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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
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classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
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cat-searcher/leandojo-benchmark-4-random | test | 2,266 | Polynomial.coeff_eq_zero_of_lt_natTrailingDegree | Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hp, <a>Polynomial.trailingDegree_zero</a>] | case pos
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : p = 0
⊢ ↑n < p.trailingDegree | case pos
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : p = 0
⊢ ↑n < ⊤ | ((:c LT.lt) (:c ENat) ((:c Preorder.toLT) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENat) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattic... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:fv FV12)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":11520,"sourceStart":11518,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11522,"sourceStart":11521,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"seman... | [] | [{"source":"hp","source_end":11524,"source_start":11522,"syntax_kind":"ident"},{"source":"trailingDegree_zero","source_end":11545,"source_start":11526,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 10 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7db4794c1763eba0e149b301e69d55e2df0781547d15a0f8603b88c9a92120a2 | 365be2059f9d40ace8275498b465f4a0eb6a66ea2b4684e4d5629588f99f20c6 | 063c9000c76c5891982f9aa1c8cccfa0e20fc5a0bbb0faf3200a8f7bc0d52285 | 5ab7ea0f2b7d989d6aefe2aa4ed8a24f63f443e59530272a9f4ba3b89a0741b6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,267 | Polynomial.coeff_eq_zero_of_lt_natTrailingDegree | Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>WithTop.coe_lt_top</a> n | case pos
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : p = 0
⊢ ↑n < ⊤ | ((:c LT.lt) (:c ENat) ((:c Preorder.toLT) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENat) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattic... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:fv FV12)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":11556,"sourceStart":11551,"tag":"atom"},{"children":[{"name":"WithTop.coe_lt_top","semanticRole":"global","source":"WithTop.coe_lt_top","sourceEnd":11575,"sourceStart":11557,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"n","sourceEnd":115... | [] | [{"source":"WithTop.coe_lt_top n","source_end":11577,"source_start":11557,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 14 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a170ba1ef53eb685b4090cbf732853041052c55ebf2cc98ebf09ff0e7fe71621 | 5ab7ea0f2b7d989d6aefe2aa4ed8a24f63f443e59530272a9f4ba3b89a0741b6 | 3dbebae4b1f0e08fa505941939b4ebe06805c42c98d93a1659556fb5feb0b34d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,268 | Polynomial.coeff_eq_zero_of_lt_natTrailingDegree | Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.trailingDegree_eq_natTrailingDegree</a> hp] | case neg
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : ¬p = 0
⊢ ↑n < p.trailingDegree | case neg
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : ¬p = 0
⊢ ↑n < ↑p.natTrailingDegree | ((:c LT.lt) (:c ENat) ((:c Preorder.toLT) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENat) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattic... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:fv FV12)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":11585,"sourceStart":11583,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11587,"sourceStart":11586,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Pol... | [] | [{"source":"trailingDegree_eq_natTrailingDegree hp","source_end":11625,"source_start":11587,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 19 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7372fdacec202d6a3b79643b9825b1c7f009531274b66abb622269e4a097d060 | 36a19e814b844b28cf90dd78053c814720354a414abecf76590692068adbe002 | cb7e08384eb9551e0529b8a7fdae28655fcac48511ecb99e572e5dade924a3fe | a78f086ec38e86be75f395a1caace8a34a0868c79c4862ba36f0418c00d273c9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,269 | Polynomial.coeff_eq_zero_of_lt_natTrailingDegree | Mathlib/Algebra/Polynomial/Degree/TrailingDegree.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>WithTop.coe_lt_coe</a>.2 h | case neg
R : Type u
S : Type v
a b : R
n✝ m : ℕ
inst✝ : Semiring R
p✝ q r p : R[X]
n : ℕ
h : n < p.natTrailingDegree
hp : ¬p = 0
⊢ ↑n < ↑p.natTrailingDegree | ((:c LT.lt) (:c ENat) ((:c Preorder.toLT) (:c ENat) ((:c PartialOrder.toPreorder) (:c ENat) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENat) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENat) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENat) ((:c CompleteLinearOrder.toCompletelyDistribLattic... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"a","sexp":"(:fv _uniq.25261)"},{"name":"b","sexp":"(:fv _uniq.25261)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.25261))"},{"name":"p✝","sexp":"((:c Polynomial) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c ENat)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c ENat))))) (:arg :explicit 2 (:fv FV12)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":11636,"sourceStart":11631,"tag":"atom"},{"children":[{"children":[{"name":"WithTop.coe_lt_coe","semanticRole":"global","source":"WithTop.coe_lt_coe","sourceEnd":11655,"sourceStart":11637,"tag":"identifier"},{"source":".","sourceEnd":11656,"sourceStart":11655,"tag":"atom"},{"ch... | [] | [{"source":"WithTop.coe_lt_coe.2 h","source_end":11659,"source_start":11637,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25261","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25263","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 22 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 675a3e2450c5a54f0ee9018216a42139124e2f7a0c1fe5ac208a0f372b444070 | a78f086ec38e86be75f395a1caace8a34a0868c79c4862ba36f0418c00d273c9 | 5c2c0a64c9f4dd687f298172d53ff28e2569fcce3e96cbbdb7908563c5046b26 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,270 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun hx => hx ▸ <a>AddCircle.norm_le_half_period</a> p hp, fun hx => ?_⟩ | p x : ℝ
hp : p ≠ 0
⊢ ‖↑x‖ = |x| ↔ |x| ≤ |p| / 2 | p x : ℝ
hp : p ≠ 0
hx : |x| ≤ |p| / 2
⊢ ‖↑x‖ = |x| | ((:c Iff) ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c Quotie... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"refine","sourceEnd":6035,"sourceStart":6029,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":6039,"sourceStart":6036,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":6042,"sourceStart":6039,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx... | [] | [{"source":"⟨fun hx => hx ▸ norm_le_half_period p hp, fun hx => ?_⟩","source_end":6097,"source_start":6036,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e360fc707904ccc3fc25ed6ce89915674d3013bfc3e5282f6e1963329168d423 | c86a04376fb4c9659c751273d1c10c6db1191ab220e125bb498220fbd579b807 | 351c982b1255a3aeb7a45af4d77cea50b0bcd1752cd798b6fe6772cf41bcbc47 | 497c7a06a0acda1ff35311416526a911643596ce9614e1f356617db3d8af10fa |
cat-searcher/leandojo-benchmark-4-random | test | 2,271 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear hx | p x : ℝ
hp : p ≠ 0
hx : |x| ≤ |p| / 2
⊢ ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x| | p x : ℝ
hp : p ≠ 0
