db434e01aaa5b3d89cccd47d0d05 | 857136435a3e8ca9b80d6cbbb5dd753eb2533a3b00109d33a1c75eacd2271d0a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,621 | MeasureTheory.Measure.restrict_toMeasurable_of_sFinite | Mathlib/MeasureTheory/Measure/Typeclasses.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.restrict_apply</a> ht, <a>Set.inter_comm</a> t, <a>MeasureTheory.Measure.measure_toMeasurable_inter_of_sFinite</a> ht, <a>MeasureTheory.Measure.restrict_apply</a> ht, <a>Set.inter_comm</a> t] | α : Type u_1
β : Type u_2
δ : Type u_3
ι : Type u_4
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
μ ν ν₁ ν₂ : Measure α
s✝ t✝ : Set α
inst✝ : SFinite μ
s t : Set α
ht : MeasurableSet t
⊢ (μ.restrict (toMeasurable μ s)) t = (μ.restrict s) t | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.186814) (:fv _uniq.186826)) ((:c Set) (:fv _uniq.186814)) (:lambda _ ((:c Set) (:fv _uniq.186814)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.186814) (:fv _uniq.186826)) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"δ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.186814))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.186817))"},{"name":"μ","sexp":"((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.186814","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.186817","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":50743,"sourceStart":50741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":50745,"sourceStart":50744,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"restrict_apply ht","source_end":50762,"source_start":50745,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inter_comm t","source_end":50776,"source_start":50764,"syntax_kind":"Lean.Parser.Term.app"},{"source":"measure_toMeasurable_inter_of_sFinite ht","source_end":50818,"source_start":50778,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.186814","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.186817","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 261 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a4a645afc0b840f70cfcde7523732431f72a7ad9e4e384f165fc69b8e654488 | 1069e03588fe6f18ce3e5fbe23770f120d78293623fba090fb8a3441a02bdb6f | 5dab9730e74908196108b9390a12fe10aa443a24d4e1e014103af9ca87c8115b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,622 | TopologicalSpace.IsTopologicalBasis.eq_of_forall_subset_iff | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hB.open_eq_sUnion' hs, hB.open_eq_sUnion' ht] | α : Type u
β : Type u_1
t✝ : TopologicalSpace α
B : Set (Set α)
s t : Set α
hB : IsTopologicalBasis B
hs : IsOpen s
ht : IsOpen t
h : ∀ U ∈ B, U ⊆ s ↔ U ⊆ t
⊢ s = t | α : Type u
β : Type u_1
t✝ : TopologicalSpace α
B : Set (Set α)
s t : Set α
hB : IsTopologicalBasis B
hs : IsOpen s
ht : IsOpen t
h : ∀ U ∈ B, U ⊆ s ↔ U ⊆ t
⊢ ⋃₀ {s_1 | s_1 ∈ B ∧ s_1 ⊆ s} = ⋃₀ {s | s ∈ B ∧ s ⊆ t} | ((:c Eq) ((:c Set) (:fv _uniq.22586)) (:fv _uniq.22599) (:fv _uniq.22758)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"t✝","sexp":"((:c TopologicalSpace) (:fv _uniq.22586))"},{"name":"B","sexp":"((:c Set) ((:c Set) (:fv _uniq.22586)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22586))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.22586))"},{"name":"hB"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22586","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22589","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":12024,"sourceStart":12022,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12026,"sourceStart":12025,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"h... | [] | [{"source":"hB.open_eq_sUnion' hs","source_end":12047,"source_start":12026,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hB.open_eq_sUnion' ht","source_end":12070,"source_start":12049,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22586","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22589","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 39 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b6906d13812bef3be6f333c9668acf44ec4c64a88e0b19bdc52ba669c5eac7e | 1141a7f7d295f78373cee5e48dd7cb211a6fb60c5999e01d143819347c20344a | 699a9e25b362e13ba5a039cfc0a349ad9164422f1de23fcfb98b20ea9033480c | 37486a8f8a1f3f1412be37e66cc91b0c1be784c2d526a3e7058e22682adf143d |
cat-searcher/leandojo-benchmark-4-random | test | 3,623 | TopologicalSpace.IsTopologicalBasis.eq_of_forall_subset_iff | Mathlib/Topology/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>congr_arg</a> _ (<a>Set.ext</a> fun U ↦ <a>and_congr_right</a> <| h _) | α : Type u
β : Type u_1
t✝ : TopologicalSpace α
B : Set (Set α)
s t : Set α
hB : IsTopologicalBasis B
hs : IsOpen s
ht : IsOpen t
h : ∀ U ∈ B, U ⊆ s ↔ U ⊆ t
⊢ ⋃₀ {s_1 | s_1 ∈ B ∧ s_1 ⊆ s} = ⋃₀ {s | s ∈ B ∧ s ⊆ t} | ((:c Eq) ((:c Set) (:fv _uniq.22586)) ((:c Set.sUnion) (:fv _uniq.22586) ((:c setOf) ((:c Set) (:fv _uniq.22586)) (:lambda s ((:c Set) (:fv _uniq.22586)) ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.22586)) ((:c Set) ((:c Set) (:fv _uniq.22586))) ((:c Set.instMembership) ((:c Set) (:fv _uniq.22586))) 0 (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u_1 1))"},{"name":"t✝","sexp":"((:c TopologicalSpace) (:fv _uniq.22586))"},{"name":"B","sexp":"((:c Set) ((:c Set) (:fv _uniq.22586)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.22586))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.22586))"},{"name":"hB"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.sUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c setOf) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22586","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22589","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":12079,"sourceStart":12074,"tag":"atom"},{"children":[{"name":"congr_arg","semanticRole":"global","source":"congr_arg","sourceEnd":12089,"sourceStart":12080,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":12091,"sourceStart":12090,"tag":"atom"}],"kind":"... | [] | [{"source":"congr_arg _ (Set.ext fun U ↦ and_congr_right <| h _)","source_end":12134,"source_start":12080,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22586","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22589","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 39 | 8 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 095b251b909096c1a5aad52d775de211c75bbbb5812fa55c227fd8b8716a3c20 | 37486a8f8a1f3f1412be37e66cc91b0c1be784c2d526a3e7058e22682adf143d | 0fb07e30ee108c06b4d1255f85be15013a7f07946de946b96ea11d7a4390c31b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,624 | List.sum_take_map_length_splitWrtComposition | Mathlib/Combinatorics/Enumerative/Composition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | n : ℕ
α : Type u_1
l : List α
c : Composition l.length
i : ℕ
⊢ (take i (map length (l.splitWrtComposition c))).sum = c.sizeUpTo i | case e_a.e_a
n : ℕ
α : Type u_1
l : List α
c : Composition l.length
i : ℕ
⊢ map length (l.splitWrtComposition c) = c.blocks | ((:c Eq) (:c Nat) ((:c List.sum) (:c Nat) (:c instAddNat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero)) ((:c List.take) (:c Nat) (:fv _uniq.59879) ((:c List.map) ((:c List) (:fv _uniq.59795)) (:c Nat) ((:c List.length) (:fv _uniq.59795)) ((:c List.splitWrtCompositio... | [{"name":"n","sexp":"(:c Nat)"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.59795))"},{"name":"c","sexp":"((:c Composition) ((:c List.length) (:fv _uniq.59795) (:fv _uniq.59877)))"},{"name":"i","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Nat))))) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 3 (:app (:c List.take) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59792","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59795","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context... | {"children":[{"source":"congr","sourceEnd":29210,"sourceStart":29205,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":29210,"sourceStart":29205,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59792","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59795","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 162 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 428216a6fb0690b227500784bce92fa459337cd9f24ac217d3bbf42d62083d40 | 9d845b4932ae7e72ce12dadc818f3f35f1f90d118d9794cb379e5b63b6eee732 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | 3167055e65a0e5adc57d280254d9cd915ffae579ec45d14ece6b270ae4593eec |
cat-searcher/leandojo-benchmark-4-random | test | 3,625 | List.sum_take_map_length_splitWrtComposition | Mathlib/Combinatorics/Enumerative/Composition.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>List.map_length_splitWrtComposition</a> l c | case e_a.e_a
n : ℕ
α : Type u_1
l : List α
c : Composition l.length
i : ℕ
⊢ map length (l.splitWrtComposition c) = c.blocks | ((:c Eq) ((:c List) (:c Nat)) ((:c List.map) ((:c List) (:fv _uniq.59795)) (:c Nat) ((:c List.length) (:fv _uniq.59795)) ((:c List.splitWrtComposition) ((:c List.length) (:fv _uniq.59795) (:fv _uniq.59877)) (:fv _uniq.59795) (:fv _uniq.59877) (:fv _uniq.59878))) ((:c Composition.blocks) ((:c List.length) (:fv _uniq.597... | [{"name":"n","sexp":"(:c Nat)"},{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.59795))"},{"name":"c","sexp":"((:c Composition) ((:c List.length) (:fv _uniq.59795) (:fv _uniq.59877)))"},{"name":"i","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c List.map) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:c Nat)) (:arg :explicit 2 (:app (:c List.length) (:arg :implicit-type 0 (:fv FV1)))) (:arg :explicit 3 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59792","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59795","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context... | {"children":[{"source":"exact","sourceEnd":29218,"sourceStart":29213,"tag":"atom"},{"children":[{"name":"List.map_length_splitWrtComposition","semanticRole":"global","source":"map_length_splitWrtComposition","sourceEnd":29249,"sourceStart":29219,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local",... | [] | [{"source":"map_length_splitWrtComposition l c","source_end":29253,"source_start":29219,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.59792","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.59795","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 162 | 5 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 849b2b58dda8e5e8ac7f2552397b8f6e9167668782953a5a98efbc95e46c9482 | 3167055e65a0e5adc57d280254d9cd915ffae579ec45d14ece6b270ae4593eec | 11ee40fc24dcf8653a6c7fa54cabf440ff937516a21f97a560473f653c4383d2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,626 | IsSl2Triple.f_ne_zero | Mathlib/Algebra/Lie/Sl2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := t.h_ne_zero | R : Type u_1
L : Type u_2
M : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : LieRing L
inst✝⁴ : LieAlgebra R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
h e f : L
t : IsSl2Triple h e f
⊢ f ≠ 0 | R : Type u_1
L : Type u_2
M : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : LieRing L
inst✝⁴ : LieAlgebra R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
h e f : L
t : IsSl2Triple h e f
this : h ≠ 0
⊢ f ≠ 0 | ((:c Ne) (:fv _uniq.19749) (:fv _uniq.20469) ((:c OfNat.ofNat) (:fv _uniq.19749) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.19749) ((:c NegZeroClass.toZero) (:fv _uniq.19749) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.19749) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.19749) ((:c SubtractionCommMonoid.toSu... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.19746))"},{"name":"inst✝⁵","sexp":"((:c LieRing) (:fv _uniq.19749))"},{"name":"inst✝⁴","sexp":"((:c LieAlgebra) (:fv _uniq.19746) (:fv _uniq.19749) ... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":2506,"sourceStart":2502,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2507,"sourceStart":2507,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2507,"sourceStart":2507,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"t.h_ne_zero","source_end":2521,"source_start":2510,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 12 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f4c91ed8919392fdb831be6013b22f185ca63bcc441438842871c5bf2f235cc | 5fe64b8ea28b797e8eeab5e901eeb7df2f39e5034c14ed1323b3ee6e03855e50 | af813f90ef9b79748fec06f3394a87662e1d00988aad62d3e052a18b6462b826 | 128a56c5c52553e1d875c1f7b8e8dce684c51ada055e412de299f526003067b4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,627 | IsSl2Triple.f_ne_zero | Mathlib/Algebra/Lie/Sl2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | contrapose! this | R : Type u_1
L : Type u_2
M : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : LieRing L
inst✝⁴ : LieAlgebra R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
h e f : L
t : IsSl2Triple h e f
this : h ≠ 0
⊢ f ≠ 0 | R : Type u_1
L : Type u_2
M : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : LieRing L
inst✝⁴ : LieAlgebra R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
h e f : L
t : IsSl2Triple h e f
this : f = 0
⊢ h = 0 | ((:c Ne) (:fv _uniq.19749) (:fv _uniq.20469) ((:c OfNat.ofNat) (:fv _uniq.19749) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.19749) ((:c NegZeroClass.toZero) (:fv _uniq.19749) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.19749) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.19749) ((:c SubtractionCommMonoid.toSu... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.19746))"},{"name":"inst✝⁵","sexp":"((:c LieRing) (:fv _uniq.19749))"},{"name":"inst✝⁴","sexp":"((:c LieAlgebra) (:fv _uniq.19746) (:fv _uniq.19749) ... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"contrapose!","sourceEnd":2535,"sourceStart":2524,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"this","sourceEnd":2540,"sourceStart":2536,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"this","sourceEnd":2540,"so... | [] | [{"source":"this","source_end":2540,"source_start":2536,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 12 | 5 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2cca66f23a4c21af6ef62a9fc749c6e7eb275a009a54b6521b160287e6c51f3 | 128a56c5c52553e1d875c1f7b8e8dce684c51ada055e412de299f526003067b4 | 406d8bdfa58b2b50306e9249c869017d1baefaee97af8b55d5354b504a108442 | 51eb7819064b65599007df3f808692599bd32d38d320d74801ff495ea9ae71a2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,628 | IsSl2Triple.f_ne_zero | Mathlib/Algebra/Lie/Sl2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [this] using t.lie_e_f.symm | R : Type u_1
L : Type u_2
M : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : LieRing L
inst✝⁴ : LieAlgebra R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
h e f : L
t : IsSl2Triple h e f
this : f = 0
⊢ h = 0 | ((:c Eq) (:fv _uniq.19749) (:fv _uniq.20465) ((:c OfNat.ofNat) (:fv _uniq.19749) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.19749) ((:c NegZeroClass.toZero) (:fv _uniq.19749) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.19749) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:fv _uniq.19749) ((:c SubtractionCommMonoid.toSu... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁶","sexp":"((:c CommRing) (:fv _uniq.19746))"},{"name":"inst✝⁵","sexp":"((:c LieRing) (:fv _uniq.19749))"},{"name":"inst✝⁴","sexp":"((:c LieAlgebra) (:fv _uniq.19746) (:fv _uniq.19749) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV10)) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:lit 0)))))))) | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simpa","sourceEnd":2548,"sourceStart":2543,"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":"this","source_end":2554,"source_start":2550,"syntax_kind":"ident"},{"source":"t.lie_e_f.symm","source_end":2576,"source_start":2562,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.19746","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19749","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 12 | 6 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 844386d3c665348290ac7e7a8893559baea80314f15841ce3e871b6dca0a3252 | 51eb7819064b65599007df3f808692599bd32d38d320d74801ff495ea9ae71a2 | 1f5f1a8047c8d60a21ad776b575eae218f392b40b2f14cd0adafca6153ab6558 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,629 | Finsupp.mem_neLocus | Mathlib/Data/Finsupp/NeLocus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Finsupp.neLocus</a>, <a>Finset.mem_filter</a>, <a>Finset.mem_union</a>, <a>Finsupp.mem_support_iff</a>, <a>and_iff_right_iff_imp</a>] using <a>Ne.ne_or_ne</a> _ | α : Type u_1
M : Type u_2
N : Type u_3
P : Type u_4
inst✝² : DecidableEq α
inst✝¹ : DecidableEq N
inst✝ : Zero N
f✝ g✝ f g : α →₀ N
a : α
⊢ a ∈ f.neLocus g ↔ f a ≠ g a | ((:c Iff) ((:c Membership.mem) (:fv _uniq.358) ((:c Finset) (:fv _uniq.358)) ((:c Finset.instMembership) (:fv _uniq.358)) (:fv _uniq.584) ((:c Finsupp.neLocus) (:fv _uniq.358) (:fv _uniq.364) (:fv _uniq.374) (:fv _uniq.383) (:fv _uniq.388) (:fv _uniq.582) (:fv _uniq.583))) ((:c Ne) (:fv _uniq.364) ((:c DFunLike.coe) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"N","sexp":"(:sort (+ u_3 1))"},{"name":"P","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.358))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.364))"},{"name":"inst✝","sexp":"((:c Zero) ... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.358","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.361","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":1303,"sourceStart":1298,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"neLocus","source_end":1317,"source_start":1310,"syntax_kind":"ident"},{"source":"Finset.mem_filter","source_end":1336,"source_start":1319,"syntax_kind":"ident"},{"source":"Finset.mem_union","source_end":1354,"source_start":1338,"syntax_kind":"ident"},{"source":"mem_support_iff","source_end":1371,"source_sta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.358","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.361","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.3... | 9 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d0eae313e8e143565ed63f8d11ca64094b302032b0a3591622b94a9b18ff853 | 32010882952276eff831b83d7016889564867cfb5ce315697d7c2f1dd899dddc | 1fa99fba9a7adb235f1fce13231d7a9e2dbbc682a211c5fccd582b07b1097415 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,630 | Order.isPredLimit_toDual_iff | Mathlib/Order/SuccPred/Limit.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Order.IsSuccLimit</a>, <a>Order.IsPredLimit</a>] | α : Type u_1
inst✝ : LT α
a : α
⊢ IsPredLimit (toDual a) ↔ IsSuccLimit a | ((:c Iff) ((:c Order.IsPredLimit) ((:c OrderDual) (:fv _uniq.15809)) ((:c OrderDual.instLT) (:fv _uniq.15809) (:fv _uniq.15812)) ((:c DFunLike.coe) ((:c Equiv) (:fv _uniq.15809) ((:c OrderDual) (:fv _uniq.15809))) (:fv _uniq.15809) (:lambda _ (:fv _uniq.15809) ((:c OrderDual) (:fv _uniq.15809))) ((:c Equiv.instFunLike)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LT) (:fv _uniq.15809))"},{"name":"a","sexp":"(:fv _uniq.15809)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Order.IsPredLimit) (:arg :implicit-type 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c OrderDual) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15809","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.15812","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LT) (:arg :explicit 0 (:... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10652,"sourceStart":10648,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"IsSuccLimit","source_end":10665,"source_start":10654,"syntax_kind":"ident"},{"source":"IsPredLimit","source_end":10678,"source_start":10667,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15809","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.15812","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 101 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fde2ba1a8250036bcb31e1f544a907e809e38697a45a715835c2653f354b1a2b | ff5801d1871470a46837777f44f6653a0c3ae5495d75537c929c2f70045a88f0 | 21cd2a67d22fe30399edcad7d23dc76c3becc7e8a11d638f70aa120d58b6f82c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,631 | Multiset.powerset_cons | Mathlib/Data/Multiset/Powerset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Multiset.quot_mk_to_coe</a>, <a>Multiset.cons_coe</a>, <a>Multiset.powerset_coe'</a>, <a>List.sublists'_cons</a>, <a>List.map_append</a>, <a>List.map_map</a>, <a>Multiset.map_coe</a>, <a>Multiset.coe_add</a>, <a>Multiset.coe_eq_coe</a>] | α : Type u_1
a : α
s : Multiset α
l : List α
⊢ (a ::ₘ ⟦l⟧).powerset = powerset ⟦l⟧ + map (cons a) (powerset ⟦l⟧) | α : Type u_1
a : α
s : Multiset α
l : List α
⊢ List.map ofList l.sublists' ++ List.map (ofList ∘ List.cons a) l.sublists' ~
List.map ofList l.sublists' ++ List.map ((fun x => a ::ₘ x) ∘ ofList) l.sublists' | ((:c Eq) ((:c Multiset) ((:c Multiset) (:fv _uniq.6882))) ((:c Multiset.powerset) (:fv _uniq.6882) ((:c Multiset.cons) (:fv _uniq.6882) (:fv _uniq.6959) ((:c Quotient.mk) ((:c List) (:fv _uniq.6882)) ((:c List.isSetoid) (:fv _uniq.6882)) (:fv _uniq.6990)))) ((:c HAdd.hAdd) ((:c Multiset) ((:c Multiset) (:fv _uniq.6882)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"a","sexp":"(:fv _uniq.6882)"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.6882))"},{"name":"l","sexp":"((:c List) (:fv _uniq.6882))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c Multiset.powerset) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6882","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6959","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":explicit","context_... | {"children":[{"source":"simp","sourceEnd":4095,"sourceStart":4091,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4100,"sourceStart":4096,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4100,"s... | [] | [{"source":"quot_mk_to_coe","source_end":4116,"source_start":4102,"syntax_kind":"ident"},{"source":"cons_coe","source_end":4126,"source_start":4118,"syntax_kind":"ident"},{"source":"powerset_coe'","source_end":4141,"source_start":4128,"syntax_kind":"ident"},{"source":"sublists'_cons","source_end":4157,"source_start":41... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6882","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6959","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 32 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69f1b1c04e4e4b07b9e6b34e0031eec295f14d107c3f14dfa40c850c83dae8ec | 3fdfbb886d2bbb5b04dbc431b38011ba79c24a09fd291a76716447f7f3df942a | 999dcaaae1f14f255555b25f5cb7c9bdc5954c8e824f001e9c3dca8f64f8f712 | c94cb375f15b6e617f44da70a34e7920f9fc8285e4361b4dfcf0ba742305b017 |
cat-searcher/leandojo-benchmark-4-random | test | 3,632 | Multiset.powerset_cons | Mathlib/Data/Multiset/Powerset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
a : α
s : Multiset α
l : List α
⊢ List.map ofList l.sublists' ++ List.map (ofList ∘ List.cons a) l.sublists' ~
List.map ofList l.sublists' ++ List.map ((fun x => a ::ₘ x) ∘ ofList) l.sublists' | ((:c List.Perm) ((:c Multiset) (:fv _uniq.6882)) ((:c HAppend.hAppend) ((:c List) ((:c Multiset) (:fv _uniq.6882))) ((:c List) ((:c Multiset) (:fv _uniq.6882))) ((:c List) ((:c Multiset) (:fv _uniq.6882))) ((:c instHAppendOfAppend) ((:c List) ((:c Multiset) (:fv _uniq.6882))) ((:c List.instAppend) ((:c Multiset) (:fv _... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"a","sexp":"(:fv _uniq.6882)"},{"name":"s","sexp":"((:c Multiset) (:fv _uniq.6882))"},{"name":"l","sexp":"((:c List) (:fv _uniq.6882))"}] | (:app (:c List.Perm) (:arg :implicit-type 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c HAppend.hAppend) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c Mul... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6882","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6959","is_instance":false,"is_let":false,"name":"a","sexp":"(:fv FV0)"},{"binder_role":":explicit","context_... | {"children":[{"source":"rfl","sourceEnd":4225,"sourceStart":4222,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":4225,"sourceStart":4222,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6882","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6959","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 32 | 6 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c07c9bed9a13dd4cb6b49356898b930efdaf3d8dd9ca8df9982d38ea1e38b019 | c94cb375f15b6e617f44da70a34e7920f9fc8285e4361b4dfcf0ba742305b017 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,633 | Polynomial.degree_erase_lt | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>lt_of_le_of_ne</a> (<a>Polynomial.degree_erase_le</a> _ _) | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
hp : p ≠ 0
⊢ (erase p.natDegree p).degree < p.degree | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
hp : p ≠ 0
⊢ (erase p.natDegree p).degree ≠ p.degree | ((:c LT.lt) ((:c WithBot) (:c Nat)) ((:c Preorder.toLT) ((: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.137869) (:fv _uniq.137886) ((:c Polynomial.... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.137869)"},{"name":"b","sexp":"(:fv _uniq.137869)"},{"name":"c","sexp":"(:fv _uniq.137869)"},{"name":"d","sexp":"(:fv _uniq.137869)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :instance 1 (:instance-of (:app (:c LT) (: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.137869","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":35566,"sourceStart":35561,"tag":"atom"},{"children":[{"name":"lt_of_le_of_ne","semanticRole":"global","source":"lt_of_le_of_ne","sourceEnd":35581,"sourceStart":35567,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":35583,"sourceStart":35582,"tag":"atom"}... | [] | [{"source":"lt_of_le_of_ne (degree_erase_le _ _)","source_end":35603,"source_start":35567,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137869","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 285 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2b3e2df42445bf300e37751b091c174683cefef1470feb5da5fb68c0f5eacfd | f10d109afc2bef27018d4010ebbe90479e6e5d04977c49d1db79a475f50eb26e | a46ba0015f4ca6b714660f33ded84b3af9e142970de2e78c1a8b4834c4503202 | 89790ca8471cbc12fbc85ff7d3b8137975da3164f7a398b20589023770ff5304 |
cat-searcher/leandojo-benchmark-4-random | test | 3,634 | Polynomial.degree_erase_lt | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.degree_eq_natDegree</a> hp, <a>Polynomial.degree</a>, <a>Polynomial.support_erase</a>] | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
hp : p ≠ 0
⊢ (erase p.natDegree p).degree ≠ p.degree | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
hp : p ≠ 0
⊢ (p.support.erase p.natDegree).max ≠ ↑p.natDegree | ((:c Ne) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.137869) (:fv _uniq.137886) ((:c Polynomial.erase) (:fv _uniq.137869) (:fv _uniq.137886) ((:c Polynomial.natDegree) (:fv _uniq.137869) (:fv _uniq.137886) (:fv _uniq.137903)) (:fv _uniq.137903))) ((:c Polynomial.degree) (:fv _uniq.137869) (:fv _uniq.1378... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.137869)"},{"name":"b","sexp":"(:fv _uniq.137869)"},{"name":"c","sexp":"(:fv _uniq.137869)"},{"name":"d","sexp":"(:fv _uniq.137869)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.erase) (:arg :implicit-type 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137869","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":35608,"sourceStart":35606,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35610,"sourceStart":35609,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Pol... | [] | [{"source":"degree_eq_natDegree hp","source_end":35632,"source_start":35610,"syntax_kind":"Lean.Parser.Term.app"},{"source":"degree","source_end":35640,"source_start":35634,"syntax_kind":"ident"},{"source":"support_erase","source_end":35655,"source_start":35642,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137869","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 285 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80309cfc7681b09571ca3700f41e60f0315c0606d245b518f0da60139d6608fd | 89790ca8471cbc12fbc85ff7d3b8137975da3164f7a398b20589023770ff5304 | ca19a00bcf389a0fd52691d7e4cd50fa811a3b0b42153d085593ccf9d6d2c022 | ae6b9246334a7dcab70086f2095cad7c9ec7947658cf90128d5d97b69f409012 |
cat-searcher/leandojo-benchmark-4-random | test | 3,635 | Polynomial.degree_erase_lt | Mathlib/Algebra/Polynomial/Degree/Definitions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun h => <a>Finset.not_mem_erase</a> _ _ (<a>Finset.mem_of_max</a> h) | R : Type u
S : Type v
a b c d : R
n m : ℕ
inst✝ : Semiring R
p✝ p q : R[X]
ι : Type u_1
hp : p ≠ 0
⊢ (p.support.erase p.natDegree).max ≠ ↑p.natDegree | ((:c Ne) ((:c WithBot) (:c Nat)) ((:c Finset.max) (:c Nat) (:c Nat.instLinearOrder) ((:c Finset.erase) (:c Nat) (:c instDecidableEqNat) ((:c Polynomial.support) (:fv _uniq.137869) (:fv _uniq.137886) (:fv _uniq.137903)) ((:c Polynomial.natDegree) (:fv _uniq.137869) (:fv _uniq.137886) (:fv _uniq.137903)))) ((:c Nat.cast)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.137869)"},{"name":"b","sexp":"(:fv _uniq.137869)"},{"name":"c","sexp":"(:fv _uniq.137869)"},{"name":"d","sexp":"(:fv _uniq.137869)"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Finset.max) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Finset.erase) (:arg :implicit-type 0 (:c Nat)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137869","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":35664,"sourceStart":35659,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":35668,"sourceStart":35665,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":35670,"sourceStart":35669,"tag":"identifier"}],"kind":"null","source":"h",... | [] | [{"source":"fun h => not_mem_erase _ _ (mem_of_max h)","source_end":35706,"source_start":35665,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.137869","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.137871","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 285 | 10 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8dde3e96bfc24577787943a821f1d8574f951f5fc7040764d2a9bb27cd471e0a | ae6b9246334a7dcab70086f2095cad7c9ec7947658cf90128d5d97b69f409012 | 917e7d15a914740cc58fee841d7496b78e7af1d2eadd4709b0e4c44cf84c8d77 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,636 | ContinuousMultilinearMap.ext_iff | Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← toMultilinearMap_injective.eq_iff, <a>MultilinearMap.ext_iff</a>] | R : Type u
ι : Type v
n : ℕ
M : Fin n.succ → Type w
M₁ : ι → Type w₁
M₁' : ι → Type w₁'
M₂ : Type w₂
M₃ : Type w₃
M₄ : Type w₄
inst✝¹⁸ : Semiring R
inst✝¹⁷ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝¹⁶ : (i : ι) → AddCommMonoid (M₁ i)
inst✝¹⁵ : (i : ι) → AddCommMonoid (M₁' i)
inst✝¹⁴ : AddCommMonoid M₂
inst✝¹³ : Add... | R : Type u
ι : Type v
n : ℕ
M : Fin n.succ → Type w
M₁ : ι → Type w₁
M₁' : ι → Type w₁'
M₂ : Type w₂
M₃ : Type w₃
M₄ : Type w₄
inst✝¹⁸ : Semiring R
inst✝¹⁷ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝¹⁶ : (i : ι) → AddCommMonoid (M₁ i)
inst✝¹⁵ : (i : ι) → AddCommMonoid (M₁' i)
inst✝¹⁴ : AddCommMonoid M₂
inst✝¹³ : Add... | ((:c Iff) ((:c Eq) ((:c ContinuousMultilinearMap) (:fv _uniq.13816) (:fv _uniq.13818) (:fv _uniq.13829) (:fv _uniq.13835) (:fv _uniq.13842) (:fv _uniq.13858) (:fv _uniq.13869) (:fv _uniq.13944) (:fv _uniq.14001) (:fv _uniq.14067) (:fv _uniq.14078)) (:fv _uniq.14546) (:fv _uniq.14547)) (:forall x (:forall i (:fv _uniq.1... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"M","sexp":"(:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.13820))) (:sort (+ w 1)))"},{"name":"M₁","sexp":"(:forall _ (:fv _uniq.13818) (:sort (+ w₁ 1)))"},{"name":"M₁'","sexp":"(:forall _ (:fv _uniq.138... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousMultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV6)) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13816","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13818","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5153,"sourceStart":5151,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5155,"sourceStart":5154,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5158,"sourceStart":... | [] | [{"source":"toMultilinearMap_injective.eq_iff","source_end":5192,"source_start":5159,"syntax_kind":"ident"},{"source":"MultilinearMap.ext_iff","source_end":5216,"source_start":5194,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13816","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13818","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 4 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ecdbf180a921053de355ebb9e813d4ee9831bfee8de8067eab16205a55228b91 | d85945419012e656f39317e51334deba2474f0246302346bd05bf27889557bb2 | 35f17444b78d2eb988239d67b529510cd718b2240485b52211c29860f8c3d676 | 6f9a247e1ee37ed8a8c6322dd3ac9a04f16b8d273c0833f77a4c413327ef6942 |
cat-searcher/leandojo-benchmark-4-random | test | 3,637 | ContinuousMultilinearMap.ext_iff | Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u
ι : Type v
n : ℕ
M : Fin n.succ → Type w
M₁ : ι → Type w₁
M₁' : ι → Type w₁'
M₂ : Type w₂
M₃ : Type w₃
M₄ : Type w₄
inst✝¹⁸ : Semiring R
inst✝¹⁷ : (i : Fin n.succ) → AddCommMonoid (M i)
inst✝¹⁶ : (i : ι) → AddCommMonoid (M₁ i)
inst✝¹⁵ : (i : ι) → AddCommMonoid (M₁' i)
inst✝¹⁴ : AddCommMonoid M₂
inst✝¹³ : Add... | ((:c Iff) (:forall x (:forall i (:fv _uniq.13818) ((:fv _uniq.13829) 0)) ((:c Eq) (:fv _uniq.13835) ((:c DFunLike.coe) ((:c MultilinearMap) (:fv _uniq.13816) (:fv _uniq.13818) (:fv _uniq.13829) (:fv _uniq.13835) (:fv _uniq.13842) (:fv _uniq.13858) (:fv _uniq.13869) (:fv _uniq.13944) (:fv _uniq.14001)) (:forall i (:fv _... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"M","sexp":"(:forall _ ((:c Fin) ((:c Nat.succ) (:fv _uniq.13820))) (:sort (+ w 1)))"},{"name":"M₁","sexp":"(:forall _ (:fv _uniq.13818) (:sort (+ w₁ 1)))"},{"name":"M₁'","sexp":"(:forall _ (:fv _uniq.138... | (:app (:c Iff) (:arg :explicit 0 (:forall x :explicit (:forall i :explicit (:fv FV1) (:app (:fv FV4) (:arg :explicit 0 0))) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MultilinearMap) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13816","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13818","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":5222,"sourceStart":5219,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":5222,"sourceStart":5219,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13816","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13818","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 9 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec60159970d58ae17472b18773c6a4e9c99aa9ae6c84657e129b0cf2d12c04de | 6f9a247e1ee37ed8a8c6322dd3ac9a04f16b8d273c0833f77a4c413327ef6942 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,638 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨?_⟩⟩ | V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
⊢ (G.subgraphOfAdj hvw).Connected | V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
⊢ (G.subgraphOfAdj hvw).coe.Preconnected | ((:c SimpleGraph.Subgraph.Connected) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1582) (:fv _uniq.1583) (:fv _uniq.1584))) | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"v","sexp":"(:fv _uniq.1541)"},{"name":"w","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Subgraph.Connected) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :implicit 2) (:arg :implicit 3) (:arg :proof 4 (:proof-of (:app (:c SimpleGraph.Adj) (:arg :implicit-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"refine","sourceEnd":2813,"sourceStart":2807,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2817,"sourceStart":2814,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":2820,"sourceStart":2817,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":2821,"sourceStart":... | [] | [{"source":"⟨⟨?_⟩⟩","source_end":2828,"source_start":2814,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d067c9e88c150da1fa6c8109da00113ca8fe62ee23aa2633158f1cd524ae3c69 | 199df2a228b3a0d5c782dbdb12e706c50281b4dfae0cd1ca5b25e53e294054c4 | dff1e773153bee5add49ca3678dbdcc9a1116752c250f785c97b64cdb3e93d04 | bf3e2c012bbb0caf257e6fc1518ad36a9b967fd80312283aa5a8135813964c45 |