⊢ ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x| | (:forall p (:c Real) (:forall _ ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:forall _ ((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) (:fv _uniq.33647)) ((:c HDiv.hDiv) (:c Real) (:... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Real... | (:forall p :explicit (:c Real) (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:ap... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"clear","sourceEnd":6501,"sourceStart":6496,"tag":"atom"},{"children":[{"contextIndex":4,"semanticRole":"local","source":"hx","sourceEnd":6504,"sourceStart":6502,"tag":"identifier"}],"kind":"null","source":"hx","sourceEnd":6504,"sourceStart":6502,"tag":"node"}],"kind":"Lean.Parser.Tactic.clear","... | [] | [{"source":"hx","source_end":6504,"source_start":6502,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 28 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 39084d3545944e62689220ce41b31a0bd718f2e275780274ecb2f77a240519b1 | 9051b4aa3fa2863a1916bc4c3f861f4aaab428ad7ba0dad6c16bcbad6ee4c0e0 | cd3c787bc37928e8ee15a17366cbe88b10d14ece3506607c8ff1f830d4bf23df | cbb19d38ad6000eb4835c9ffd27cd03623d10094029a0002cd5868f5eea56b7f |
cat-searcher/leandojo-benchmark-4-random | test | 2,272 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro p hp hx | p x : ℝ
hp : p ≠ 0
⊢ ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x| | p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
⊢ ‖↑x‖ = |x| | (:forall p (:c Real) (:forall _ ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0) (:forall _ ((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) (:fv _uniq.33647)) ((:c HDiv.hDiv) (:c Real) (:... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"}] | (:forall p :explicit (:c Real) (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:ap... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"intro","sourceEnd":6512,"sourceStart":6507,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"p","sourceEnd":6514,"sourceStart":6513,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hp","sourceEnd":6517,"sourceStart":6515,"tag":"identifier"},{"semanticRole":"scoped_l... | [{"role":"fresh_name","source":"p","source_end":6514,"source_start":6513,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp","source_end":6517,"source_start":6515,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":6520,"source_start":6518,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 29 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 58f6ff77604a854482813ebfa846d7d53ffb96ce7ff339c51a4e0eb7b2b80518 | cbb19d38ad6000eb4835c9ffd27cd03623d10094029a0002cd5868f5eea56b7f | 85e4d210964b6d56e91d10d43f0438f74696203a1b3ff3f1230df93d53d60e90 | a9a4490e75871a504cf027bd6b2125a7b96f79214f729e203952c4e058b9a4a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,274 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices <a>round</a> (p⁻¹ * x) = 0 by simp [<a>AddCircle.norm_eq</a>, this] | case inr
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
⊢ ‖↑x‖ = |x| | case inr
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
⊢ round (p⁻¹ * x) = 0 | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"source":"suffices","sourceEnd":6613,"sourceStart":6605,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":6614,"sourceStart":6614,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6614,"sourceStart":6614,"tag":"node"},{"children":[{"children":[{"name":"round","semanticRole":... | [] | [{"source":"round (p⁻¹ * x) = 0","source_end":6636,"source_start":6614,"syntax_kind":"«term_=_»"},{"source":"norm_eq","source_end":6653,"source_start":6646,"syntax_kind":"ident"},{"source":"this","source_end":6659,"source_start":6655,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 36 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 75717edaf2478343b77e6490ceb80c52372aadd903ba38a125827165c5f23dfc | 5dd20536df0cdfdead11115edee68167360f7bb880f0ef7043c9b7dc7f36c013 | 8492be86a2a3502c6442981e56ae0c9d14438a28e3a808b2f2f166a607a414c6 | 6948835325af6bca54cc35ecc8c68364f561b9a5b5251a65ad3625415f35ad34 |
cat-searcher/leandojo-benchmark-4-random | test | 2,275 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>round_eq_zero_iff</a>] | case inr
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
⊢ round (p⁻¹ * x) = 0 | case inr
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | ((:c Eq) (:c Int) ((:c round) (:c Real) (:c Real.instLinearOrderedRing) (:c Real.instFloorRing) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.34637)) (:fv _uniq.33647))) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c round) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedRing) (:arg :explicit 0 (:c Real))))) (:arg :instance 2 (:instance-of (:app (:c FloorRing) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"source":"rw","sourceEnd":6665,"sourceStart":6663,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6667,"sourceStart":6666,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"round_eq_zero_iff","... | [] | [{"source":"round_eq_zero_iff","source_end":6684,"source_start":6667,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 40 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0fddf766f924ae1fe4aae39ce6ab653b0488aaeba750852dc5d7aede1e80ac21 | 6948835325af6bca54cc35ecc8c68364f561b9a5b5251a65ad3625415f35ad34 | b65ad67c23532c539854e05223f044a276295072e03d3df82832879823927471 | 86fc47c02dbf34e8129d028b3a0faaadfabffe69d46fa264c769018bdf5ea38f |
cat-searcher/leandojo-benchmark-4-random | test | 2,276 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨hx₁, hx₂⟩ := abs_le.mp hx | case inr
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | case inr.intro
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x ≤ p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.34637)) (:fv _uniq.33647)) ((:c Set.Ico) (:c Real) ((:c PartialOrder.toPreorder) (:c Real... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HMul.hMul) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"source":"obtain","sourceEnd":6694,"sourceStart":6688,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6698,"sourceStart":6695,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx₁","sourceEnd"... | [] | [{"source":"abs_le.mp hx","source_end":6729,"source_start":6717,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨hx₁, hx₂⟩","source_end":6713,"source_start":6695,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 43 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e532b45eac41c8fa7774487b26a785ffc40f15b9c7ef75c5e51f834b2f32d13 | 86fc47c02dbf34e8129d028b3a0faaadfabffe69d46fa264c769018bdf5ea38f | ea596ee1de2046f1dd967864a1d1bea0722a1df22d437bf086f73cb3b09d5f8f | bd9883c88dcdf225747c46ee8e79a39f9518f4cc33229f52c693b6811f7fecff |
cat-searcher/leandojo-benchmark-4-random | test | 2,277 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace hx₂ := <a>Ne.lt_of_le</a> hx' hx₂ | case inr.intro
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x ≤ p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | case inr.intro