cat-searcher/leandojo-benchmark-4-random | test | 3,639 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨a, ha⟩ ⟨b, hb⟩ | V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
⊢ (G.subgraphOfAdj hvw).coe.Preconnected | case mk.mk
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
a : V
ha : a ∈ (G.subgraphOfAdj hvw).verts
b : V
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha⟩ ⟨b, hb⟩ | ((:c SimpleGraph.Preconnected) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1582) (:fv _uniq.1583) (:fv _uniq.1584)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c ... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"v","sexp":"(:fv _uniq.1541)"},{"name":"w","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Preconnected) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"rintro","sourceEnd":2837,"sourceStart":2831,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":2841,"sourceStart":2838,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":2842,"sourceSt... | [{"role":"fresh_name","source":"a","source_end":2842,"source_start":2841,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":2846,"source_start":2844,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":2854,"source_start":2853,"syntax_kind":"ident"},{"role":"fresh_name","source":"hb... | [{"source":"⟨a, ha⟩","source_end":2849,"source_start":2838,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"⟨b, hb⟩","source_end":2861,"source_start":2850,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e288195d031b9581d2a689b87a635e41b1a4429d2e16575c6362ef96a3c91f6f | bf3e2c012bbb0caf257e6fc1518ad36a9b967fd80312283aa5a8135813964c45 | 6852615160507afa15f239dab2c6ae7167ce021ad50ad3ac8e96264c35dedd29 | d579c3029b3ed680f8ca6c78222b88e3e20e35aaa71ef16dcbe0fc5235eba1ba |
cat-searcher/leandojo-benchmark-4-random | test | 3,640 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>SimpleGraph.subgraphOfAdj_verts</a>, <a>Set.mem_insert_iff</a>, <a>Set.mem_singleton_iff</a>] at ha hb | case mk.mk
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
a : V
ha : a ∈ (G.subgraphOfAdj hvw).verts
b : V
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha⟩ ⟨b, hb⟩ | case mk.mk
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
a : V
ha✝ : a ∈ (G.subgraphOfAdj hvw).verts
b : V
hb✝ : b ∈ (G.subgraphOfAdj hvw).verts
ha : a = v ∨ a = w
hb : b = v ∨ b = w
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha✝⟩ ⟨b, hb✝⟩ | ((:c SimpleGraph.Reachable) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1582) (:fv _uniq.1583) (:fv _uniq.1584)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c Sim... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"v","sexp":"(:fv _uniq.1541)"},{"name":"w","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Reachable) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"simp","sourceEnd":2868,"sourceStart":2864,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":2873,"sourceStart":2869,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":2873,"s... | [] | [{"source":"subgraphOfAdj_verts","source_end":2894,"source_start":2875,"syntax_kind":"ident"},{"source":"Set.mem_insert_iff","source_end":2914,"source_start":2896,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":2937,"source_start":2916,"syntax_kind":"ident"},{"source":"ha","source_end":2944,"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 6 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7494c9b49f6f6e265b4f09de2b62bd1f43b35a9cf795ee737d731c7ae5f43d75 | d579c3029b3ed680f8ca6c78222b88e3e20e35aaa71ef16dcbe0fc5235eba1ba | 98b63a6b71bcd65b0bfc1dd2ec5d2d7e3c37c8bb9c803f30fd19ac7a60fbd0ee | e77823725e262bcad838381ebb3d9c40aa401e2f445ea121cd12547fd5fde8a9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,641 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl | rfl := ha <;> obtain rfl | rfl := hb <;> first | rfl | (apply <a>SimpleGraph.Adj.reachable</a>; simp) | case mk.mk
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v w : V
hvw : G.Adj v w
a : V
ha✝ : a ∈ (G.subgraphOfAdj hvw).verts
b : V
hb✝ : b ∈ (G.subgraphOfAdj hvw).verts
ha : a = v ∨ a = w
hb : b = v ∨ b = w
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha✝⟩ ⟨b, hb✝⟩ | ((:c SimpleGraph.Reachable) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1582) (:fv _uniq.1583) (:fv _uniq.1584)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c Sim... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"v","sexp":"(:fv _uniq.1541)"},{"name":"w","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Reachable) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"source":"obtain","sourceEnd":2956,"sourceStart":2950,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":2960,"sourceStart":2957,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl",... | [] | [{"source":"ha","source_end":2972,"source_start":2970,"syntax_kind":"ident"},{"source":"rfl | rfl","source_end":2966,"source_start":2957,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"},{"source":"hb","source_end":2999,"source_start":2997,"syntax_kind":"ident"},{"source":"rfl | rfl","source_end":2993,"source_start":298... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eeb7f455eae3a233820e14356ff00fb04df4c228073ed72f1eb15a9a5b3b8859 | e77823725e262bcad838381ebb3d9c40aa401e2f445ea121cd12547fd5fde8a9 | 88c8068456e615f589d6d2253109d50f7bb0d76c6ae33802a417443ae31d0def | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,642 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case mk.mk.inr.inr
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
v b : V
hvw : G.Adj v b
ha hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨b, ha⟩ ⟨b, hb⟩ | ((:c SimpleGraph.Reachable) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1582) (:fv _uniq.1739) (:fv _uniq.2216)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c Sim... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"v","sexp":"(:fv _uniq.1541)"},{"name":"b","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Reachable) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":3019,"sourceStart":3016,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3019,"sourceStart":3016,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":3019,"sourceStart":3016,"tag":"node"}],"kind":"Lean.Pars... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 43 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | caf022eaea36f0178468c91d072fed59cbcf0fb3decef8ff4b566f1f79523e3b | 29a468b61b582b39fe33da7b7bcba63a6125684920d554a6961bd555124b947c | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,643 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | (apply <a>SimpleGraph.Adj.reachable</a>; simp) | case mk.mk.inr.inl
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
a b : V
hvw : G.Adj b a
ha : a ∈ (G.subgraphOfAdj hvw).verts
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha⟩ ⟨b, hb⟩ | ((:c SimpleGraph.Reachable) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1739) (:fv _uniq.1718) (:fv _uniq.2199)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c Sim... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"a","sexp":"(:fv _uniq.1541)"},{"name":"b","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Reachable) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":3023,"sourceStart":3022,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":3028,"sourceStart":3023,"tag":"atom"},{"name":"SimpleGraph.Adj.reachable","semanticRole":"global","source":"Adj.reachable"... | [] | [{"source":"Adj.reachable","source_end":3042,"source_start":3029,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 34 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1abbbf995d22cfcd325b653089811880451a13b202a8581bbb0a302753a43f3 | 769e5c9cc98416b3f1a33c194d495e07f7d09334c39b269d3053eb5d9f1e03f6 | 91bdda2e7c19a9b4c24613494865b69ef193116eda6e095da818a0c5a14706de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,644 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>SimpleGraph.Adj.reachable</a> | case mk.mk.inr.inl
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
a b : V
hvw : G.Adj b a
ha : a ∈ (G.subgraphOfAdj hvw).verts
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Reachable ⟨a, ha⟩ ⟨b, hb⟩ | case mk.mk.inr.inl.h
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
a b : V
hvw : G.Adj b a
ha : a ∈ (G.subgraphOfAdj hvw).verts
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Adj ⟨a, ha⟩ ⟨b, hb⟩ | ((:c SimpleGraph.Reachable) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1739) (:fv _uniq.1718) (:fv _uniq.2199)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c Sim... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"a","sexp":"(:fv _uniq.1541)"},{"name":"b","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Reachable) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"apply","sourceEnd":3028,"sourceStart":3023,"tag":"atom"},{"name":"SimpleGraph.Adj.reachable","semanticRole":"global","source":"Adj.reachable","sourceEnd":3042,"sourceStart":3029,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Adj.reachable","sourceEnd":3042,"sourceStart":3... | [] | [{"source":"Adj.reachable","source_end":3042,"source_start":3029,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 39 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7942034c03da66d8b4bcb02cc079bb0b10e62466a7b71a814526fac08b4d6eeb | 769e5c9cc98416b3f1a33c194d495e07f7d09334c39b269d3053eb5d9f1e03f6 | fb7981d9b0a158c97baf67c8389f20ecfb9e97aeee9621cf99f90ec033232f4b | 08ad05f43a8410a97fd39c3d433faa161071168ef9896a835adcf331de00d77b |
cat-searcher/leandojo-benchmark-4-random | test | 3,645 | SimpleGraph.Subgraph.subgraphOfAdj_connected | Mathlib/Combinatorics/SimpleGraph/Connectivity/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case mk.mk.inr.inl.h
V : Type u
V' : Type v
G : SimpleGraph V
G' : SimpleGraph V'
a b : V
hvw : G.Adj b a
ha : a ∈ (G.subgraphOfAdj hvw).verts
hb : b ∈ (G.subgraphOfAdj hvw).verts
⊢ (G.subgraphOfAdj hvw).coe.Adj ⟨a, ha⟩ ⟨b, hb⟩ | ((:c SimpleGraph.Adj) ((:c Set.Elem) (:fv _uniq.1541) ((:c SimpleGraph.Subgraph.verts) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGraph.subgraphOfAdj) (:fv _uniq.1541) (:fv _uniq.1546) (:fv _uniq.1739) (:fv _uniq.1718) (:fv _uniq.2199)))) ((:c SimpleGraph.Subgraph.coe) (:fv _uniq.1541) (:fv _uniq.1546) ((:c SimpleGra... | [{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"V'","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.1541))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.1543))"},{"name":"a","sexp":"(:fv _uniq.1541)"},{"name":"b","sexp":"(:fv _uniq.1541)"},{"name":"hvw","sexp":"((:c SimpleGraph.Adj) (:f... | (:app (:c SimpleGraph.Adj) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.verts) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.subgraphOfAdj) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"simp","sourceEnd":3048,"sourceStart":3044,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1541","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1543","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 19 | 41 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ff0f2a7a620b0cc98b7d13fcc719a19ceb9cc2e349328a9a83fa3a2ea9c19d5 | 08ad05f43a8410a97fd39c3d433faa161071168ef9896a835adcf331de00d77b | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,646 | CliffordAlgebra.ι_sq_scalar | Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [← <a>AlgHom.map_mul</a>, <a>RingQuot.mkAlgHom_rel</a> R (<a>CliffordAlgebra.Rel.of</a> m), <a>AlgHom.commutes</a>] | R : Type u_1
inst✝² : CommRing R
M : Type u_2
inst✝¹ : AddCommGroup M
inst✝ : Module R M
Q : QuadraticForm R M
n : ℕ
m : M
⊢ (ι Q) m * (ι Q) m = (algebraMap R (CliffordAlgebra Q)) (Q m) | R : Type u_1
inst✝² : CommRing R
M : Type u_2
inst✝¹ : AddCommGroup M
inst✝ : Module R M
Q : QuadraticForm R M
n : ℕ
m : M
⊢ (algebraMap R (RingQuot (Rel Q))) (Q m) = (algebraMap R (CliffordAlgebra Q)) (Q m) | ((:c Eq) ((:c CliffordAlgebra) (:fv _uniq.57481) (:fv _uniq.57484) (:fv _uniq.57487) (:fv _uniq.57490) (:fv _uniq.58103) (:fv _uniq.58518)) ((:c HMul.hMul) ((:c CliffordAlgebra) (:fv _uniq.57481) (:fv _uniq.57484) (:fv _uniq.57487) (:fv _uniq.57490) (:fv _uniq.58103) (:fv _uniq.58518)) ((:c CliffordAlgebra) (:fv _uniq.... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.57481))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.57487))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.57481) (:fv _uniq.57487) ((:c CommSemiring.toSemiring) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CliffordAlgebra) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57481","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.57484","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"erw","sourceEnd":4735,"sourceStart":4732,"tag":"atom"},{"children":[{"source":"[","sourceEnd":4737,"sourceStart":4736,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4740,"sourceStart":4737,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"AlgHom.map_mul","source_end":4755,"source_start":4741,"syntax_kind":"ident"},{"source":"RingQuot.mkAlgHom_rel R (Rel.of m)","source_end":4791,"source_start":4757,"syntax_kind":"Lean.Parser.Term.app"},{"source":"AlgHom.commutes","source_end":4808,"source_start":4793,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57481","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.57484","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 27 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6d056450a96c3a6f1391dc6fe6959a98d1fd01fa04d8ec54345de69a9edd7d1 | e5cfcfc22364d8a5a6325ae9adc9e6cfe126ec12c88fdcf8474897dfa533b174 | e2d5e16660344ba539d855a4ca74d9c3cf4e9e3adaf2b3754e27f616c5164c00 | b5d89a42dd8a04514182b9b9df5c79ca19a24955744720c81b2b59a20b5a895a |
cat-searcher/leandojo-benchmark-4-random | test | 3,647 | CliffordAlgebra.ι_sq_scalar | Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | R : Type u_1
inst✝² : CommRing R
M : Type u_2
inst✝¹ : AddCommGroup M
inst✝ : Module R M
Q : QuadraticForm R M
n : ℕ
m : M
⊢ (algebraMap R (RingQuot (Rel Q))) (Q m) = (algebraMap R (CliffordAlgebra Q)) (Q m) | ((:c Eq) ((:c CliffordAlgebra) (:fv _uniq.57481) (:fv _uniq.57484) (:fv _uniq.57487) (:fv _uniq.57490) (:fv _uniq.58103) (:fv _uniq.58518)) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.57481) ((:c RingQuot) ((:c TensorAlgebra) (:fv _uniq.57481) ((:c CommRing.toCommSemiring) (:fv _uniq.57481) (:fv _uniq.57484)) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CommRing) (:fv _uniq.57481))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.57487))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.57481) (:fv _uniq.57487) ((:c CommSemiring.toSemiring) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CliffordAlgebra) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57481","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.57484","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rfl","sourceEnd":4815,"sourceStart":4812,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":4815,"sourceStart":4812,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.57481","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.57484","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 27 | 9 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33532fafd0869ce22f2549c09bd6292470bfb0a5c95ccdeb142468324be12ec3 | b5d89a42dd8a04514182b9b9df5c79ca19a24955744720c81b2b59a20b5a895a | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,649 | Polynomial.eval₂_mul_noncomm | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases p with ⟨p⟩ | R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
p q r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
hf : ∀ (k : ℕ), Commute (f (q.coeff k)) x
⊢ eval₂ f x (p * q) = eval₂ f x p * eval₂ f x q | case ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
q r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
hf : ∀ (k : ℕ), Commute (f (q.coeff k)) x
p : R[ℕ]
⊢ eval₂ f x ({ toFinsupp := p } * q) = eval₂ f x { toFinsupp := p } * eval₂ f x q | ((:c Eq) (:fv _uniq.45332) ((:c Polynomial.eval₂) (:fv _uniq.45330) (:fv _uniq.45332) (:fv _uniq.45347) (:fv _uniq.45371) (:fv _uniq.45407) (:fv _uniq.45409) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:f... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.45330)"},{"name":"b","sexp":"(:fv _uniq.45330)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":6615,"sourceStart":6609,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"p","sourceEnd":6617,"sourceStart":6616,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"p","source_end":6617,"source_start":6616,"syntax_kind":"ident"},{"source":"⟨p⟩","source_end":6630,"source_start":6623,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 60 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09628a7ba3ff5d99a0ecbaf83dffab151fa9ff6fbdd033131dbc356465f073c6 | b65ccbf3555ff29ee49cadae0395dea5f2e7c21d865395907d614fc66e84ecaf | e161be96b21eca5630025f26f31ca832f31810a1083aa5dc9816c86fa28f47de | aac3c573fcf02c1496d8e93b7568bc7890fd767b6edceba00679f86cedcd09f1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,650 | Polynomial.eval₂_mul_noncomm | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases q with ⟨q⟩ | case ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
q r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
hf : ∀ (k : ℕ), Commute (f (q.coeff k)) x
p : R[ℕ]
⊢ eval₂ f x ({ toFinsupp := p } * q) = eval₂ f x { toFinsupp := p } * eval₂ f x q | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f ({ toFinsupp := q }.coeff k)) x
⊢ eval₂ f x ({ toFinsupp := p } * { toFinsupp := q }) = eval₂ f x { toFinsupp :... | ((:c Eq) (:fv _uniq.45332) ((:c Polynomial.eval₂) (:fv _uniq.45330) (:fv _uniq.45332) (:fv _uniq.45347) (:fv _uniq.45371) (:fv _uniq.45407) (:fv _uniq.45409) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:f... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.45330)"},{"name":"b","sexp":"(:fv _uniq.45330)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":6638,"sourceStart":6632,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"q","sourceEnd":6640,"sourceStart":6639,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"q","source_end":6640,"source_start":6639,"syntax_kind":"ident"},{"source":"⟨q⟩","source_end":6653,"source_start":6646,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 60 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 57c9affc6e51992740a6bd76b96f8dbe79ac698de273459b919985d01098a4da | aac3c573fcf02c1496d8e93b7568bc7890fd767b6edceba00679f86cedcd09f1 | 914e6b9a74930aadaf8b8fd7dfa5cf140c46f039f9dccb9a78a011bc6a2d50a4 | 5d46ed46688947fa4dbd58d1ad3ebd8a5322ef835da8a07b3ae466db5c79b3de |
cat-searcher/leandojo-benchmark-4-random | test | 3,651 | Polynomial.eval₂_mul_noncomm | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Polynomial.coeff</a>] at hf | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f ({ toFinsupp := q }.coeff k)) x
⊢ eval₂ f x ({ toFinsupp := p } * { toFinsupp := q }) = eval₂ f x { toFinsupp :... | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f (q k)) x
⊢ eval₂ f x ({ toFinsupp := p } * { toFinsupp := q }) = eval₂ f x { toFinsupp := p } * eval₂ f x { toF... | ((:c Eq) (:fv _uniq.45332) ((:c Polynomial.eval₂) (:fv _uniq.45330) (:fv _uniq.45332) (:fv _uniq.45347) (:fv _uniq.45371) (:fv _uniq.45407) (:fv _uniq.45409) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:f... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.45330)"},{"name":"b","sexp":"(:fv _uniq.45330)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":6660,"sourceStart":6656,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6665,"sourceStart":6661,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6665,"s... | [] | [{"source":"coeff","source_end":6672,"source_start":6667,"syntax_kind":"ident"},{"source":"hf","source_end":6679,"source_start":6677,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 60 | 7 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32fab840bcdc965bde31daa29c925e7057ce2159ad7df6ebd8dd79c282a4fb93 | 5d46ed46688947fa4dbd58d1ad3ebd8a5322ef835da8a07b3ae466db5c79b3de | 2015208ecb2a4f827fdff4bac1d7110756cd14f6e2e26a279516d48677b05c71 | bef63079c77feee5ffc8eb15b9f95344ddb4e0acb6f0f39e211eec11ed533a95 |
cat-searcher/leandojo-benchmark-4-random | test | 3,652 | Polynomial.eval₂_mul_noncomm | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Polynomial.ofFinsupp_mul</a>, <a>Polynomial.eval₂_ofFinsupp</a>] | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f (q k)) x
⊢ eval₂ f x ({ toFinsupp := p } * { toFinsupp := q }) = eval₂ f x { toFinsupp := p } * eval₂ f x { toF... | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f (q k)) x
⊢ (liftNC ↑f ⇑((powersHom S) x)) (p * q) = (liftNC ↑f ⇑((powersHom S) x)) p * (liftNC ↑f ⇑((powersHom ... | ((:c Eq) (:fv _uniq.45332) ((:c Polynomial.eval₂) (:fv _uniq.45330) (:fv _uniq.45332) (:fv _uniq.45347) (:fv _uniq.45371) (:fv _uniq.45407) (:fv _uniq.45409) ((:c HMul.hMul) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:fv _uniq.45347)) ((:c Polynomial) (:fv _uniq.45330) (:f... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.45330)"},{"name":"b","sexp":"(:fv _uniq.45330)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Polynomial.eval₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":6686,"sourceStart":6682,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6691,"sourceStart":6687,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":6691,"s... | [] | [{"source":"ofFinsupp_mul","source_end":6710,"source_start":6697,"syntax_kind":"ident"},{"source":"eval₂_ofFinsupp","source_end":6729,"source_start":6712,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 60 | 8 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 746bfb7e6baca0edc6f82b5c0e6568676d7c9026ea855ad8a6380cf0e7e93432 | bef63079c77feee5ffc8eb15b9f95344ddb4e0acb6f0f39e211eec11ed533a95 | 8d4aeb12ad64aacac53aa26d4f8e8e27b4c60d0dbb9cb5c4df89c884b23cc92d | a750d590b874f0964b49e1dda4bc994e94e4d6a4d00ec3b738515920b4f14b67 |
cat-searcher/leandojo-benchmark-4-random | test | 3,653 | Polynomial.eval₂_mul_noncomm | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>AddMonoidAlgebra.liftNC_mul</a> _ _ p q fun {k n} _hn => (hf k).<a>Commute.pow_right</a> n | case ofFinsupp.ofFinsupp
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝² : Semiring R
r : R[X]
inst✝¹ : Semiring S
f : R →+* S
x : S
inst✝ : Semiring T
p q : R[ℕ]
hf : ∀ (k : ℕ), Commute (f (q k)) x
⊢ (liftNC ↑f ⇑((powersHom S) x)) (p * q) = (liftNC ↑f ⇑((powersHom S) x)) p * (liftNC ↑f ⇑((powersHom ... | ((:c Eq) (:fv _uniq.45332) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c AddMonoidAlgebra) (:fv _uniq.45330) (:c Nat) (:fv _uniq.45347)) (:fv _uniq.45332) ((:c AddMonoid.toAddZeroClass) ((:c AddMonoidAlgebra) (:fv _uniq.45330) (:c Nat) (:fv _uniq.45347)) ((:c AddCommMonoid.toAddMonoid) ((:c AddMonoidAlgebra) (:fv _uniq.45... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.45330)"},{"name":"b","sexp":"(:fv _uniq.45330)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝²","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c AddMonoidAlgebra) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":6738,"sourceStart":6733,"tag":"atom"},{"children":[{"name":"AddMonoidAlgebra.liftNC_mul","semanticRole":"global","source":"liftNC_mul","sourceEnd":6749,"sourceStart":6739,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":6751,"sourceStart":6750,"tag":"ato... | [] | [{"source":"liftNC_mul _ _ p q fun {k n} _hn => (hf k).pow_right n","source_end":6793,"source_start":6739,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.45330","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.45332","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 60 | 9 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e43a272d6b9adbe65086a31a59f23bc8117f338871daf8b1584f9e9e5419873d | a750d590b874f0964b49e1dda4bc994e94e4d6a4d00ec3b738515920b4f14b67 | c239273241b1b9cd54facbafcc1b171beaeac40286ea41e23622d77e43a415bb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,654 | Stream'.get_succ_iterate | Mathlib/Data/Stream/Init.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Stream'.get_succ</a>, <a>Stream'.tail_iterate</a>] | α : Type u
β : Type v
δ : Type w
n : ℕ
f : α → α
a : α
⊢ (iterate f a).get n.succ = (iterate f (f a)).get n | ((:c Eq) (:fv _uniq.8108) ((:c Stream'.get) (:fv _uniq.8108) ((:c Stream'.iterate) (:fv _uniq.8108) (:fv _uniq.8147) (:fv _uniq.8148)) ((:c Nat.succ) (:fv _uniq.8146))) ((:c Stream'.get) (:fv _uniq.8108) ((:c Stream'.iterate) (:fv _uniq.8108) (:fv _uniq.8147) ((:fv _uniq.8147) (:fv _uniq.8148))) (:fv _uniq.8146))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"δ","sexp":"(:sort (+ w 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.8108) (:fv _uniq.8108))"},{"name":"a","sexp":"(:fv _uniq.8108)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Stream'.get) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Stream'.iterate) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV6)))) (:arg :explicit 2 (:app (:c Nat.succ) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8108","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":9439,"sourceStart":9437,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9441,"sourceStart":9440,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"get_succ","source_end":9449,"source_start":9441,"syntax_kind":"ident"},{"source":"tail_iterate","source_end":9463,"source_start":9451,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.8108","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.8110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 118 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e03f03256ee701d918e19bddbb34e66b8eaf846d5343690a1faffa39a7726bde | 0640f74646aa544355a693a909bdf727f7bc1e49236e40da6016b42a7b24f876 | d1a17d9e8a4b95f60586a10d08dc1f617428545a3c955185eb49af901dde04fb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,655 | Real.volume_ball | Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.ball_eq_Ioo</a>, <a>Real.volume_Ioo</a>, ← <a>sub_add</a>, <a>add_sub_cancel_left</a>, <a>two_mul</a>] | ι : Type u_1
inst✝ : Fintype ι
a r : ℝ
⊢ volume (Metric.ball a r) = ofReal (2 * r) | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace))) ((:c Set) (:c Real)) (:lambda _ ((:c Set) (:c Real)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:c Real) ((:c MeasureTheory.MeasureSpace.toMeas... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Fintype) (:fv _uniq.22026))"},{"name":"a","sexp":"(:c Real)"},{"name":"r","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:c Real))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22026","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22029","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Fintype) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4621,"sourceStart":4619,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4623,"sourceStart":4622,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"ball_eq_Ioo","source_end":4634,"source_start":4623,"syntax_kind":"ident"},{"source":"volume_Ioo","source_end":4646,"source_start":4636,"syntax_kind":"ident"},{"source":"sub_add","source_end":4659,"source_start":4652,"syntax_kind":"ident"},{"source":"add_sub_cancel_left","source_end":4680,"source_start":4661... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22026","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22029","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":3,"interna... | 27 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e16c0af3ac4842eb8c494c3813005943d57d36b124da396fe565e8711480aca | 6574806bb52ac2d07eec3d0aa3af1ec417c7abac1d66ea172565636def1041ab | 146ad527455e5409e37788803672f494774d75a4039a30d2d5a6e62a19e33799 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,656 | ProbabilityTheory.IsCondKernelCDF.setLIntegral | Mathlib/Probability/Kernel/Disintegration/CdfToKernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.ofReal_integral_eq_lintegral_ofReal</a> (hf.integrable a x).<a>MeasureTheory.Integrable.restrict</a> (<a>MeasureTheory.ae_of_all</a> _ (fun _ ↦ hf.nonneg _ _)), hf.setIntegral a hs x, <a>ENNReal.ofReal_toReal</a>] | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
κ : ↥(kernel α (β × ℝ))
ν : ↥(kernel α β)
f✝ : α × β → StieltjesFunction
inst✝ : IsFiniteKernel κ
f : α × β → StieltjesFunction
hf : IsCondKernelCDF f κ ν
a : α
s : Set β
hs : MeasurableSet s
x : ℝ
⊢ ∫⁻ (b : β) in s, ENNReal.ofReal (↑(f (a, b)) x) ... | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
κ : ↥(kernel α (β × ℝ))
ν : ↥(kernel α β)
f✝ : α × β → StieltjesFunction
inst✝ : IsFiniteKernel κ
f : α × β → StieltjesFunction
hf : IsCondKernelCDF f κ ν
a : α
s : Set β
hs : MeasurableSet s
x : ℝ
⊢ (κ a) (s ×ˢ Iic x) ≠ ⊤ | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.96103) (:fv _uniq.96109) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.96103) (:fv _uniq.96109) ((:c DFunLike.coe) ((:c Subtype) (:forall _ (:fv _uniq.96100) ((:c MeasureTheory.Measure) (:fv _uniq.96103) (:fv _uniq.96109))) (:lambda x (:forall _ (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.96100))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.96103))"},{"name":"κ","sexp":"((:c Subtype) (:forall _ (:fv _uniq.96100) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uni... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96100","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96103","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":23839,"sourceStart":23837,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23841,"sourceStart":23840,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":23844,"sourceSt... | [] | [{"source":"ofReal_integral_eq_lintegral_ofReal (hf.integrable a x).restrict\n (ae_of_all _ (fun _ ↦ hf.nonneg _ _))","source_end":23953,"source_start":23845,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hf.setIntegral a hs x","source_end":23976,"source_start":23955,"syntax_kind":"Lean.Parser.Term.app"},{"source"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96100","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96103","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 51 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4110fbd195fbf64354ae8ad3e1a3547327b138e31b045cc6182d83de1b6866c4 | caa9f748f0537c439693ab5db44d95d92430a61cf22372d486b48925bfb99799 | 23fda23d73bc4bb68ffa66ffef9eaa2190ada9d42c1a902fc98943fdebea142b | c1ac7b558da1fe9e000181c67aa425003ff1e6ed23d34d90e7319d2d7f2d06e2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,657 | ProbabilityTheory.IsCondKernelCDF.setLIntegral | Mathlib/Probability/Kernel/Disintegration/CdfToKernel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.measure_ne_top</a> _ _ | α : Type u_1
β : Type u_2
mα : MeasurableSpace α
mβ : MeasurableSpace β
κ : ↥(kernel α (β × ℝ))
ν : ↥(kernel α β)
f✝ : α × β → StieltjesFunction
inst✝ : IsFiniteKernel κ
f : α × β → StieltjesFunction
hf : IsCondKernelCDF f κ ν
a : α
s : Set β
hs : MeasurableSet s
x : ℝ
⊢ (κ a) (s ×ˢ Iic x) ≠ ⊤ | ((:c Ne) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uniq.96103) (:c Real)) ((:c Prod.instMeasurableSpace) (:fv _uniq.96103) (:c Real) (:fv _uniq.96109) (:c Real.measurableSpace))) ((:c Set) ((:c Prod) (:fv _uniq.96103) (:c Real))) (:lambda _ ((:c Set) ((:c Prod) (:fv _uniq.96103) (:c R... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.96100))"},{"name":"mβ","sexp":"((:c MeasurableSpace) (:fv _uniq.96103))"},{"name":"κ","sexp":"((:c Subtype) (:forall _ (:fv _uniq.96100) ((:c MeasureTheory.Measure) ((:c Prod) (:fv _uni... | (:app (:c Ne) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96100","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96103","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":24008,"sourceStart":24003,"tag":"atom"},{"children":[{"name":"MeasureTheory.measure_ne_top","semanticRole":"global","source":"measure_ne_top","sourceEnd":24023,"sourceStart":24009,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":24025,"sourceStart":24024... | [] | [{"source":"measure_ne_top _ _","source_end":24027,"source_start":24009,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.96100","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.96103","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 51 | 9 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04de64f26840952de5326d63996c581fb1018f0f2881639327c6281fcbeb81d6 | c1ac7b558da1fe9e000181c67aa425003ff1e6ed23d34d90e7319d2d7f2d06e2 | f0ed3e82e5ece417bda2be3fc80aa752cf2f62f6ae46717bfcbe1d11d3b13b07 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,658 | Affine.Simplex.reindex_reindex_symm | Mathlib/LinearAlgebra/AffineSpace/Independent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Affine.Simplex.reindex_trans</a>, <a>Equiv.self_trans_symm</a>, <a>Affine.Simplex.reindex_refl</a>] | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
m n : ℕ
s : Simplex k P m
e : Fin (m + 1) ≃ Fin (n + 1)
⊢ (s.reindex e).reindex e.symm = s | ((:c Eq) ((:c Affine.Simplex) (:fv _uniq.326750) (:fv _uniq.326753) (:fv _uniq.326756) (:fv _uniq.326759) (:fv _uniq.326762) (:fv _uniq.327349) (:fv _uniq.327438) (:fv _uniq.327848)) ((:c Affine.Simplex.reindex) (:fv _uniq.326750) (:fv _uniq.326753) (:fv _uniq.326756) (:fv _uniq.326759) (:fv _uniq.326762) (:fv _uniq.32... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.326750))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.326753))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.326750) (:fv _uniq.326753)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Affine.Simplex) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV1)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.326750","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.326753","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":47161,"sourceStart":47159,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":47163,"sourceStart":47162,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"reindex_trans","source_end":47180,"source_start":47167,"syntax_kind":"ident"},{"source":"Equiv.self_trans_symm","source_end":47203,"source_start":47182,"syntax_kind":"ident"},{"source":"reindex_refl","source_end":47217,"source_start":47205,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.326750","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.326753","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 147 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7aa66c0d27da26667bceb7cbd15fdb18282c4a3d0b587db5129046cb8bc5444a | 9989022ab43ad08ce7502e2de84acc21312192f0f9c15211f718f7ae7bb1d90f | 557cbb22da9a0b4c80f13a8eb9738f4568c4d360091c3ecf000b918d87223344 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,659 | AlgebraicGeometry.diagonal_targetAffineLocally_eq_targetAffineLocally | Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext _ _ f | P : AffineTargetMorphismProperty
hP : P.IsLocal
⊢ (targetAffineLocally P).diagonal = targetAffineLocally P.diagonal | case h
P : AffineTargetMorphismProperty
hP : P.IsLocal
X✝ Y✝ : Scheme
f : X✝ ⟶ Y✝