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.34637)) (:fv _uniq.33647)) ((:c Set.Ico) (:c Real) ((:c PartialOrder.toPreorder) (:c Real... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HMul.hMul) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"source":"replace","sourceEnd":6739,"sourceStart":6732,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx₂","sourceEnd":6745,"sourceStart":6740,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hx₂","sourceEnd":6745,"sourceStart":6740,"tag":"node... | [] | [{"source":"Ne.lt_of_le hx' hx₂","source_end":6770,"source_start":6749,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 44 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d67bacb8bbadec56e6bd839129af34bb7c32a70d2a4a1b178ed2dbbba53b950f | bd9883c88dcdf225747c46ee8e79a39f9518f4cc33229f52c693b6811f7fecff | 28cdf443711ea0512a06cec0786a0f77cc016aa7cb1e79ba6ab1099714042a14 | 2d640173ddb2694637d305c1750637112f9911ca995f322d96735b2effe618b6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,278 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case inr.intro
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ p⁻¹ * x ∈ Ico (-(1 / 2)) (1 / 2) | case inr.intro.left
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ -(1 / 2) ≤ p⁻¹ * x
case inr.intro.right
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ p⁻¹ * x < 1 / 2 | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.34637)) (:fv _uniq.33647)) ((:c Set.Ico) (:c Real) ((:c PartialOrder.toPreorder) (:c Real... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HMul.hMul) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"source":"constructor","sourceEnd":6784,"sourceStart":6773,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":6784,"sourceStart":6773,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 45 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1e008f0863a967695986e2659ce8562576d110bae82ea9141a59b6d6ebc0ece | 2d640173ddb2694637d305c1750637112f9911ca995f322d96735b2effe618b6 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 1ca2788993aeea306ec7459a4b5d5280610fff09b623ab9039ce1c6537cad6ac |
cat-searcher/leandojo-benchmark-4-random | test | 2,279 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hp.symm.lt_or_lt with (hp | hp) | p x : ℝ
hp : p ≠ 0
hx : |x| ≤ |p| / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
⊢ ‖↑x‖ = |x| | case inl
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ |p| / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : 0 < p
⊢ ‖↑x‖ = |x|
case inr
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ |p| / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : p < 0
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Real... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"rcases","sourceEnd":6279,"sourceStart":6273,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Ne.lt_or_lt","semanticRole":"global","source":"hp.symm.lt_or_lt","sourceEnd":6296,"sourceStart":6280,"tag":"identifier"}],"kind":"Lean.Parser.Tactic... | [] | [{"source":"hp.symm.lt_or_lt","source_end":6296,"source_start":6280,"syntax_kind":"ident"},{"source":"(hp | hp)","source_end":6311,"source_start":6302,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 8 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be0d7a3d245b59fc65aebc58ed31ce2945a52b534f4609ca864522a871f2190f | bd12b1765d394f194d92935ef767304af5f2f13063f7c1a0982e2d64a7ed15df | c4bd366bbd9d701dce45b3cdbb4f56170207baa2810e3fe53f0af648fd482175 | 084f889ab9cb055974c4f27c53658df300514aae67eed3d5897708e4eaca08f7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,280 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [abs_eq_self.mpr hp.le] at hx | case inl
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ |p| / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : 0 < p
⊢ ‖↑x‖ = |x| | case inl
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ p / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : 0 < p
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"rw","sourceEnd":6321,"sourceStart":6319,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6323,"sourceStart":6322,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"abs_e... | [] | [{"source":"hx","source_end":6351,"source_start":6349,"syntax_kind":"ident"},{"source":"abs_eq_self.mpr hp.le","source_end":6344,"source_start":6323,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 13 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 64d9a32cd76ba72a6e9c1b9392fbec76ef8a8ef2a528e4813d1d5ddd564f78b8 | 303861abc23b874eaff529576147bd8490a9aa21e235d6af9871eea21d1f9738 | aba83fc7101c88dd91c5b4e05c8412fcd3791a4d1a6dfeebf0ed1a77b4601e2f | 698914b46118f0afe79705c88bf3b61624f19d976308f0231a707190a132738e |
cat-searcher/leandojo-benchmark-4-random | test | 2,281 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this p hp hx | case inl
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ p / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : 0 < p
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"exact","sourceEnd":6363,"sourceStart":6358,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"this","sourceEnd":6368,"sourceStart":6364,"tag":"identifier"},{"children":[{"contextIndex":0,"semanticRole":"local","source":"p","sourceEnd":6370,"sourceStart":6369,"tag":"ide... | [] | [{"source":"this p hp hx","source_end":6376,"source_start":6364,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 16 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29e98f74989e0a17dfbe71e82dcef5bc8b15040c79bed7e8f98c8af55dc9da20 | 698914b46118f0afe79705c88bf3b61624f19d976308f0231a707190a132738e | 367f45f0300abf038a22a3f0eda52ab6a618f64813c9797726197e788d837976 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,282 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [abs_eq_neg_self.mpr hp.le] at hx | case inr
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ |p| / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : p < 0
⊢ ‖↑x‖ = |x| | case inr
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ -p / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : p < 0
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"rw","sourceEnd":6417,"sourceStart":6415,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6419,"sourceStart":6418,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"abs_e... | [] | [{"source":"hx","source_end":6451,"source_start":6449,"syntax_kind":"ident"},{"source":"abs_eq_neg_self.mpr hp.le","source_end":6444,"source_start":6419,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 24 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9ab67ce513e62f7330ff2a9dba09c4753ab0fb588348dc8ff7ed7420a9fe5ae | 0fa9cc5879b31a6b0be4fa7499e7d690248dd4fd9e99ade6b30ab0d7df23c1bd | a92a3eaafa177fa373f2f1ebb06f1e07a88b1b2f3054efcb25917696487b59d9 | eab4adad4a6a6310697e08c03b54642ee9bce27630eac4f0d5536eb0ad7bd074 |
cat-searcher/leandojo-benchmark-4-random | test | 2,283 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this (-p) (neg_pos.mpr hp) hx | case inr
p x : ℝ
hp✝ : p ≠ 0
hx : |x| ≤ -p / 2
this : ∀ (p : ℝ), 0 < p → |x| ≤ p / 2 → ‖↑x‖ = |x|
hp : p < 0
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c abs) (:c Real) (:c Real.lattice) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"exact","sourceEnd":6463,"sourceStart":6458,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"this","sourceEnd":6468,"sourceStart":6464,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":6470,"sourceStart":6469,"tag":"atom"},{"children":[{"source":... | [] | [{"source":"this (-p) (neg_pos.mpr hp) hx","source_end":6493,"source_start":6464,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 23 | 27 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbaf354c2d73bb808079c498092f09889da6ebf33bd3c5d750a4b00c0ec7e92e | eab4adad4a6a6310697e08c03b54642ee9bce27630eac4f0d5536eb0ad7bd074 | 97c24b9550cb2a28f4022f6e0df0e8390c4fcb7d9f7ab5f589a6318459716555 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,284 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>abs_div</a>, <a>abs_two</a>] | case inl