⊢ (targetAffineLocally P).diagonal f ↔ targetAffineLocally P.diagonal f | ((:c Eq) ((:c CategoryTheory.MorphismProperty) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory)) ((:c CategoryTheory.MorphismProperty.diagonal) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory) (:c AlgebraicGeometry.Scheme.Pullback.instHasPullbacks) ((:c AlgebraicGeometry.... | [{"name":"P","sexp":"(:c AlgebraicGeometry.AffineTargetMorphismProperty)"},{"name":"hP","sexp":"((:c AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal) (:fv _uniq.64735))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.MorphismProperty) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))))) (:arg :explicit 1 (:app (:c CategoryTheory.MorphismProperty.diagonal) ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.64735","is_instance":false,"is_let":false,"name":"P","sexp":"(:c AlgebraicGeometry.AffineTargetMorphismProperty)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.64736","is_instance":false,"is_let":false,"name":"hP","sexp":"(:app ... | {"children":[{"source":"ext","sourceEnd":7448,"sourceStart":7445,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":7450,"sourceStart":7449,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":7450,"sourceStart":7449,"tag":"node"}],"kind":"Lean.Parser.Tactic.r... | [{"role":"fresh_name","source":"f","source_end":7454,"source_start":7453,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.64735","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.64736","is_instance":false,"is_let":false,"user_name":"hP"}] | 18 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8635e9e5ce7400efbef539b14b9f395d2008df244d96858b683d032f139233a5 | 6b455d977feb07fb0caa30731611deba051b3ebe728371482e191221f1c1f510 | 5bbe639ff8ae31dd3751a70f018b5f1297592e1fa9dbd951df33b13897c4a939 | 00f22a6490934306367394f6a8a45f4222b1cb8f71381d920f76d5d0f354c0a8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,660 | AlgebraicGeometry.diagonal_targetAffineLocally_eq_targetAffineLocally | Mathlib/AlgebraicGeometry/Morphisms/Constructors.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((hP.diagonal_affine_openCover_TFAE f).<a>List.TFAE.out</a> 0 1).<a>Iff.trans</a> ((hP.diagonal.affine_openCover_TFAE f).<a>List.TFAE.out</a> 1 0) | case h
P : AffineTargetMorphismProperty
hP : P.IsLocal
X✝ Y✝ : Scheme
f : X✝ ⟶ Y✝
⊢ (targetAffineLocally P).diagonal f ↔ targetAffineLocally P.diagonal f | ((:c Iff) ((:c CategoryTheory.MorphismProperty.diagonal) (:c AlgebraicGeometry.Scheme) (:c AlgebraicGeometry.Scheme.instCategory) (:c AlgebraicGeometry.Scheme.Pullback.instHasPullbacks) ((:c AlgebraicGeometry.targetAffineLocally) (:fv _uniq.64735)) (:fv _uniq.64780) (:fv _uniq.64783) (:fv _uniq.64786)) ((:c AlgebraicGe... | [{"name":"P","sexp":"(:c AlgebraicGeometry.AffineTargetMorphismProperty)"},{"name":"hP","sexp":"((:c AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal) (:fv _uniq.64735))"},{"name":"X✝","sexp":"(:c AlgebraicGeometry.Scheme)"},{"name":"Y✝","sexp":"(:c AlgebraicGeometry.Scheme)"},{"name":"f","sexp":"((:c Quiver.Hom)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c CategoryTheory.MorphismProperty.diagonal) (:arg :implicit-type 0 (:c AlgebraicGeometry.Scheme)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c AlgebraicGeometry.Scheme))))) (:arg :instance 2 (:instance-of (:app (:c CategoryTheory.Limit... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.64735","is_instance":false,"is_let":false,"name":"P","sexp":"(:c AlgebraicGeometry.AffineTargetMorphismProperty)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.64736","is_instance":false,"is_let":false,"name":"hP","sexp":"(:app ... | {"children":[{"source":"exact","sourceEnd":7462,"sourceStart":7457,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7464,"sourceStart":7463,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7465,"sourceStart":7464,"tag":"atom"},{"children":[{"source":"hP.diagon... | [] | [{"source":"((hP.diagonal_affine_openCover_TFAE f).out 0 1).trans\n ((hP.diagonal.affine_openCover_TFAE f).out 1 0)","source_end":7568,"source_start":7463,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.64735","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.64736","is_instance":false,"is_let":false,"user_name":"hP"},{"binder_role":":strict-implicit","context_index":3,"internal_na... | 18 | 5 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ca622f0982cf7147df537045cb08cac3cebb3544569ef8bb914dc9f32fc8305 | 00f22a6490934306367394f6a8a45f4222b1cb8f71381d920f76d5d0f354c0a8 | 2d938124c0ddbb5372d5a394f7767d1920c7acdb6e39d2b5528ca7450af93cd3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,661 | Filter.HasBasis.frequently_iff | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Filter.Frequently</a>, hl.eventually_iff] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
q : α → Prop
⊢ (∃ᶠ (x : α) in l, q x) ↔ ∀ (i : ι), p i → ∃ x ∈ s i, q x | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
q : α → Prop
⊢ (¬∃ i, p i ∧ ∀ ⦃x : α⦄, x ∈ s i → ¬q x) ↔ ∀ (i : ι), p i → ∃ x ∈ s i, q x | ((:c Iff) ((:c Filter.Frequently) (:fv _uniq.18516) (:lambda x (:fv _uniq.18516) ((:fv _uniq.18632) 0)) (:fv _uniq.18531)) (:forall i (:fv _uniq.18525) (:forall _ ((:fv _uniq.18538) 0) ((:c Exists) (:fv _uniq.18516) (:lambda x (:fv _uniq.18516) ((:c And) ((:c Membership.mem) (:fv _uniq.18516) ((:c Set) (:fv _uniq.18516... | [{"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)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"p","sexp":"(... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Filter.Frequently) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:fv FV16) (:arg :explicit 0 0)))) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:forall i :explicit (:fv FV3) (:forall _ :explicit (:app (:fv FV7) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":17072,"sourceStart":17068,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17077,"sourceStart":17073,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":170... | [] | [{"source":"Filter.Frequently","source_end":17096,"source_start":17079,"syntax_kind":"ident"},{"source":"hl.eventually_iff","source_end":17115,"source_start":17098,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e21782dadfc0b1e2ff6cf7b52be77beb14154a45df2cc89592ac22672945204d | 376d34950f7e4752995704566e467f6011a77e6412180d76ee4f26fb94ecd544 | fd28d13a9fcb6307da28eedfa107266cef95294900ec99cd3ddcad427c5fb854 | 00fee9cd78c36ddd7deb07b5ee180bf821c9c2b570df3a9cbb11d9302c1cc9de |
cat-searcher/leandojo-benchmark-4-random | test | 3,662 | Filter.HasBasis.frequently_iff | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | push_neg | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
q : α → Prop
⊢ (¬∃ i, p i ∧ ∀ ⦃x : α⦄, x ∈ s i → ¬q x) ↔ ∀ (i : ι), p i → ∃ x ∈ s i, q x | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
q : α → Prop
⊢ (∀ (i : ι), p i → ∃ x ∈ s i, q x) ↔ ∀ (i : ι), p i → ∃ x ∈ s i, q x | ((:c Iff) ((:c Not) ((:c Exists) (:fv _uniq.18525) (:lambda i (:fv _uniq.18525) ((:c And) ((:fv _uniq.18538) 0) (:forall x (:fv _uniq.18516) (:forall _ ((:c Membership.mem) (:fv _uniq.18516) ((:c Set) (:fv _uniq.18516)) ((:c Set.instMembership) (:fv _uniq.18516)) 0 ((:fv _uniq.18543) 1)) ((:c Not) ((:fv _uniq.18632) 1)... | [{"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)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"p","sexp":"(... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda i :explicit (:fv FV3) (:app (:c And) (:arg :explicit 0 (:app (:fv FV7) (:arg :explicit 0 0))) (:arg :explicit 1 (:forall x :strict-implicit (:fv FV0) (:forall _ :explicit (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"push_neg","sourceEnd":17126,"sourceStart":17118,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.PushNeg.tacticPush_neg_","source":"push_neg","sourceEnd":17126,"sourceStart":17118,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 6 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b4592520d39ba56bc38f5898e2263df23f22348dd800d82053cce3ce3603fba | 00fee9cd78c36ddd7deb07b5ee180bf821c9c2b570df3a9cbb11d9302c1cc9de | b0ca1774ed2e892f05294629909df3ac01eea8fadab4999a2254832ded4e7412 | 248c7cbe8ec589a67d7f6958b816ce194c627094c3f45f3f74b7d23af9fbab6f |
cat-searcher/leandojo-benchmark-4-random | test | 3,663 | Filter.HasBasis.frequently_iff | Mathlib/Order/Filter/Bases.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
l l' : Filter α
p : ι → Prop
s : ι → Set α
t : Set α
i : ι
p' : ι' → Prop
s' : ι' → Set α
i' : ι'
hl : l.HasBasis p s
q : α → Prop
⊢ (∀ (i : ι), p i → ∃ x ∈ s i, q x) ↔ ∀ (i : ι), p i → ∃ x ∈ s i, q x | ((:c Iff) (:forall i (:fv _uniq.18525) (:forall _ ((:fv _uniq.18538) 0) ((:c Exists) (:fv _uniq.18516) (:lambda x (:fv _uniq.18516) ((:c And) ((:c Membership.mem) (:fv _uniq.18516) ((:c Set) (:fv _uniq.18516)) ((:c Set.instMembership) (:fv _uniq.18516)) 0 ((:fv _uniq.18543) 2)) ((:fv _uniq.18632) 0)) :strictImplicit)))... | [{"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)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"l'","sexp":"((:c Filter) (:fv _uniq.18516))"},{"name":"p","sexp":"(... | (:app (:c Iff) (:arg :explicit 0 (:forall i :explicit (:fv FV3) (:forall _ :explicit (:app (:fv FV7) (:arg :explicit 0 0)) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :strict-implicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":17131,"sourceStart":17128,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":17131,"sourceStart":17128,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18516","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18519","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 101 | 8 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ae031349f87a0fb5dd19b2e10a1d20effc05807d7a7b4dda51d2f60a8e0a1c1 | 248c7cbe8ec589a67d7f6958b816ce194c627094c3f45f3f74b7d23af9fbab6f | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,664 | MvPolynomial.vanishingIdeal_pointToPoint | Mathlib/RingTheory/Nullstellensatz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | infer_instance | k : Type u_1
inst✝ : Field k
σ : Type u_2
V : Set (σ → k)
p : MvPolynomial σ k
hp : p ∈ PrimeSpectrum.vanishingIdeal (pointToPoint '' V)
x : σ → k
hx : x ∈ V
⊢ (vanishingIdeal {x}).IsPrime | ((:c Ideal.IsPrime) ((:c MvPolynomial) (:fv _uniq.33623) (:fv _uniq.33617) ((:c Semifield.toCommSemiring) (:fv _uniq.33617) ((:c Field.toSemifield) (:fv _uniq.33617) (:fv _uniq.33620)))) ((:c CommSemiring.toSemiring) ((:c MvPolynomial) (:fv _uniq.33623) (:fv _uniq.33617) ((:c Semifield.toCommSemiring) (:fv _uniq.33617)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.33617))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"V","sexp":"((:c Set) (:forall _ (:fv _uniq.33623) (:fv _uniq.33617)))"},{"name":"p","sexp":"((:c MvPolynomial) (:fv _uniq.33623) (:fv _uniq.33617) ((:c Semifield.toCommSemir... | (:app (:c Ideal.IsPrime) (:arg :implicit-type 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:app (:c MvPolynomial) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33617","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.33620","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Field) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"infer_instance","sourceEnd":7230,"sourceStart":7216,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticInfer_instance","source":"infer_instance","sourceEnd":7230,"sourceStart":7216,"tag":"node"}],"kind":"null","source":"infer_instance","sourceEnd":7230,"source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33617","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.33620","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 42 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e983f714d9161b7e91aa319a30c00413ae4b1572f87f8916135938388f9ee517 | 397c4d5e938911a49cb4cf70eb7a9fae741c15f219bcfd1bb48da505672f5d46 | 1be023dbb859162463cfcba2e9fc80f1c85bab9d31edeb816d1518206e2b70fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,665 | MvPolynomial.vanishingIdeal_pointToPoint | Mathlib/RingTheory/Nullstellensatz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨x, ⟨hx, <a>rfl</a>⟩⟩ | k : Type u_1
inst✝ : Field k
σ : Type u_2
V : Set (σ → k)
p : MvPolynomial σ k
hp : p ∈ PrimeSpectrum.vanishingIdeal (pointToPoint '' V)
x : σ → k
hx : x ∈ V
⊢ { asIdeal := vanishingIdeal {x}, isPrime := ⋯ } ∈ pointToPoint '' V | ((:c Membership.mem) ((:c PrimeSpectrum) ((:c MvPolynomial) (:fv _uniq.33623) (:fv _uniq.33617) ((:c Semifield.toCommSemiring) (:fv _uniq.33617) ((:c Field.toSemifield) (:fv _uniq.33617) (:fv _uniq.33620)))) ((:c MvPolynomial.commSemiring) (:fv _uniq.33617) (:fv _uniq.33623) ((:c Semifield.toCommSemiring) (:fv _uniq.33... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.33617))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"V","sexp":"((:c Set) (:forall _ (:fv _uniq.33623) (:fv _uniq.33617)))"},{"name":"p","sexp":"((:c MvPolynomial) (:fv _uniq.33623) (:fv _uniq.33617) ((:c Semifield.toCommSemir... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PrimeSpectrum) (:arg :explicit 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c CommSemiring) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33617","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.33620","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Field) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7255,"sourceStart":7250,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":7259,"sourceStart":7256,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"x","sourceEnd":7260,"sourceStart":7259,"tag":"identifier"},... | [] | [{"source":"⟨x, ⟨hx, rfl⟩⟩","source_end":7278,"source_start":7256,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.33617","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.33620","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 42 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eea531e59ad67b7043597c6283f8798eeda694720a288c8636028bc9e189ff3a | 563cc0b571d9a3a23d99b79ee61aa4eea396e95bc86c38e468087a924048539b | f7d5b14f2557cfa4935138077b5746771ab362cbcff219bad79ae467f5c229fe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,666 | List.permutationsAux_cons | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.permutationsAux</a>, <a>List.permutationsAux.rec</a>] | α : Type u_1
β : Type u_2
t : α
ts is : List α
⊢ (t :: ts).permutationsAux is =
foldr (fun y r => (permutationsAux2 t ts r y id).2) (ts.permutationsAux (t :: is)) is.permutations | α : Type u_1
β : Type u_2
t : α
ts is : List α
⊢ foldr (fun y r => (permutationsAux2 t ts r y id).2)
(permutationsAux.rec (fun x => [])
(fun t ts is IH1 IH2 => foldr (fun y r => (permutationsAux2 t ts r y id).2) IH1 (is :: IH2)) ts (t :: is))
(is ::
permutationsAux.rec (fun x => [])
... | ((:c Eq) ((:c List) ((:c List) (:fv _uniq.16850))) ((:c List.permutationsAux) (:fv _uniq.16850) ((:c List.cons) (:fv _uniq.16850) (:fv _uniq.16909) (:fv _uniq.16910)) (:fv _uniq.16911)) ((:c List.foldr) ((:c List) (:fv _uniq.16850)) ((:c List) ((:c List) (:fv _uniq.16850))) (:lambda y ((:c List) (:fv _uniq.16850)) (:la... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"t","sexp":"(:fv _uniq.16850)"},{"name":"ts","sexp":"((:c List) (:fv _uniq.16850))"},{"name":"is","sexp":"((:c List) (:fv _uniq.16850))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c List.permutationsAux) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"rw","sourceEnd":10959,"sourceStart":10957,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10961,"sourceStart":10960,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"List.permutation... | [] | [{"source":"permutationsAux","source_end":10976,"source_start":10961,"syntax_kind":"ident"},{"source":"permutationsAux.rec","source_end":10997,"source_start":10978,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 44 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | afec7b30bd05d59b4a14a3ce0467a6b1e05ddf00a461a3181f18da7e04cd3871 | 88e1bf4ec6a0a3d8afd14491473540a5c97cacb5441d610ca8be31de1026f80c | e0bd8f1a9fecb1cf384388bf5e98ea519f6e7fe5dcf393ac768ac4143314b5c3 | 2514ed69a0c30881ea947f687dba634894631368d6efcd229f5b5848ede7c0ca |
cat-searcher/leandojo-benchmark-4-random | test | 3,667 | List.permutationsAux_cons | Mathlib/Data/List/Permutation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
β : Type u_2
t : α
ts is : List α
⊢ foldr (fun y r => (permutationsAux2 t ts r y id).2)
(permutationsAux.rec (fun x => [])
(fun t ts is IH1 IH2 => foldr (fun y r => (permutationsAux2 t ts r y id).2) IH1 (is :: IH2)) ts (t :: is))
(is ::
permutationsAux.rec (fun x => [])
... | ((:c Eq) ((:c List) ((:c List) (:fv _uniq.16850))) ((:c List.foldr) ((:c List) (:fv _uniq.16850)) ((:c List) ((:c List) (:fv _uniq.16850))) (:lambda y ((:c List) (:fv _uniq.16850)) (:lambda r ((:c List) ((:c List) (:fv _uniq.16850))) ((:c Prod.snd) ((:c List) (:fv _uniq.16850)) ((:c List) ((:c List) (:fv _uniq.16850)))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"t","sexp":"(:fv _uniq.16850)"},{"name":"ts","sexp":"((:c List) (:fv _uniq.16850))"},{"name":"is","sexp":"((:c List) (:fv _uniq.16850))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))))) (:arg :explicit 1 (:app (:c List.foldr) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16850","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","con... | {"children":[{"source":"rfl","sourceEnd":11003,"sourceStart":11000,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":11003,"sourceStart":11000,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16850","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16853","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 44 | 9 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a60e60bec6366c7f2800daaf6e52a855fdde4ee0946cb358b05882794fca021b | 2514ed69a0c30881ea947f687dba634894631368d6efcd229f5b5848ede7c0ca | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,668 | Nat.factorization_eq_zero_of_not_dvd | Mathlib/Data/Nat/Factorization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Nat.factorization_eq_zero_iff</a>, h] | a b m n✝ p✝ n p : ℕ
h : ¬p ∣ n
⊢ n.factorization p = 0 | ((:c Eq) (:c Nat) ((:c DFunLike.coe) ((:c Finsupp) (:c Nat) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instLinearOrderedCommMonoidWithZero))) (:c Nat) (:lambda _ (:c Nat) (:c Nat)) ((:c Finsupp.instFunLike) (:c Nat) (:c Nat) ((:c LinearOrderedCommMonoidWithZero.toZero) (:c Nat) (:c Nat.instL... | [{"name":"a","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"p✝","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"p","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.22392) (:fv _uniq.2... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Nat))))))) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit 2) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22306","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22308","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6152,"sourceStart":6148,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"factorization_eq_zero_iff","source_end":6179,"source_start":6154,"syntax_kind":"ident"},{"source":"h","source_end":6182,"source_start":6181,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22306","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22308","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 38 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 18dcceaaeb31bdeb630d2686289dce990075bba23b69617cc482847a385f45fa | 7ac211b7645d635b676464225d10301cd8bb09641e26e74cef4863332cb95a33 | 8c6baa40c425328e2e86c0d471d324a4fefda73ba840b6dc8daa59d5aa8d754e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,669 | Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h := <a>Field.lift_rank_mul_lift_sepDegree_of_isSeparable</a> F (<a>separableClosure</a> F E) K | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : Algebra.IsAlgebraic F E
⊢ Cardinal.lift.{w, v} (sepDegree F E) * Cardinal.lift.{v, w} (sepDegree E K) = Cardinal.lift.{v, w} (sepDegree ... | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : Algebra.IsAlgebraic F E
h :
Cardinal.lift.{w, v} (Module.rank F ↥(separableClosure F E)) *
Cardinal.lift.{v, w} (sepDegree (↥(se... | ((:c Eq) (:c Cardinal) ((:c HMul.hMul) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHMul) (:c Cardinal) (:c Cardinal.instMul)) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _uniq.272836) (:fv _uniq.272838) (:fv _uniq.272841) (:fv _uniq.272844) (:fv _uniq.272931))) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.272836))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.272838))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.272836) (:fv _uniq.272838) ((:c Semifield.toCommSemiring) (:fv _uniq.272836... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Cardinal)) (:arg :explicit 1 (:c Cardinal)) (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":52440,"sourceStart":52436,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":52442,"sourceStart":52441,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":52442,"sourceStart":52441,"tag":"node"... | [] | [{"source":"lift_rank_mul_lift_sepDegree_of_isSeparable F (separableClosure F E) K","source_end":52516,"source_start":52446,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal... | 128 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b53b56fc6d03efa44d1ffba99220041f7d000dcade941e99029d3da69d477acc | 5be2ca3c46089e118783711eb1dd0ada3ced639a7aace3edd417fd9a76c117ef | 448166e9e7bbd7890510cd8e54aeab113027079148a784c44f83b3096cd76ada | 7bcf6b23b3d385423b14216fe2c5e9d4934e0997ba59311a4439e30ca366d878 |
cat-searcher/leandojo-benchmark-4-random | test | 3,670 | Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>separableClosure.isPurelyInseparable</a> F E | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : Algebra.IsAlgebraic F E
h :
Cardinal.lift.{w, v} (Module.rank F ↥(separableClosure F E)) *
Cardinal.lift.{v, w} (sepDegree (↥(se... | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : Algebra.IsAlgebraic F E
h :
Cardinal.lift.{w, v} (Module.rank F ↥(separableClosure F E)) *
Cardinal.lift.{v, w} (sepDegree (↥(se... | ((:c Eq) (:c Cardinal) ((:c HMul.hMul) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHMul) (:c Cardinal) (:c Cardinal.instMul)) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _uniq.272836) (:fv _uniq.272838) (:fv _uniq.272841) (:fv _uniq.272844) (:fv _uniq.272931))) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.272836))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.272838))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.272836) (:fv _uniq.272838) ((:c Semifield.toCommSemiring) (:fv _uniq.272836... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Cardinal)) (:arg :explicit 1 (:c Cardinal)) (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"haveI","sourceEnd":52524,"sourceStart":52519,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":52525,"sourceStart":52525,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":52525,"sourceStart":52525,"tag":"node"}],"kind":"Lean.Parser.Term.ha... | [] | [{"source":"separableClosure.isPurelyInseparable F E","source_end":52568,"source_start":52528,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal... | 128 | 5 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b22e85f9486a1f5eaf0fc8808a422a0fb1acc32ff7c4c34d6cba90c2e20eee91 | 7bcf6b23b3d385423b14216fe2c5e9d4934e0997ba59311a4439e30ca366d878 | 2d2af2043434075942e9dea4d78e88f7099b4ce9e23cefaf1a7c4ced151e78c6 | 32adb1ba769cef3a28841339487af75721ebf27be65957f3ffdac74867510fad |
cat-searcher/leandojo-benchmark-4-random | test | 3,671 | Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic | Mathlib/FieldTheory/PurelyInseparable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Field.sepDegree_eq_of_isPurelyInseparable</a> (<a>separableClosure</a> F E) E K] at h | F : Type u
E : Type v
inst✝⁷ : Field F
inst✝⁶ : Field E
inst✝⁵ : Algebra F E
K : Type w
inst✝⁴ : Field K
inst✝³ : Algebra F K
inst✝² : Algebra E K
inst✝¹ : IsScalarTower F E K
inst✝ : Algebra.IsAlgebraic F E
h :
Cardinal.lift.{w, v} (Module.rank F ↥(separableClosure F E)) *
Cardinal.lift.{v, w} (sepDegree (↥(se... | ((:c Eq) (:c Cardinal) ((:c HMul.hMul) (:c Cardinal) (:c Cardinal) (:c Cardinal) ((:c instHMul) (:c Cardinal) (:c Cardinal.instMul)) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _uniq.272836) (:fv _uniq.272838) (:fv _uniq.272841) (:fv _uniq.272844) (:fv _uniq.272931))) ((:c Cardinal.lift) ((:c Field.sepDegree) (:fv _... | [{"name":"F","sexp":"(:sort (+ u 1))"},{"name":"E","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁷","sexp":"((:c Field) (:fv _uniq.272836))"},{"name":"inst✝⁶","sexp":"((:c Field) (:fv _uniq.272838))"},{"name":"inst✝⁵","sexp":"((:c Algebra) (:fv _uniq.272836) (:fv _uniq.272838) ((:c Semifield.toCommSemiring) (:fv _uniq.272836... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Cardinal)) (:arg :implicit-type 1 (:c Cardinal)) (:arg :implicit-type 2 (:c Cardinal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Cardinal)) (:arg :explicit 1 (:c Cardinal)) (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rwa","sourceEnd":52574,"sourceStart":52571,"tag":"atom"},{"children":[{"source":"[","sourceEnd":52576,"sourceStart":52575,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Field.sepDegree_eq_of_isPurelyInseparable","semanticRole"... | [] | [{"source":"h","source_end":52644,"source_start":52643,"syntax_kind":"ident"},{"source":"sepDegree_eq_of_isPurelyInseparable (separableClosure F E) E K","source_end":52638,"source_start":52576,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.272836","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.272838","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal... | 128 | 6 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 453eb8dcf77a15c65685116f1560b8e11f75d9afcc998c36a4946da779b0a108 | 32adb1ba769cef3a28841339487af75721ebf27be65957f3ffdac74867510fad | 086a67856c527a5ab4e8f6c9a1fdbba954313a9d929edfd0d4c9261dfb6882e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,672 | HasLineDerivAt.le_of_lipschitzOn | Mathlib/Analysis/Calculus/LineDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hf.le_of_lip' C.coe_nonneg ?_ | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
F : Type u_2
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
E : Type u_3
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
f✝ f₀ f₁ : E → F
f'✝ : F
s✝ t : Set E
x v : E
L : E →L[𝕜] F
f : E → F
f' : F
x₀ : E
hf : HasLineDerivAt 𝕜 f f' x₀ v
s : Set E
hs : ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
F : Type u_2
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
E : Type u_3
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
f✝ f₀ f₁ : E → F
f'✝ : F
s✝ t : Set E
x v : E
L : E →L[𝕜] F
f : E → F
f' : F
x₀ : E
hf : HasLineDerivAt 𝕜 f f' x₀ v
s : Set E
hs : ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.250086) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.250086) (:fv _uniq.250089)) (:fv _uniq.253146)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c NNReal.toReal) (:fv _uniq.253151)) ((:c Norm.norm) (:fv _uni... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.250080))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.250086))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.250080) (:fv _uniq.250086) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV19)))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.250080","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.250083","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"refine","sourceEnd":20088,"sourceStart":20082,"tag":"atom"},{"children":[{"source":"hf.le_of_lip'","sourceEnd":20102,"sourceStart":20089,"tag":"identifier"},{"children":[{"name":"NNReal.coe_nonneg","semanticRole":"global","source":"C.coe_nonneg","sourceEnd":20115,"sourceStart":20103,"tag":"ident... | [] | [{"source":"hf.le_of_lip' C.coe_nonneg ?_","source_end":20118,"source_start":20089,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.250080","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.250083","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 75 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 98fec9b1ea9d6b30638c927e5a8772bd8deb0d9966f9f25374d669db0301ae37 | a680ba6e789f42dfb5303b2213fc64f24a39a58451c147c9ed4ae0f5d2b0c4e5 | 262448de2a8f1abfb1d1e23e39a7ebce5f6d72608ce9ed53cdd9e4106d4e9e6e | dfbb798359a3ce29911845dc38a0c47e2c2bd7df6c2897d43467e30b8ad7741f |
cat-searcher/leandojo-benchmark-4-random | test | 3,673 | HasLineDerivAt.le_of_lipschitzOn | Mathlib/Analysis/Calculus/LineDeriv/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hs] with x hx using hlip.norm_sub_le hx (<a>mem_of_mem_nhds</a> hs) | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
F : Type u_2
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
E : Type u_3
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
f✝ f₀ f₁ : E → F
f'✝ : F
s✝ t : Set E
x v : E
L : E →L[𝕜] F
f : E → F
f' : F
x₀ : E
hf : HasLineDerivAt 𝕜 f f' x₀ v
s : Set E
hs : ... | ((:c Filter.Eventually) (:fv _uniq.250200) (:lambda x (:fv _uniq.250200) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.250086) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.250086) (:fv _uniq.250089)) ((:c HSub.hSub) (:fv _uniq.250086) (:fv _uniq.250086) (:fv _uniq.250086) ((:c instHSub) (:fv _uniq.250... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.250080))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.250086))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.250080) (:fv _uniq.250086) ((:c Non... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV2)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.250080","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.250083","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"filter_upwards","sourceEnd":20135,"sourceStart":20121,"tag":"atom"},{"children":[{"source":"[","sourceEnd":20137,"sourceStart":20136,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"hs","sourceEnd":20139,"sourceStart":20137,"tag":"identifier"}],"kind":"null","source... | [] | [{"source":"hs","source_end":20139,"source_start":20137,"syntax_kind":"ident"},{"source":"hlip.norm_sub_le hx (mem_of_mem_nhds hs)","source_end":20197,"source_start":20157,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.250080","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.250083","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 75 | 5 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d1fcdedc6fa6bb31b7b6c70b0c5b822af073fc6d35ab71f62f8b269c1b1d274 | dfbb798359a3ce29911845dc38a0c47e2c2bd7df6c2897d43467e30b8ad7741f | 8891e27ce6e3d1c3ab49905b2d6a3e638f8dea1fdef94cb148ca3d48969fc47e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,674 | LinearIndependent.cardinal_mk_le_finrank | Mathlib/LinearAlgebra/Dimension/Finite.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Cardinal.lift_le</a>.{max v w}] | R : Type u
M M₁ : Type v
M' : Type v'
ι✝ : Type w
inst✝⁸ : Ring R
inst✝⁷ : AddCommGroup M
inst✝⁶ : AddCommGroup M'
inst✝⁵ : AddCommGroup M₁
inst✝⁴ : Module R M
inst✝³ : Module R M'
inst✝² : Module R M₁
inst✝¹ : StrongRankCondition R
inst✝ : Module.Finite R M
ι : Type w
b : ι → M
h : LinearIndependent R b
⊢ #ι ≤ ↑(finra... | R : Type u
M M₁ : Type v
M' : Type v'
ι✝ : Type w
inst✝⁸ : Ring R
inst✝⁷ : AddCommGroup M
inst✝⁶ : AddCommGroup M'
inst✝⁵ : AddCommGroup M₁
inst✝⁴ : Module R M
inst✝³ : Module R M'
inst✝² : Module R M₁
inst✝¹ : StrongRankCondition R
inst✝ : Module.Finite R M
ι : Type w
b : ι → M
h : LinearIndependent R b
⊢ lift.{max v ... | ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.mk) (:fv _uniq.155186)) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) ((:c FiniteDimensional.finrank) (:fv _uniq.152035) (:fv _uniq.152037) ((:c Ring.toSemiring) (:fv _uniq.152035) (:fv _uniq.152046)) (:fv _uniq.152049) (:fv _uniq.152689)))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"M₁","sexp":"(:sort (+ v 1))"},{"name":"M'","sexp":"(:sort (+ v' 1))"},{"name":"ι✝","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁸","sexp":"((:c Ring) (:fv _uniq.152035))"},{"name":"inst✝⁷","sexp":"((:c AddCommGroup) (:fv _uniq.152037))"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.mk) (:arg :explicit 0 (:fv FV15)))) (:arg :explicit 3 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152035","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152037","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":6582,"sourceStart":6580,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6584,"sourceStart":6583,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6587,"sourceStart":... | [] | [{"source":"lift_le.{max v w}","source_end":6605,"source_start":6588,"syntax_kind":"Lean.Parser.Term.explicitUniv"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152035","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152037","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 48 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe6821620f46b4c5b35cea5d511cca5f9134e7c5aeebd6c52f3c36f407bee0ee | e6eb4b6afabb5810a008d63e08c300cd8d5881350a338c7b6ca76da38d8817ae | c4cc1f677b25a842db7ac59a2ad9cc73ccec31356021f087d1a831a97fb00583 | 173afa0e290a3ae8039a07e3828e7780bc1b1ea8bea38266ca5ec324a68a90b8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,675 | LinearIndependent.cardinal_mk_le_finrank | Mathlib/LinearAlgebra/Dimension/Finite.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>finrank_eq_rank</a>, <a>Cardinal.lift_natCast</a>, <a>Cardinal.lift_le_nat_iff</a>] using h.cardinal_lift_le_rank | R : Type u
M M₁ : Type v
M' : Type v'
ι✝ : Type w
inst✝⁸ : Ring R
inst✝⁷ : AddCommGroup M
inst✝⁶ : AddCommGroup M'
inst✝⁵ : AddCommGroup M₁
inst✝⁴ : Module R M
inst✝³ : Module R M'
inst✝² : Module R M₁
inst✝¹ : StrongRankCondition R
inst✝ : Module.Finite R M
ι : Type w
b : ι → M
h : LinearIndependent R b
⊢ lift.{max v ... | ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.lift) ((:c Cardinal.mk) (:fv _uniq.155186))) ((:c Cardinal.lift) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) ((:c FiniteDimensional.finrank) (:fv _uniq.152035) (:fv _uniq.152037) ((:c Ring.toSemiring) (:fv _uniq.152035) (:fv _uniq.152046)) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"M₁","sexp":"(:sort (+ v 1))"},{"name":"M'","sexp":"(:sort (+ v' 1))"},{"name":"ι✝","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁸","sexp":"((:c Ring) (:fv _uniq.152035))"},{"name":"inst✝⁷","sexp":"((:c AddCommGroup) (:fv _uniq.152037))"},{... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.lift) (:arg :explicit 0 (:app (:c Cardinal.mk) (:arg :explicit 0 (:fv FV15)))))) (:arg :explicit 3 (:app (:c Cardinal.lift) (:arg :explicit 0 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152035","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152037","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simpa","sourceEnd":6614,"sourceStart":6609,"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":"finrank_eq_rank","source_end":6640,"source_start":6625,"syntax_kind":"ident"},{"source":"lift_natCast","source_end":6654,"source_start":6642,"syntax_kind":"ident"},{"source":"lift_le_nat_iff","source_end":6671,"source_start":6656,"syntax_kind":"ident"},{"source":"h.cardinal_lift_le_rank","source_end":6702,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.152035","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.152037","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 48 | 7 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80a767d4e1bce0b1d7d513fe97d72397d74eaf86510d25c89a1d1b3ff5beea77 | 173afa0e290a3ae8039a07e3828e7780bc1b1ea8bea38266ca5ec324a68a90b8 | f7b5e6e27c70e71d700afbcc10abbf63bca1995b345dfde61872eccf97514fb6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,676 | prime_dvd_prime_iff_eq | Mathlib/Algebra/Associated.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [pp.dvd_prime_iff_associated qp, ← <a>associated_eq_eq</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : Monoid α
inst✝² : Unique αˣ
M : Type u_5
inst✝¹ : CancelCommMonoidWithZero M
inst✝ : Unique Mˣ
p q : M
pp : Prime p
qp : Prime q