p✝ : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |p / 2| ≤ p / 2
⊢ ‖↑(p / 2)‖ = |p / 2| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Ze... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.33648","is_instance":false,"is_let":false,"name":"hp✝","sexp":"(:app (:c Ne) (:arg :implicit-type 0 (:c Real)... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6583,"sourceStart":6579,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"abs_div","source_end":6592,"source_start":6585,"syntax_kind":"ident"},{"source":"abs_two","source_end":6601,"source_start":6594,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.33648","is_instance":false,"is_let":false,"user_name":"hp✝"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 23 | 33 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 828e092d484254890c0e262ec39a7cbe9731cd4b39c70b5120f7024583754bee | 6a3b37ad2d312f9e331f81b00defd521400467fe4ebd477415bcf1e02acbe92a | bb96df5928d9681997eb9f02e28fc7e08a52d9ffd261a5535e1fbd3efb9a17f3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,285 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>AddCircle.norm_eq</a>, this] | p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
this : round (p⁻¹ * x) = 0
⊢ ‖↑x‖ = |x| | ((:c Eq) (:c Real) ((:c Norm.norm) ((:c HasQuotient.Quotient) (:c Real) ((:c AddSubgroup) (:c Real) ((:c AddCommGroup.toAddGroup) (:c Real) ((:c OrderedAddCommGroup.toAddCommGroup) (:c Real) ((:c LinearOrderedAddCommGroup.toOrderedAddCommGroup) (:c Real) (:c Real.instLinearOrderedAddCommGroup))))) ((:c QuotientAddGroup... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Norm.norm) (:arg :implicit-type 0 (:app (:c HasQuotient.Quotient) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c AddSubgroup) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c AddGroup) (:arg :explicit 0 (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6644,"sourceStart":6640,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"norm_eq","source_end":6653,"source_start":6646,"syntax_kind":"ident"},{"source":"this","source_end":6659,"source_start":6655,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 37 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aedf7cf93afbf09ae09863ee1b0be200f67a8467fd5262b3ff06b745d5d8254f | 252e543e667a6f2485b7e1a09307647ccc67428b0975073acc2ab2f03197e255 | 967d6c02054d6c4346b30ec42f529a3f980c47c718fde9a0482b2433d3887513 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,286 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>mul_le_mul_left</a> hp, ← <a>mul_assoc</a>, <a>mul_inv_cancel</a> hp.ne.symm, <a>one_mul</a>, <a>mul_neg</a>, ← <a>mul_div_assoc</a>, <a>mul_one</a>] | case inr.intro.left
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ -(1 / 2) ≤ p⁻¹ * x | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedRing.toPartialOrder) (:c Real) ((:c LinearOrderedRing.toStrictOrderedRing) (:c Real) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:c Real) ((:c LinearOrderedField.toLinearOrderedCommRing) (:c Real) (:c Real... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (: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 Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":6793,"sourceStart":6790,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6795,"sourceStart":6794,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6798,"sourceStart":6795,"tag":"ato... | [] | [{"source":"mul_le_mul_left hp","source_end":6817,"source_start":6799,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_assoc","source_end":6832,"source_start":6823,"syntax_kind":"ident"},{"source":"mul_inv_cancel hp.ne.symm","source_end":6859,"source_start":6834,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 48 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a7625bc7067f8ad3d373ea175075ea6e99d1cf301f19029a8f2fb11080726d7 | 45c04856fd2f4563c443dc01a732bd3fe5a1ad7ba935ac728940e6ba751a5c50 | 5ed493949f784239c295c8a361b748219adae525b6b42fb83cf85429498f3697 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,287 | AddCircle.norm_coe_eq_abs_iff | Mathlib/Analysis/Normed/Group/AddCircle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>mul_lt_mul_left</a> hp, ← <a>mul_assoc</a>, <a>mul_inv_cancel</a> hp.ne.symm, <a>one_mul</a>, ← <a>mul_div_assoc</a>, <a>mul_one</a>] | case inr.intro.right
p✝ x : ℝ
hp✝ : p✝ ≠ 0
p : ℝ
hp : 0 < p
hx : |x| ≤ p / 2
hx' : x ≠ p / 2
hx₁ : -(p / 2) ≤ x
hx₂ : x < p / 2
⊢ p⁻¹ * x < 1 / 2 | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedRing.toPartialOrder) (:c Real) ((:c LinearOrderedRing.toStrictOrderedRing) (:c Real) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:c Real) ((:c LinearOrderedField.toLinearOrderedCommRing) (:c Real) (:c Real... | [{"name":"p✝","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hp✝","sexp":"((:c Ne) (:c Real) (:fv _uniq.33155) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"},{"name":"p","sexp":"(:c Real)"},{"name":"hp","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.o... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"name":"p✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":6921,"sourceStart":6918,"tag":"atom"},{"children":[{"source":"[","sourceEnd":6923,"sourceStart":6922,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":6926,"sourceStart":6923,"tag":"ato... | [] | [{"source":"mul_lt_mul_left hp","source_end":6945,"source_start":6927,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_assoc","source_end":6960,"source_start":6951,"syntax_kind":"ident"},{"source":"mul_inv_cancel hp.ne.symm","source_end":6987,"source_start":6962,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.33155","is_instance":false,"is_let":false,"user_name":"p✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33647","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 23 | 61 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 516305695c8139e52bf23ea568ee07ea74d726e3798c6e32ff0fd56eb64ac2ee | 11e83b0da396159f416ff46e80d379af0d31085c49843e30948fe1519efe8f03 | 48d10a6d1d6dae5f7db0f8ac1bb0bf324f768f9444db20e6fac1619f441aba90 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,288 | Nat.multinomial_insert | Mathlib/Data/Nat/Choose/Multinomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Finset.cons_eq_insert</a> _ _ ha, <a>Nat.multinomial_cons</a>] | α : Type u_1
s : Finset α
f✝ : α → ℕ
a b : α
n : ℕ
inst✝ : DecidableEq α
ha : a ∉ s
f : α → ℕ