⊢ p ∣ q ↔ p = q | ((:c Iff) ((:c Dvd.dvd) (:fv _uniq.105951) ((:c semigroupDvd) (:fv _uniq.105951) ((:c SemigroupWithZero.toSemigroup) (:fv _uniq.105951) ((:c MonoidWithZero.toSemigroupWithZero) (:fv _uniq.105951) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.105951) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.105687))"},{"name":"inst✝²","sexp":"((:c Unique) ((:c Units) (:fv _uniq.105687) (:fv _uniq.105699)))"},{"name"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:fv FV7)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:fv FV7))))) (:arg :explicit 2 (:fv FV10)) (:arg :explicit 3 (:fv FV11)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:fv FV10... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.105687","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.105690","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":33443,"sourceStart":33441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":33445,"sourceStart":33444,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"pp.dvd_prime_iff_associated qp","source_end":33475,"source_start":33445,"syntax_kind":"Lean.Parser.Term.app"},{"source":"associated_eq_eq","source_end":33497,"source_start":33481,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.105687","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.105690","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 241 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 81ccdb95d6552765e1f767154684e9609c1c304284d8ac408a1c23504514db29 | b0036c927f7d2777559248e2c8368aafce53ae1e3a27a342e83b0527ad542eef | e061668169a26cd661bb08c16a2f79a86c16a90511a40ce986f11627c698f7ce | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,677 | NNRat.add_def | Mathlib/Data/NNRat/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | p q✝ : ℚ≥0
n₁ n₂ d₁ d₂ d : ℕ
q r : ℚ≥0
⊢ q + r = divNat (q.num * r.den + r.num * q.den) (q.den * r.den) | case a
p q✝ : ℚ≥0
n₁ n₂ d₁ d₂ d : ℕ
q r : ℚ≥0
⊢ ↑(q + r) = ↑(divNat (q.num * r.den + r.num * q.den) (q.den * r.den)) | ((:c Eq) (:c NNRat) ((:c HAdd.hAdd) (:c NNRat) (:c NNRat) (:c NNRat) ((:c instHAdd) (:c NNRat) ((:c Distrib.toAdd) (:c NNRat) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c NNRat) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNRat) ((:c Semiring.toNonAssocSemiring) (:c NNRat) ((:c OrderedSemiring.toSemiring) (... | [{"name":"p","sexp":"(:c NNRat)"},{"name":"q✝","sexp":"(:c NNRat)"},{"name":"n₁","sexp":"(:c Nat)"},{"name":"n₂","sexp":"(:c Nat)"},{"name":"d₁","sexp":"(:c Nat)"},{"name":"d₂","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"q","sexp":"(:c NNRat)"},{"name":"r","sexp":"(:c NNRat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c NNRat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c NNRat)) (:arg :implicit-type 1 (:c NNRat)) (:arg :implicit-type 2 (:c NNRat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c NNRat)) (:arg :explicit 1 (:c NNRat)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51560","is_instance":false,"is_let":false,"name":"p","sexp":"(:c NNRat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51562","is_instance":false,"is_let":false,"name":"q✝","sexp":"(:c NNRat)"},{"binder_role":":implicit","contex... | {"children":[{"source":"ext","sourceEnd":16175,"sourceStart":16172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":16175,"sourceStart":16172,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51560","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51562","is_instance":false,"is_let":false,"user_name":"q✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 176 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73aef9958542da45482db2f995f50f664b15e208e556a542d3ba7b67562a639e | 4557b7e56affa7841caf15d87c41a56d720be532613538a0cd6ee03434e0d96c | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 2e54a1c1f93d0075ace2c4d5240f29d238552c0ff55192fff6f346a2f40264e3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,678 | NNRat.add_def | Mathlib/Data/NNRat/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rat.add_def'</a>, <a>Rat.mkRat_eq_divInt</a>, <a>NNRat.num_coe</a>, <a>NNRat.den_coe</a>] | case a
p q✝ : ℚ≥0
n₁ n₂ d₁ d₂ d : ℕ
q r : ℚ≥0
⊢ ↑(q + r) = ↑(divNat (q.num * r.den + r.num * q.den) (q.den * r.den)) | ((:c Eq) (:c Rat) ((:c NNRat.cast) (:c Rat) (:c Rat.instNNRatCast) ((:c HAdd.hAdd) (:c NNRat) (:c NNRat) (:c NNRat) ((:c instHAdd) (:c NNRat) ((:c Distrib.toAdd) (:c NNRat) ((:c NonUnitalNonAssocSemiring.toDistrib) (:c NNRat) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:c NNRat) ((:c Semiring.toNonAssocSemiring... | [{"name":"p","sexp":"(:c NNRat)"},{"name":"q✝","sexp":"(:c NNRat)"},{"name":"n₁","sexp":"(:c Nat)"},{"name":"n₂","sexp":"(:c Nat)"},{"name":"d₁","sexp":"(:c Nat)"},{"name":"d₂","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"q","sexp":"(:c NNRat)"},{"name":"r","sexp":"(:c NNRat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c NNRat.cast) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c NNRatCast) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c NNRat)) (:arg :implicit-type 1 (:c NNRat)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51560","is_instance":false,"is_let":false,"name":"p","sexp":"(:c NNRat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51562","is_instance":false,"is_let":false,"name":"q✝","sexp":"(:c NNRat)"},{"binder_role":":implicit","contex... | {"children":[{"source":"simp","sourceEnd":16181,"sourceStart":16177,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16183,"sourceStart":16182,"tag":"a... | [] | [{"source":"Rat.add_def'","source_end":16195,"source_start":16183,"syntax_kind":"ident"},{"source":"Rat.mkRat_eq_divInt","source_end":16216,"source_start":16197,"syntax_kind":"ident"},{"source":"num_coe","source_end":16225,"source_start":16218,"syntax_kind":"ident"},{"source":"den_coe","source_end":16234,"source_start"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.51560","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.51562","is_instance":false,"is_let":false,"user_name":"q✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 176 | 6 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 594cadd3484de5655552c222b7f2db4ca7097dfd51ad9920960f9f87fc2e3756 | 2e54a1c1f93d0075ace2c4d5240f29d238552c0ff55192fff6f346a2f40264e3 | 148e79d1590d0ff79383865f1a57db67eb0297276585b4f12e78a69c26aaf50a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,679 | dualTensorHomEquivOfBasis_apply | Mathlib/LinearAlgebra/Contraction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | ι : Type w
R : Type u
M : Type v₁
N : Type v₂
P : Type v₃
Q : Type v₄
inst✝¹⁰ : CommRing R
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : AddCommGroup P
inst✝⁶ : AddCommGroup Q
inst✝⁵ : Module R M
inst✝⁴ : Module R N
inst✝³ : Module R P
inst✝² : Module R Q
inst✝¹ : DecidableEq ι
inst✝ : Fintype ι
b : Basis ι ... | case h
ι : Type w
R : Type u
M : Type v₁
N : Type v₂
P : Type v₃
Q : Type v₄
inst✝¹⁰ : CommRing R
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : AddCommGroup P
inst✝⁶ : AddCommGroup Q
inst✝⁵ : Module R M
inst✝⁴ : Module R N
inst✝³ : Module R P
inst✝² : Module R Q
inst✝¹ : DecidableEq ι
inst✝ : Fintype ι
b : B... | ((:c Eq) ((:c LinearMap) (:fv _uniq.141170) (:fv _uniq.141170) ((:c CommSemiring.toSemiring) (:fv _uniq.141170) ((:c CommRing.toCommSemiring) (:fv _uniq.141170) (:fv _uniq.141181))) ((:c CommSemiring.toSemiring) (:fv _uniq.141170) ((:c CommRing.toCommSemiring) (:fv _uniq.141170) (:fv _uniq.141181))) ((:c RingHom.id) (:... | [{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v₁ 1))"},{"name":"N","sexp":"(:sort (+ v₂ 1))"},{"name":"P","sexp":"(:sort (+ v₃ 1))"},{"name":"Q","sexp":"(:sort (+ v₄ 1))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.141170))"},{"name":"inst✝⁹","sexp":... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 4 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141168","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141170","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":7455,"sourceStart":7452,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":7455,"sourceStart":7452,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141168","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141170","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 48 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7eab834326f6a77af60d96db7cda49b6fe4b6a80ed835c424d1c7919ffeeae5 | 57795b426a246f24d6244d137195e0daf321f417958ceb10f50f1e024fe7dde0 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | e192c62b76b3bdc08f23c293cb4c14c7a7cd977406f9697bf62f7a6dd7f7f82a |
cat-searcher/leandojo-benchmark-4-random | test | 3,680 | dualTensorHomEquivOfBasis_apply | Mathlib/LinearAlgebra/Contraction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h
ι : Type w
R : Type u
M : Type v₁
N : Type v₂
P : Type v₃
Q : Type v₄
inst✝¹⁰ : CommRing R
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : AddCommGroup P
inst✝⁶ : AddCommGroup Q
inst✝⁵ : Module R M
inst✝⁴ : Module R N
inst✝³ : Module R P
inst✝² : Module R Q
inst✝¹ : DecidableEq ι
inst✝ : Fintype ι
b : B... | ((:c Eq) (:fv _uniq.141174) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.141170) (:fv _uniq.141170) ((:c CommSemiring.toSemiring) (:fv _uniq.141170) ((:c CommRing.toCommSemiring) (:fv _uniq.141170) (:fv _uniq.141181))) ((:c CommSemiring.toSemiring) (:fv _uniq.141170) ((:c CommRing.toCommSemiring) (:fv _uniq.141170) (:... | [{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"M","sexp":"(:sort (+ v₁ 1))"},{"name":"N","sexp":"(:sort (+ v₂ 1))"},{"name":"P","sexp":"(:sort (+ v₃ 1))"},{"name":"Q","sexp":"(:sort (+ v₄ 1))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.141170))"},{"name":"inst✝⁹","sexp":... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141168","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141170","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":7460,"sourceStart":7457,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":7460,"sourceStart":7457,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141168","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141170","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 48 | 6 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30ba783b1fd074e42ca1ab1807b57e13b7c1b71f77606cf6d3eb4ed3921b4314 | e192c62b76b3bdc08f23c293cb4c14c7a7cd977406f9697bf62f7a6dd7f7f82a | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,681 | FloorRing.exists_prime_mul_pow_div_factorial_lt_one | Mathlib/Algebra/Order/Floor/Prime.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>div_lt_one</a> (α := K) (Nat.cast_pos.mpr (<a>Nat.factorial_pos</a> _))] | K : Type u_1
inst✝¹ : LinearOrderedField K
inst✝ : FloorRing K
n : ℕ
a c : K
⊢ ∃ p > n, Nat.Prime p ∧ a * c ^ p / ↑(p - 1)! < 1 | K : Type u_1
inst✝¹ : LinearOrderedField K
inst✝ : FloorRing K
n : ℕ
a c : K
⊢ ∃ p > n, Nat.Prime p ∧ a * c ^ p < ↑(p - 1)! | ((:c Exists) (:c Nat) (:lambda p (:c Nat) ((:c And) ((:c GT.gt) (:c Nat) (:c instLTNat) 0 (:fv _uniq.14887)) ((:c And) ((:c Nat.Prime) 0) ((:c LT.lt) (:fv _uniq.14174) ((:c Preorder.toLT) (:fv _uniq.14174) ((:c PartialOrder.toPreorder) (:fv _uniq.14174) ((:c StrictOrderedRing.toPartialOrder) (:fv _uniq.14174) ((:c Line... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.14174))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.14174) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.14174) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.14174) (:fv _uniq.14885)... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda p :explicit (:c Nat) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 (:fv FV4)))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14174","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.14885","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:a... | {"children":[{"source":"simp_rw","sourceEnd":1316,"sourceStart":1309,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1318,"sourceStart":1317,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"di... | [] | [{"source":"div_lt_one (α := K) (Nat.cast_pos.mpr (Nat.factorial_pos _))","source_end":1379,"source_start":1318,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14174","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.14885","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 5 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42f6884412e6cce1f7f8c877583d7521ec6f54325cc5ca92c8b1c842b353eaa6 | 520d9c7ad69e5713bd222d5ab2e0f67a2f178243ac180a0b97d8fb88d904b8f2 | e7fc2f273283b6cadceccd6ec83dbf8332bc79b8c8d01cfa140accecfd836816 | 97d4875655428e270523efb0a03706e6f84cf0d448dece5b9eaf0096b9917db4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,682 | FloorRing.exists_prime_mul_pow_div_factorial_lt_one | Mathlib/Algebra/Order/Floor/Prime.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>FloorRing.exists_prime_mul_pow_lt_factorial</a> .. | K : Type u_1
inst✝¹ : LinearOrderedField K
inst✝ : FloorRing K
n : ℕ
a c : K
⊢ ∃ p > n, Nat.Prime p ∧ a * c ^ p < ↑(p - 1)! | ((:c Exists) (:c Nat) (:lambda p (:c Nat) ((:c And) ((:c GT.gt) (:c Nat) (:c instLTNat) 0 (:fv _uniq.14887)) ((:c And) ((:c Nat.Prime) 0) ((:c LT.lt) (:fv _uniq.14174) ((:c Preorder.toLT) (:fv _uniq.14174) ((:c PartialOrder.toPreorder) (:fv _uniq.14174) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.14174) ((:c ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedField) (:fv _uniq.14174))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.14174) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:fv _uniq.14174) ((:c LinearOrderedField.toLinearOrderedCommRing) (:fv _uniq.14174) (:fv _uniq.14885)... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda p :explicit (:c Nat) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 (:fv FV4)))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14174","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.14885","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrderedField) (:a... | {"children":[{"source":"exact","sourceEnd":1388,"sourceStart":1383,"tag":"atom"},{"children":[{"name":"FloorRing.exists_prime_mul_pow_lt_factorial","semanticRole":"global","source":"exists_prime_mul_pow_lt_factorial","sourceEnd":1422,"sourceStart":1389,"tag":"identifier"},{"children":[{"children":[{"source":"..","sourc... | [] | [{"source":"exists_prime_mul_pow_lt_factorial ..","source_end":1425,"source_start":1389,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14174","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.14885","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 5 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 235598d8c2488af66089497982cbd015a495348b78da39c6bde43fdd4db0353a | 97d4875655428e270523efb0a03706e6f84cf0d448dece5b9eaf0096b9917db4 | a23fe217201cb8f80c2a1e882d768e6890e39d690c3de398dd89f02322a5d18f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,683 | Option.map₂_coe_right | Mathlib/Data/Option/NAry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases a <;> rfl | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
f✝ : α → β → γ
a✝ : Option α
b✝ : Option β
c : Option γ
f : α → β → γ
a : Option α
b : β
⊢ map₂ f a (some b) = Option.map (fun a => f a b) a | ((:c Eq) ((:c Option) (:fv _uniq.1523)) ((:c Option.map₂) (:fv _uniq.1517) (:fv _uniq.1520) (:fv _uniq.1523) (:fv _uniq.1667) (:fv _uniq.1668) ((:c Option.some) (:fv _uniq.1520) (:fv _uniq.1669))) ((:c Option.map) (:fv _uniq.1517) (:fv _uniq.1523) (:lambda a (:fv _uniq.1517) ((:fv _uniq.1667) 0 (:fv _uniq.1669))) (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.1517) (:forall _ (:fv _uniq.1520) (:fv _uniq.1523)))"},{"name":"a✝","sexp":"((:c Option) (:fv _uniq.1517))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Option.map₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV9)) (:arg :explicit 4 (:fv FV10)) (:arg :explicit 5 (:app (:c Opti... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1517","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1520","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":2857,"sourceStart":2852,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"a","sourceEnd":2859,"sourceStart":2858,"tag":"identifi... | [] | [{"source":"a","source_end":2859,"source_start":2858,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1517","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1520","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11143762cf57c79d8fa08a2f7eb56a425f4417d9a2e040b7730dfdd078b2df7f | ca4bafcfc093fa4c0d766860096a8c62547566e894a76ebc4ceb49a57e42f730 | b3a40cf9567e285a349c24133d705e1dd422023556f3f85526f5e056d54641c5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,684 | Fin.foldl_zero | .lake/packages/batteries/Batteries/Data/Fin/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Fin.foldl</a>, <a>Fin.foldl.loop</a>] | α : Sort u_1
f : α → Fin 0 → α
x : α
⊢ foldl 0 f x = x | ((:c Eq) (:fv _uniq.6805) ((:c Fin.foldl) (:fv _uniq.6805) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) (:fv _uniq.6806) (:fv _uniq.6807)) (:fv _uniq.6807)) | [{"name":"α","sexp":"(:sort u_1)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.6805) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:fv _uniq.6805)))"},{"name":"x","sexp":"(:fv _uniq.6805)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Fin.foldl) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6805","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6806","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV1) (:forall _ :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2808,"sourceStart":2804,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"foldl","source_end":2815,"source_start":2810,"syntax_kind":"ident"},{"source":"foldl.loop","source_end":2827,"source_start":2817,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6805","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.6806","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2062e82f09dc00be1f2a57161e71a9181512b787a24f5fba27fc084435bceefc | aa434888ee0df13795807b51e697c401474de20e6a3066df4b589af0b5667117 | df0fc5c3bf019b8fa3762914672a7660e6d80ee0f41b31a278929db3fd67b6c1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,685 | Complex.sin_add_sin | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>Complex.sin_sub_sin</a> x (-y) | x y : ℂ