⊢ multinomial (insert a s) f = (f a + ∑ i ∈ s, f i).choose (f a) * multinomial s f | ((:c Eq) (:c Nat) ((:c Nat.multinomial) (:fv _uniq.2945) ((:c Insert.insert) (:fv _uniq.2945) ((:c Finset) (:fv _uniq.2945)) ((:c Finset.instInsert) (:fv _uniq.2945) (:fv _uniq.3165)) (:fv _uniq.2954) (:fv _uniq.2948)) (:fv _uniq.3167)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.2945))"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.2945) (:c Nat))"},{"name":"a","sexp":"(:fv _uniq.2945)"},{"name":"b","sexp":"(:fv _uniq.2945)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.294... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.multinomial) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Insert.insert) (: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 Ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2945","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2948","is_instance":false,"is_let":false,"name":"s","sexp":"(:app (:c Finset) (:arg :explicit 0 (:fv FV0)))"... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2525,"sourceStart":2523,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2527,"sourceStart":2526,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"cons_eq_insert _ _ ha","source_end":2552,"source_start":2531,"syntax_kind":"Lean.Parser.Term.app"},{"source":"multinomial_cons","source_end":2570,"source_start":2554,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2945","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2948","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 17 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e85b84aa91eaa9e033018628930861285c83af79e6f074f1e9e8bbd3cd5d9ed | a14fdc5ed401029329334d3182afffb8eeb517627fbbaa6712449f0472e40332 | 55e00409f1b90f9100c640e1f44f81d53e67512f615bab59af1354de69d35d17 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,289 | Prefunctor.mapPath_comp | Mathlib/Combinatorics/Quiver/Path.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp | V : Type u₁
inst✝¹ : Quiver V
W : Type u₂
inst✝ : Quiver W
F : V ⥤q W
a b : V
p : Path a b
c b✝ : V
q : Path b b✝
e : b✝ ⟶ c
⊢ F.mapPath (p.comp (q.cons e)) = (F.mapPath p).comp (F.mapPath (q.cons e)) | V : Type u₁
inst✝¹ : Quiver V
W : Type u₂
inst✝ : Quiver W
F : V ⥤q W
a b : V
p : Path a b
c b✝ : V
q : Path b b✝
e : b✝ ⟶ c
⊢ (F.mapPath (p.comp q)).cons (F.map e) = ((F.mapPath p).comp (F.mapPath q)).cons (F.map e) | ((:c Eq) ((:c Quiver.Path) (:fv _uniq.13957) (:fv _uniq.13960) ((:c Prefunctor.obj) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960) (:fv _uniq.13976) (:fv _uniq.14130)) ((:c Prefunctor.obj) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960) (:fv _uniq.13976) (:fv _uniq.14302... | [{"name":"V","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c Quiver) (:fv _uniq.13952))"},{"name":"W","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c Quiver) (:fv _uniq.13957))"},{"name":"F","sexp":"((:c Prefunctor) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960))"},{"name":"a",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Path) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13952","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13955","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Quiver) (:arg :explicit... | {"children":[{"source":"dsimp","sourceEnd":8505,"sourceStart":8500,"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":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13952","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13955","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 77 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4d755325ce58235c9e893015ccbe19c1d8b72daa5384f481a9bfb3da44200b8 | fad4a493d7f9080d8f2912094c8258d27606da3b1d001879ac66618d4ce9af21 | 7854eab90b5d1f0eed9d2f7f6b885100cc44bc732b41c876b3af083c01260845 | 2b26e5489e0a3ae8fe4338aa47f370f2120834d894c13b2fadf92636124ef8d8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,290 | Prefunctor.mapPath_comp | Mathlib/Combinatorics/Quiver/Path.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [mapPath_comp p q] | V : Type u₁
inst✝¹ : Quiver V
W : Type u₂
inst✝ : Quiver W
F : V ⥤q W
a b : V
p : Path a b
c b✝ : V
q : Path b b✝
e : b✝ ⟶ c
⊢ (F.mapPath (p.comp q)).cons (F.map e) = ((F.mapPath p).comp (F.mapPath q)).cons (F.map e) | ((:c Eq) ((:c Quiver.Path) (:fv _uniq.13957) (:fv _uniq.13960) ((:c Prefunctor.obj) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960) (:fv _uniq.13976) (:fv _uniq.14130)) ((:c Prefunctor.obj) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960) (:fv _uniq.13976) (:fv _uniq.14302... | [{"name":"V","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝¹","sexp":"((:c Quiver) (:fv _uniq.13952))"},{"name":"W","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c Quiver) (:fv _uniq.13957))"},{"name":"F","sexp":"((:c Prefunctor) (:fv _uniq.13952) (:fv _uniq.13955) (:fv _uniq.13957) (:fv _uniq.13960))"},{"name":"a",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Path) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13952","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13955","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Quiver) (:arg :explicit... | {"children":[{"source":"rw","sourceEnd":8509,"sourceStart":8507,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8511,"sourceStart":8510,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":... | [] | [{"source":"mapPath_comp p q","source_end":8527,"source_start":8511,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13952","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.13955","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 77 | 6 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c8f84ea145277e6dafc588747382b2caaef808e3a8972d89c9189b151c74ad1 | 2b26e5489e0a3ae8fe4338aa47f370f2120834d894c13b2fadf92636124ef8d8 | e4eeffcf325326f590b653c94cf84b523991cd3c3f327f8656e72658b71db789 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,291 | MeasureTheory.predictablePart_zero | Mathlib/Probability/Martingale/Centering.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.predictablePart</a>, <a>Finset.range_zero</a>, <a>Finset.sum_empty</a>] | Ω : Type u_1
E : Type u_2
m0 : MeasurableSpace Ω
μ : Measure Ω
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℝ E
inst✝ : CompleteSpace E
f : ℕ → Ω → E
ℱ : Filtration ℕ m0
n : ℕ
⊢ predictablePart f ℱ μ 0 = 0 | ((:c Eq) (:forall _ (:fv _uniq.2448) (:fv _uniq.2451)) ((:c MeasureTheory.predictablePart) (:fv _uniq.2448) (:fv _uniq.2451) (:fv _uniq.2466) (:fv _uniq.2576) (:fv _uniq.2688) (:fv _uniq.2454) (:fv _uniq.2694) (:fv _uniq.2828) (:fv _uniq.2463) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c OfNa... | [{"name":"Ω","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.2448))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.2448) (:fv _uniq.2454))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2451))"},{"name":"inst✝¹","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:fv FV1))) (:arg :explicit 1 (:app (:c MeasureTheory.predictablePart) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2448","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2451","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":2117,"sourceStart":2110,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2119,"sourceStart":2118,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":""... | [] | [{"source":"predictablePart","source_end":2134,"source_start":2119,"syntax_kind":"ident"},{"source":"Finset.range_zero","source_end":2153,"source_start":2136,"syntax_kind":"ident"},{"source":"Finset.sum_empty","source_end":2171,"source_start":2155,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2448","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2451","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 8 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ea04b3455bb49f61d4db3bc938169cea343713e1560eeb7fc97cb30ff315d87 | 9687ae9cbeb67ca006e90dd6230afda3f8739e9d7c67e83afe80e32f1f79ea47 | 41b25931376b1b0fc8c978dc0abe579fcb069629b82613115b53ef618377eec6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,292 | List.takeWhile_cons_of_pos | Mathlib/Data/List/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.takeWhile_cons</a>, h] | ι : Type u_1
α : Type u
β : Type v
γ : Type w
l₁ l₂ : List α
p : α → Bool
l : List α
x : α
h : p x = true
⊢ takeWhile p (x :: l) = x :: takeWhile p l | ((:c Eq) ((:c List) (:fv _uniq.221399)) ((:c List.takeWhile) (:fv _uniq.221399) (:fv _uniq.221413) ((:c List.cons) (:fv _uniq.221399) (:fv _uniq.221451) (:fv _uniq.221416))) ((:c List.cons) (:fv _uniq.221399) (:fv _uniq.221451) ((:c List.takeWhile) (:fv _uniq.221399) (:fv _uniq.221413) (:fv _uniq.221416)))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.221399))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.221399))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.221399) (:c Boo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c List.takeWhile) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:fv FV7)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221397","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221399","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":116526,"sourceStart":116522,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sour... | [] | [{"source":"takeWhile_cons","source_end":116542,"source_start":116528,"syntax_kind":"ident"},{"source":"h","source_end":116545,"source_start":116544,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221397","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221399","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,039 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88555991f75487911f79ca70b87fb8f9205fb921fe838d372de3c9b40b62cd79 | d142e7e91e6624c75344b1becee3ca8f4c677ca03a0e51b2cb6c95f6d18ddfe4 | 06c708dec5546a92109a632ccc5e8de6a6d9e60b3dc70b7975c5378ef781c871 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,293 | Zspan.repr_ceil_apply | Mathlib/Algebra/Module/Zlattice/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical simp only [<a>Zspan.ceil</a>, <a>zsmul_eq_smul_cast</a> K, b.repr.map_smul, <a>Finsupp.single_apply</a>, <a>Finset.sum_apply'</a>, <a>Basis.repr_self</a>, <a>Finsupp.smul_single'</a>, <a>mul_one</a>, <a>Finset.sum_ite_eq'</a>, <a>Submodule.coe_sum</a>, <a>Finset.mem_univ</a>, <a>if_true</a>, <a>Submodule.coe_... | E : Type u_1
ι : Type u_2
K : Type u_3
inst✝⁴ : NormedLinearOrderedField K
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace K E
b : Basis ι K E
inst✝¹ : FloorRing K
inst✝ : Fintype ι
m : E
i : ι
⊢ (b.repr ↑(ceil b m)) i = ↑⌈(b.repr m) i⌉ | ((:c Eq) (:fv _uniq.63642) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.63639) (:fv _uniq.63642) ((:c MonoidWithZero.toZero) (:fv _uniq.63642) ((:c Semiring.toMonoidWithZero) (:fv _uniq.63642) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.63642) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.63642) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c NormedLinearOrderedField) (:fv _uniq.63642))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.63636))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63636","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63639","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":4440,"sourceStart":4431,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4445,"sourceStart":4441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"ceil","source_end":4456,"source_start":4452,"syntax_kind":"ident"},{"source":"zsmul_eq_smul_cast K","source_end":4478,"source_start":4458,"syntax_kind":"Lean.Parser.Term.app"},{"source":"b.repr.map_smul","source_end":4495,"source_start":4480,"syntax_kind":"ident"},{"source":"Finsupp.single_apply","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63636","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63639","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1bb0f01a0a4f8694282c9cf7fc156228283bd693365456e7d94d2c2d41aff2c6 | 8f504385694baf02681b8cd472763e263c007624261328a78dddd1a1192b8eeb | 44feca51004ff4f5f766643e859e9a3d3c74604e2508f8b4099a8339b4e37d6c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,294 | Zspan.repr_ceil_apply | Mathlib/Algebra/Module/Zlattice/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Zspan.ceil</a>, <a>zsmul_eq_smul_cast</a> K, b.repr.map_smul, <a>Finsupp.single_apply</a>, <a>Finset.sum_apply'</a>, <a>Basis.repr_self</a>, <a>Finsupp.smul_single'</a>, <a>mul_one</a>, <a>Finset.sum_ite_eq'</a>, <a>Submodule.coe_sum</a>, <a>Finset.mem_univ</a>, <a>if_true</a>, <a>Submodule.coe_smul_of_to... | E : Type u_1
ι : Type u_2
K : Type u_3
inst✝⁴ : NormedLinearOrderedField K
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace K E
b : Basis ι K E
inst✝¹ : FloorRing K
inst✝ : Fintype ι
m : E
i : ι
⊢ (b.repr ↑(ceil b m)) i = ↑⌈(b.repr m) i⌉ | ((:c Eq) (:fv _uniq.63642) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.63639) (:fv _uniq.63642) ((:c MonoidWithZero.toZero) (:fv _uniq.63642) ((:c Semiring.toMonoidWithZero) (:fv _uniq.63642) ((:c StrictOrderedSemiring.toSemiring) (:fv _uniq.63642) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.63642) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"K","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁴","sexp":"((:c NormedLinearOrderedField) (:fv _uniq.63642))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.63636))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV2))))))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63636","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63639","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4445,"sourceStart":4441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4450,"sourceStart":4446,"tag":"atom"}],"kind":"nu... | [] | [{"source":"ceil","source_end":4456,"source_start":4452,"syntax_kind":"ident"},{"source":"zsmul_eq_smul_cast K","source_end":4478,"source_start":4458,"syntax_kind":"Lean.Parser.Term.app"},{"source":"b.repr.map_smul","source_end":4495,"source_start":4480,"syntax_kind":"ident"},{"source":"Finsupp.single_apply","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.63636","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.63639","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 27 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f47ffde02e84df32070042daf35bf624da1b82b1e4df38d9e6dd7d5ea118f07d | 8f504385694baf02681b8cd472763e263c007624261328a78dddd1a1192b8eeb | fb5a8a647a86a832c5cb9d5db10e6457e353fe81869e81d50f904b0db922a2f2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,295 | SignType.le_antisymm | Mathlib/Data/Sign.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases a <;> cases b <;> trivial | a b : SignType
x✝¹ : a ≤ b
x✝ : b ≤ a
⊢ a = b | ((:c Eq) (:c SignType) (:fv _uniq.7548) (:fv _uniq.7549)) | [{"name":"a","sexp":"(:c SignType)"},{"name":"b","sexp":"(:c SignType)"},{"name":"x✝¹","sexp":"((:c LE.le) (:c SignType) (:c SignType.instLE) (:fv _uniq.7548) (:fv _uniq.7549))"},{"name":"x✝","sexp":"((:c LE.le) (:c SignType) (:c SignType.instLE) (:fv _uniq.7549) (:fv _uniq.7548))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV2))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7548","is_instance":false,"is_let":false,"name":"a","sexp":"(:c SignType)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.7549","is_instance":false,"is_let":false,"name":"b","sexp":"(:c SignType)"},{"binder_role":":explicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":3331,"sourceStart":3326,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":1,"semanticRole":"local","source":"a","sourceEnd":3333,"sourceStart":3332,"ta... | [] | [{"source":"a","source_end":3333,"source_start":3332,"syntax_kind":"ident"},{"source":"b","source_end":3345,"source_start":3344,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.7548","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.7549","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 27 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4a96363b04c4fe85c0c54da7d2e39c19395760c33e27e91a17dfe3e73152e7d | b1e7744eecb3a56e714a4774b10e6fddc62ad0b5fd46f0c810af0ca3f91900b2 | 792c2dcc1f86ce07aac190a60f28ff04e61d5413f6da07361bdc87b55ac9f765 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,296 | MvQPF.Fix.rec_unique | Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