⊢ sin x + sin y = 2 * sin ((x + y) / 2) * cos ((x - y) / 2) | ((:c Eq) (:c Complex) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) ((:c Complex.sin) (:fv _uniq.109958)) ((:c Complex.sin) (:fv _uniq.109960))) ((:c HMul.hMul) (:c Complex) (:c Complex) (:c Complex) ((:c instHMul) (:c Complex) (:c Complex.instMul)) ((:c HMul.h... | [{"name":"x","sexp":"(:c Complex)"},{"name":"y","sexp":"(:c Complex)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.109958","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.109960","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Complex)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":22182,"sourceStart":22177,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"sin_sub_sin x (-y)","source_end":22207,"source_start":22189,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.109958","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.109960","is_instance":false,"is_let":false,"user_name":"y"}] | 214 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80e69e61e35e7e110e488e778766b1b9669825de85bf2c099fe0b456332bb7d6 | 984b6104d50cdf7647c57ba1b9c51d956b876d30fe38d436840607c1fec9e3ed | a71c64ec7e3fb2695f1fea9dc3c17bb8bcde7f50caa5c78ce237de4f5c10a826 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,686 | Complex.monotone_ofReal | Mathlib/Data/Complex/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x y hxy | ⊢ Monotone ofReal' | x y : ℝ
hxy : x ≤ y
⊢ ↑x ≤ ↑y | ((:c Monotone) (:c Real) (:c Complex) (:c Real.instPreorder) ((:c PartialOrder.toPreorder) (:c Complex) (:c Complex.partialOrder)) (:c Complex.ofReal')) | [] | (:app (:c Monotone) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Complex)) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 4 (:c Complex.ofReal'))) | [] | {"children":[{"source":"intro","sourceEnd":4388,"sourceStart":4383,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":4390,"sourceStart":4389,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y","sourceEnd":4392,"sourceStart":4391,"tag":"identifier"},{"semanticRole":"scoped_lo... | [{"role":"fresh_name","source":"x","source_end":4390,"source_start":4389,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":4392,"source_start":4391,"syntax_kind":"ident"},{"role":"fresh_name","source":"hxy","source_end":4396,"source_start":4393,"syntax_kind":"ident"}] | [] | [] | 35 | 4 | exact | true | 1 | 0 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5bb44ce5132fdae3068fcad239bd8af2b33b59ef73b2683126fd26050ced0acf | 01b8d2f39f37cdf3054132b4274732005ebf7a0f75b18260aab0b534aa2ab1fb | 9d18871bcc40256d494e3c2910f4536b5629b313423890104c3b65cedfcfdac0 | 9725b8f85330a8cb245904c0840457af3d35e8e5493aab465f20dde8740654a5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,687 | Complex.monotone_ofReal | Mathlib/Data/Complex/Order.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.ofReal_eq_coe</a>, <a>Complex.real_le_real</a>, hxy] | x y : ℝ
hxy : x ≤ y
⊢ ↑x ≤ ↑y | ((:c LE.le) (:c Complex) ((:c Preorder.toLE) (:c Complex) ((:c PartialOrder.toPreorder) (:c Complex) (:c Complex.partialOrder))) ((:c Complex.ofReal') (:fv _uniq.7556)) ((:c Complex.ofReal') (:fv _uniq.7559))) | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"hxy","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) (:fv _uniq.7556) (:fv _uniq.7559))"}] | (:app (:c LE.le) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c Complex.ofReal') (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 3 (:app (:c Complex.ofReal') (:arg :explicit 0 (:fv FV2))))) | [{"binder_role":":strict-implicit","context_index":1,"internal_name":"_uniq.7556","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":strict-implicit","context_index":2,"internal_name":"_uniq.7559","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":explicit... | {"children":[{"source":"simp","sourceEnd":4403,"sourceStart":4399,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4408,"sourceStart":4404,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4408,"s... | [] | [{"source":"ofReal_eq_coe","source_end":4423,"source_start":4410,"syntax_kind":"ident"},{"source":"real_le_real","source_end":4437,"source_start":4425,"syntax_kind":"ident"},{"source":"hxy","source_end":4442,"source_start":4439,"syntax_kind":"ident"}] | [{"binder_role":":strict-implicit","context_index":1,"internal_name":"_uniq.7556","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":strict-implicit","context_index":2,"internal_name":"_uniq.7559","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":explicit","context_index":3,"interna... | 35 | 5 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1abb4c2ebe4824049e22116e41975bcf433da8c7364eb970e0929d21bb754f04 | 9725b8f85330a8cb245904c0840457af3d35e8e5493aab465f20dde8740654a5 | 2335851cd71c05d3e8a5b51e57d4f653ad3f19626c8d08d602ca67c866d0a932 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,688 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext y | R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCommGroup V
in... | case h
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCommGro... | ((:c Eq) ((:c Submodule) (:fv _uniq.245324) (:fv _uniq.245333) ((:c CommSemiring.toSemiring) (:fv _uniq.245324) ((:c CommRing.toCommSemiring) (:fv _uniq.245324) ((:c Field.toCommRing) (:fv _uniq.245324) (:fv _uniq.245345)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.245333) (:fv _uniq.245348)) (:fv _uniq.245888)) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV12)) (:arg :explicit 1 (:fv FV15)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV12))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV15))))) (:arg :instance 4 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext","sourceEnd":15628,"sourceStart":15625,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":15630,"sourceStart":15629,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"y","sourceEnd":15630,"sourceStart":15629,"tag... | [{"role":"fresh_name","source":"y","source_end":15630,"source_start":15629,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 4 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee7e707e750683b7cd898ce3acf1fc78d06e7c668a3c31af7dba5be41434350d | d0edfcd53395d167278293f138924b83412b9d134d33eb6fd8e1a040eddb3b13 | 37d49c45b1abbe86a4687a0eab685a29b148c16e65ed2a21b8d9a8fd1054d53a | 346a476523902d4cd6557fb8f9ef754c7804cbe359073ce44bcf8ef2b9f808af |
cat-searcher/leandojo-benchmark-4-random | test | 3,689 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Submodule.mem_orthogonalBilin_iff</a>, <a>LinearMap.mem_ker</a>, <a>Submodule.mem_span_singleton</a>] | case h
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCommGro... | case h
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCommGro... | ((:c Iff) ((:c Membership.mem) (:fv _uniq.245333) ((:c Submodule) (:fv _uniq.245324) (:fv _uniq.245333) ((:c CommSemiring.toSemiring) (:fv _uniq.245324) ((:c CommRing.toCommSemiring) (:fv _uniq.245324) ((:c Field.toCommRing) (:fv _uniq.245324) (:fv _uniq.245345)))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.245333) ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV15)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV12)) (:arg :explicit 1 (:fv FV15)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV12))))) (:arg :instance 3 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp_rw","sourceEnd":15640,"sourceStart":15633,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15642,"sourceStart":15641,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Submodule.m... | [] | [{"source":"Submodule.mem_orthogonalBilin_iff","source_end":15675,"source_start":15642,"syntax_kind":"ident"},{"source":"LinearMap.mem_ker","source_end":15694,"source_start":15677,"syntax_kind":"ident"},{"source":"Submodule.mem_span_singleton","source_end":15724,"source_start":15696,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 5 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 620c1836fcc383996f62e7892d18c3c0ac7c39c48fa370ecf3b256a829934ea6 | 346a476523902d4cd6557fb8f9ef754c7804cbe359073ce44bcf8ef2b9f808af | 87b19e6063f3fec82bacccaf79838095e554de76274bcb5b5d25db56454d87af | a140d086f610083c2e8fdc04f98e38a49be9c790243c4a78f00e887e052faa15 |
cat-searcher/leandojo-benchmark-4-random | test | 3,690 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case h
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCommGro... | case h.mp
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddComm... | ((:c Iff) (:forall n (:fv _uniq.245333) (:forall _ ((:c Exists) (:fv _uniq.245324) (:lambda a (:fv _uniq.245324) ((:c Eq) (:fv _uniq.245333) ((:c HSMul.hSMul) (:fv _uniq.245324) (:fv _uniq.245333) (:fv _uniq.245333) ((:c instHSMul) (:fv _uniq.245324) (:fv _uniq.245333) ((:c SMulZeroClass.toSMul) (:fv _uniq.245324) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:app (:c Iff) (:arg :explicit 0 (:forall n :explicit (:fv FV15) (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV12)) (:arg :explicit 1 (:lambda a :explicit (:fv FV12) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV15)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV12)) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"constructor","sourceEnd":15739,"sourceStart":15728,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":15739,"sourceStart":15728,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 10 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8acbacedefd6a1dc3fcdc9d0b351e0ca91c0d0af878029310aaf0d1a0c6a79fc | a140d086f610083c2e8fdc04f98e38a49be9c790243c4a78f00e887e052faa15 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 71caf4e1cc8028f11d4a259dcda89b8ea5e5697e153a9313cc37b353c6fed7c8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,691 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun h ↦ h x ⟨1, <a>one_smul</a> _ _⟩ | case h.mp
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddComm... | (:forall _ (:forall n (:fv _uniq.245333) (:forall _ ((:c Exists) (:fv _uniq.245324) (:lambda a (:fv _uniq.245324) ((:c Eq) (:fv _uniq.245333) ((:c HSMul.hSMul) (:fv _uniq.245324) (:fv _uniq.245333) (:fv _uniq.245333) ((:c instHSMul) (:fv _uniq.245324) (:fv _uniq.245333) ((:c SMulZeroClass.toSMul) (:fv _uniq.245324) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:forall _ :explicit (:forall n :explicit (:fv FV15) (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV12)) (:arg :explicit 1 (:lambda a :explicit (:fv FV12) (:app (:c Eq) (:arg :implicit-type 0 (:fv FV15)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV12)) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":15750,"sourceStart":15745,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":15754,"sourceStart":15751,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":15756,"sourceStart":15755,"tag":"id... | [] | [{"source":"fun h ↦ h x ⟨1, one_smul _ _⟩","source_end":15786,"source_start":15751,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 13 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 610fcc34f3bb38080f770f8362e5830a675b53d2cf6907d1c48e8cc2a59e1fad | b57dd02247b7eaaff2dfc911426c500497a63a13b9388815589b0aff68e6a36f | 0c5cad031b5445a7e801dc9aad08ad73a38c2d22b5ebfe5e09d3abc43abf0776 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,692 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro h _ ⟨z, rfl⟩ | case h.mpr
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : AddCom... | case h.mpr.intro
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : ... | (:forall _ ((:c Eq) (:fv _uniq.245339) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.245324) (:fv _uniq.245324) ((:c DivisionSemiring.toSemiring) (:fv _uniq.245324) ((:c Semifield.toDivisionSemiring) (:fv _uniq.245324) ((:c Field.toSemifield) (:fv _uniq.245324) (:fv _uniq.245345)))) ((:c DivisionSemiring.toSemiring) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:fv FV17)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV12)) (:arg :implicit-type 1 (:fv FV12)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV12))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rintro","sourceEnd":15798,"sourceStart":15792,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":15800,"sourceStart":15799,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"h","sourceEnd":15800,"sourceStart":15799,"... | [{"role":"fresh_name","source":"h","source_end":15800,"source_start":15799,"syntax_kind":"ident"},{"role":"fresh_name","source":"z","source_end":15807,"source_start":15806,"syntax_kind":"ident"}] | [{"source":"⟨z, rfl⟩","source_end":15815,"source_start":15803,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 20 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ae685f871e5f01fc869c03e2b937f6d33f4d3c4c269007337f3ec60cf835510 | d85a9ce316f9ac4cf4c53b2515ef8216cb5da896897524795be7f98df376b1c5 | 65aab85c00cbe7bc72a57143474addb96184964f0f56a415d5a68a058b2e700d | 796d6db989208076c84adf973d44b75e350fb2d70803b54d5d00bb3087da76ef |
cat-searcher/leandojo-benchmark-4-random | test | 3,693 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.isOrtho_def</a>, <a>LinearMap.map_smulₛₗ₂</a>, <a>smul_eq_zero</a>] | case h.mpr.intro
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : ... | case h.mpr.intro
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : ... | ((:c LinearMap.IsOrtho) (:fv _uniq.245324) (:fv _uniq.245324) (:fv _uniq.245324) (:fv _uniq.245339) (:fv _uniq.245333) (:fv _uniq.245333) ((:c CommRing.toCommSemiring) (:fv _uniq.245324) ((:c Field.toCommRing) (:fv _uniq.245324) (:fv _uniq.245345))) ((:c CommRing.toCommSemiring) (:fv _uniq.245324) ((:c Field.toCommRing... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:app (:c LinearMap.IsOrtho) (:arg :implicit-type 0 (:fv FV12)) (:arg :implicit-type 1 (:fv FV12)) (:arg :implicit-type 2 (:fv FV12)) (:arg :implicit-type 3 (:fv FV17)) (:arg :implicit-type 4 (:fv FV15)) (:arg :implicit-type 5 (:fv FV15)) (:arg :instance 6 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":15822,"sourceStart":15820,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15824,"sourceStart":15823,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.isOrth... | [] | [{"source":"isOrtho_def","source_end":15835,"source_start":15824,"syntax_kind":"ident"},{"source":"map_smulₛₗ₂","source_end":15854,"source_start":15837,"syntax_kind":"ident"},{"source":"smul_eq_zero","source_end":15868,"source_start":15856,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 21 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 12d6aeaa2176226fe1756898656e80b0af68fb062aaae4fccaf3a6e97ae5d311 | 796d6db989208076c84adf973d44b75e350fb2d70803b54d5d00bb3087da76ef | 4fa3746cb474d8b9c69560fe6cc83ddd13c61d6655d7d73d0074fef310cbf2da | db86b2ea6d92baf1a4999a525fd68667e0758783005aa9e45cbb1adfc0289440 |
cat-searcher/leandojo-benchmark-4-random | test | 3,694 | LinearMap.orthogonal_span_singleton_eq_to_lin_ker | Mathlib/LinearAlgebra/SesquilinearForm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.intro_right</a> _ h | case h.mpr.intro
R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
M : Type u_5
M₁ : Type u_6
M₂ : Type u_7
M₃ : Type u_8
Mₗ₁ : Type u_9
Mₗ₁' : Type u_10
Mₗ₂ : Type u_11
Mₗ₂' : Type u_12
K : Type u_13
K₁ : Type u_14
K₂ : Type u_15
V : Type u_16
V₁ : Type u_17
V₂ : Type u_18
n : Type u_19
inst✝⁷ : Field K
inst✝⁶ : ... | ((:c Or) ((:c Eq) (:fv _uniq.245324) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.245324) (:fv _uniq.245324) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.245324) ((:c DivisionSemiring.toSemiring) (:fv _uniq.245324) ((:c Semifield.toDivisionSemiring) (:fv _uniq.245324) ((:c Field.toSemifield) (:fv _uniq.245324) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M₁","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV12)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV12)) (:arg :explicit 1 (:fv FV12)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV12))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":15879,"sourceStart":15874,"tag":"atom"},{"children":[{"name":"Or.intro_right","semanticRole":"global","source":"Or.intro_right","sourceEnd":15894,"sourceStart":15880,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":15896,"sourceStart":15895,"tag":"atom"}... | [] | [{"source":"Or.intro_right _ h","source_end":15898,"source_start":15880,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.245288","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.245291","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 122 | 26 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 002c3ec05448d79f737b0c0b73e6b357175ff6c06b66962fe804ee15129b8b4c | db86b2ea6d92baf1a4999a525fd68667e0758783005aa9e45cbb1adfc0289440 | 2091aa1aaffff0c6e06f7666dd12cfa50f909fb8a600020d353672800071cd67 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,695 | MvPowerSeries.inv_eq_zero | Mathlib/RingTheory/MvPowerSeries/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>congr_arg</a> (<a>MvPowerSeries.constantCoeff</a> σ k) h | σ : Type u_1
R : Type u_2
k : Type u_3
inst✝ : Field k
φ : MvPowerSeries σ k
h : φ⁻¹ = 0
⊢ (constantCoeff σ k) φ = 0 | ((:c Eq) (:fv _uniq.56254) ((:c DFunLike.coe) ((:c RingHom) ((:c MvPowerSeries) (:fv _uniq.56248) (:fv _uniq.56254)) (:fv _uniq.56254) ((:c Semiring.toNonAssocSemiring) ((:c MvPowerSeries) (:fv _uniq.56248) (:fv _uniq.56254)) ((:c MvPowerSeries.instSemiring) (:fv _uniq.56248) (:fv _uniq.56254) ((:c DivisionSemiring.toS... | [{"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) ((:c MvPowerSeries) (:fv _uniq.562... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:app (:c MvPowerSeries) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiri... | [{"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":"simpa","sourceEnd":7737,"sourceStart":7732,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"congr_arg (constantCoeff σ k) h","source_end":7776,"source_start":7744,"syntax_kind":"Lean.Parser.Term.app"}] | [{"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 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e2ca17480af560bc3e9052b832e075576d4bf029987388ab4565a1a82b37006 | ea5818e158260a28cbf953949e72c5bf4522bd6bc1c793f4dd31211253d29036 | 6cb509cd9705a8687c4a95ec6e215c0dd2acc95c857cbc1a8ba9b712cf68ff48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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