⊢ rec g = h | case h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x : Fix F α
⊢ rec g x = h x | ((:c Eq) (:forall _ ((:c MvQPF.Fix) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471)) (:fv _uniq.48872)) ((:c MvQPF.Fix.rec) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471) (:fv _uniq.48872) (:fv _uniq.48873)) (:fv _uniq.48874)) | [{"name":"n","sexp":"(:c Nat)"},{"name":"F","sexp":"(:forall _ ((:c TypeVec) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.48397) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c MvQPF) ((:c HAdd.hAdd) (:c Na... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c MvQPF.Fix) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MvQPF) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1))))) (:arg :explicit 3 (:fv FV3))) (:fv FV5))) (:arg :explicit 1 (:app (:c MvQPF.Fix.rec) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:app (:c TypeVec) (:arg :exp... | {"children":[{"source":"ext","sourceEnd":11507,"sourceStart":11504,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":11509,"sourceStart":11508,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":11509,"sourceStart":11508,"tag... | [{"role":"fresh_name","source":"x","source_end":11509,"source_start":11508,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0d417a5a84c7a29fd1a8f5b4bdb2978e53e107c87affe1228eafffddc56b404 | 6b7b57b79cbb2f34d2514e13d4757bb94b867c8a50d1fa3157ad3a4e47d47169 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | f7f0f0075a039c426d4b1431c1e93c16f2094b36f28c25c56af078496a3f0dcd |
cat-searcher/leandojo-benchmark-4-random | test | 2,297 | MvQPF.Fix.rec_unique | Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MvQPF.Fix.ind_rec</a> | case h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x : Fix F α
⊢ rec g x = h x | case h.h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x : Fix F α
⊢ ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: rec g) <$$> x = (TypeVec.id ::: h) <$$> x → rec g (mk x) = h (mk... | ((:c Eq) (:fv _uniq.48872) ((:c MvQPF.Fix.rec) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471) (:fv _uniq.48872) (:fv _uniq.48873) (:fv _uniq.48911)) ((:fv _uniq.48874) (:fv _uniq.48911))) | [{"name":"n","sexp":"(:c Nat)"},{"name":"F","sexp":"(:forall _ ((:c TypeVec) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.48397) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c MvQPF) ((:c HAdd.hAdd) (:c Na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c MvQPF.Fix.rec) (:arg :implicit 0) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c MvQPF) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1))))) (:arg :implicit 3) (:arg :implicit-type 4 (:fv FV5)) (:arg :explicit 5 (:fv FV6)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:app (:c TypeVec) (:arg :exp... | {"children":[{"source":"apply","sourceEnd":11517,"sourceStart":11512,"tag":"atom"},{"name":"MvQPF.Fix.ind_rec","semanticRole":"global","source":"Fix.ind_rec","sourceEnd":11529,"sourceStart":11518,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Fix.ind_rec","sourceEnd":11529,"sourceStart":11512,"t... | [] | [{"source":"Fix.ind_rec","source_end":11529,"source_start":11518,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3c801e5b9076df3fc180bcad83bfbd4eccdec5ba02ac7cab6f41f51a004d8c4 | f7f0f0075a039c426d4b1431c1e93c16f2094b36f28c25c56af078496a3f0dcd | 22d4c59b63d5390a4599dba3c6e6725f1050302456f7b47584eaf84012849fd3 | 318661f6338da29bc18b6a4340183aa918519f2c4d1ea15d7748d46c19e1fda4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,298 | MvQPF.Fix.rec_unique | Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hyp' | case h.h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x : Fix F α
⊢ ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: rec g) <$$> x = (TypeVec.id ::: h) <$$> x → rec g (mk x) = h (mk... | case h.h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x✝ : Fix F α
x : F (α ::: Fix F α)
hyp' : (TypeVec.id ::: rec g) <$$> x = (TypeVec.id ::: h) <$$> x
⊢ rec g (mk x) = h (m... | (:forall x ((:fv _uniq.48459) ((:c TypeVec.append1) (:fv _uniq.48397) (:fv _uniq.48471) ((:c MvQPF.Fix) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471)))) (:forall _ ((:c Eq) ((:fv _uniq.48459) ((:c TypeVec.append1) (:fv _uniq.48397) (:fv _uniq.48471) (:fv _uniq.48872))) ((:c MvFunctor.map) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"F","sexp":"(:forall _ ((:c TypeVec) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.48397) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c MvQPF) ((:c HAdd.hAdd) (:c Na... | (:forall x :explicit (:app (:fv FV1) (:arg :explicit 0 (:app (:c TypeVec.append1) (:arg :implicit 0) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c MvQPF.Fix) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c MvQPF) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1))))) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:app (:c TypeVec) (:arg :exp... | {"children":[{"source":"intro","sourceEnd":11537,"sourceStart":11532,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":11539,"sourceStart":11538,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hyp'","sourceEnd":11544,"sourceStart":11540,"tag":"identifier"}],"kind":"null","s... | [{"role":"fresh_name","source":"x","source_end":11539,"source_start":11538,"syntax_kind":"ident"},{"role":"fresh_name","source":"hyp'","source_end":11544,"source_start":11540,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 6 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 051a82f121ef36b6aaf88fefc5160906198c2104251b031ba8d88d8777099803 | 318661f6338da29bc18b6a4340183aa918519f2c4d1ea15d7748d46c19e1fda4 | 343109c36f6acd69fabab48c96f1d60e6d53ff0fdf7bb6da19538701de0fe24c | 02c81a1afed34a2aa9ae2eff03cd27b850280b9a7b1e82f6240096decfd30d22 |
cat-searcher/leandojo-benchmark-4-random | test | 2,299 | MvQPF.Fix.rec_unique | Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hyp, ← hyp', <a>MvQPF.Fix.rec_eq</a>] | case h.h
n : ℕ
F : TypeVec.{u} (n + 1) → Type u
q : MvQPF F
α : TypeVec.{u} n
β : Type u
g : F (α ::: β) → β
h : Fix F α → β
hyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)
x✝ : Fix F α
x : F (α ::: Fix F α)
hyp' : (TypeVec.id ::: rec g) <$$> x = (TypeVec.id ::: h) <$$> x
⊢ rec g (mk x) = h (m... | ((:c Eq) (:fv _uniq.48872) ((:c MvQPF.Fix.rec) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471) (:fv _uniq.48872) (:fv _uniq.48873) ((:c MvQPF.Fix.mk) (:fv _uniq.48397) (:fv _uniq.48459) (:fv _uniq.48469) (:fv _uniq.48471) (:fv _uniq.48939))) ((:fv _uniq.48874) ((:c MvQPF.Fix.mk) (:fv _uniq.48397... | [{"name":"n","sexp":"(:c Nat)"},{"name":"F","sexp":"(:forall _ ((:c TypeVec) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.48397) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:sort (+ u 1)))"},{"name":"q","sexp":"((:c MvQPF) ((:c HAdd.hAdd) (:c Na... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:app (:c MvQPF.Fix.rec) (:arg :implicit 0) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c MvQPF) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1))))) (:arg :implicit 3) (:arg :implicit-type 4 (:fv FV5)) (:arg :explicit 5 (:fv FV6)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"name":"F","sexp":"(:forall _ :explicit (:app (:c TypeVec) (:arg :exp... | {"children":[{"source":"rw","sourceEnd":11549,"sourceStart":11547,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11551,"sourceStart":11550,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semant... | [] | [{"source":"hyp","source_end":11554,"source_start":11551,"syntax_kind":"ident"},{"source":"hyp'","source_end":11564,"source_start":11560,"syntax_kind":"ident"},{"source":"Fix.rec_eq","source_end":11576,"source_start":11566,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48397","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48459","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 56 | 7 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f94b59c29870919beab5e228f827ba652b749d200739bfe9f8be2c59a302411 | 02c81a1afed34a2aa9ae2eff03cd27b850280b9a7b1e82f6240096decfd30d22 | 645a7b6fe8738ee7aefce452e8e98961d32d95758f5bd1cb26f7034d944f67bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,300 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let i₀ := hι.some | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
⊢ (⋂ i, t i).Nonempty | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
⊢ (⋂ i, t i).Nonemp... | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Set.iInter) (:fv _uniq.23378) (:fv _uniq.23561) (:lambda i (:fv _uniq.23561) ((:fv _uniq.23563) 0)))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.iInter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda i :explicit (:fv FV8) (:app (:fv FV10) (:arg :explicit 0 0))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"let","sourceEnd":15902,"sourceStart":15899,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"i₀","sourceEnd":15907,"sourceStart":15903,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},... | [] | [{"source":"hι.some","source_end":15919,"source_start":15911,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d02048740af1b520821e1aeca78a448c81b621529621e0896583acc8d6cc4489 | 7b57eb6da18c9e73d7d7bfcd9aeafe84fe10e219d316851092bb03c95b261d1b | 5dbe4e0aaf400fe4c38d67cb01982659812082b242dbe3b7159bd8cfc65f3160 | 2cd7307e506e98dc70c5dbb88fc54becc02fc1f93bed2d4adf75446e59b060a7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,301 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices (t i₀ ∩ ⋂ i, t i).<a>Set.Nonempty</a> by rwa [inter_eq_right.mpr (<a>Set.iInter_subset</a> _ i₀)] at this | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
⊢ (⋂ i, t i).Nonemp... | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
⊢ (t i₀ ∩ ⋂ i, t i)... | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Set.iInter) (:fv _uniq.23378) (:fv _uniq.23561) (:lambda i (:fv _uniq.23561) ((:fv _uniq.23563) 0)))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.iInter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda i :explicit (:fv FV8) (:app (:fv FV10) (:arg :explicit 0 0))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"suffices","sourceEnd":15930,"sourceStart":15922,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":15931,"sourceStart":15931,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":15931,"sourceStart":15931,"tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd"... | [] | [{"source":"(t i₀ ∩ ⋂ i, t i).Nonempty","source_end":15963,"source_start":15931,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"this","source_end":16026,"source_start":16022,"syntax_kind":"ident"},{"source":"inter_eq_right.mpr (iInter_subset _ i₀)","source_end":16017,"source_start":15976,"syntax_kind":"Lean.Parser.Te... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 5 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32caf88740924623f810d710de02c1b9581d5dc199c2d35b6f099ab9030f5d0c | 2cd7307e506e98dc70c5dbb88fc54becc02fc1f93bed2d4adf75446e59b060a7 | edf84e6ad5d7546411ccbff79e6b2e3dd44b67c3565d54f9eaad8dc63afba30d | 6b24b675be663ac0110f2588d1d99f545e69186fce1d77c4bb7f7150fc949e96 |
cat-searcher/leandojo-benchmark-4-random | test | 2,302 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.nonempty_iff_ne_empty</a>] at htn ⊢ | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
⊢ (t i₀ ∩ ⋂ i, t i)... | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ t i₀ ∩ ⋂ i, t i ≠ ∅ | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Inter.inter) ((:c Set) (:fv _uniq.23378)) ((:c Set.instInter) (:fv _uniq.23378)) ((:fv _uniq.23563) (:fv _uniq.23579)) ((:c Set.iInter) (:fv _uniq.23378) (:fv _uniq.23561) (:lambda i (:fv _uniq.23561) ((:fv _uniq.23563) 0))))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:fv FV10) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":16033,"sourceStart":16029,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16038,"sourceStart":16034,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":160... | [] | [{"source":"nonempty_iff_ne_empty","source_end":16061,"source_start":16040,"syntax_kind":"ident"},{"source":"htn","source_end":16069,"source_start":16066,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 11 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 728220f15742ee80bde69bab95478764f8d98490eb50769442dbf1e9f009a1cb | 6b24b675be663ac0110f2588d1d99f545e69186fce1d77c4bb7f7150fc949e96 | 8a6c5f50b6da053bb36999f317f9058b2693c542be891f60d261fd1d85cc4234 | 7c98534e5061ad78329dead82c150a98d36385ca3e2e57d04cb2e2a4fa1b0bba |
cat-searcher/leandojo-benchmark-4-random | test | 2,303 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mt</a> ((htc i₀).<a>IsCompact.elim_directed_family_closed</a> t htcl) | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ t i₀ ∩ ⋂ i, t i ≠ ∅ | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ ¬(Directed (fun x x_1 =>... | ((:c Ne) ((:c Set) (:fv _uniq.23378)) ((:c Inter.inter) ((:c Set) (:fv _uniq.23378)) ((:c Set.instInter) (:fv _uniq.23378)) ((:fv _uniq.23563) (:fv _uniq.23579)) ((:c Set.iInter) (:fv _uniq.23378) (:fv _uniq.23561) (:lambda i (:fv _uniq.23561) ((:fv _uniq.23563) 0)))) ((:c EmptyCollection.emptyCollection) ((:c Set) (:f... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":16081,"sourceStart":16076,"tag":"atom"},{"children":[{"name":"mt","semanticRole":"global","source":"mt","sourceEnd":16084,"sourceStart":16082,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":16086,"sourceStart":16085,"tag":"atom"},{"children":[{"children... | [] | [{"source":"mt ((htc i₀).elim_directed_family_closed t htcl)","source_end":16132,"source_start":16082,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 12 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8aacb5563f9bdc46ada2408d30ab98855ff924ef899d4670a6f3f8e267bbed6c | 7c98534e5061ad78329dead82c150a98d36385ca3e2e57d04cb2e2a4fa1b0bba | 8f5a91f723385f279ec1e89a17d07b8838340d787dfcf8c71d801c1fea8c4f5a | d0e01e9187f5e38e401707dde1a0f80aa20e5e22d98b5bf7facff767d0a2813c |
cat-searcher/leandojo-benchmark-4-random | test | 2,304 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | push_neg | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ ¬(Directed (fun x x_1 =>... | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ Directed (fun x x_1 => x... | ((:c Not) (:forall hdt ((:c Directed) ((:c Set) (:fv _uniq.23378)) (:fv _uniq.23561) (:lambda _ ((:c Set) (:fv _uniq.23378)) (:lambda _ ((:c Set) (:fv _uniq.23378)) ((:c Superset) ((:c Set) (:fv _uniq.23378)) ((:c Set.instHasSubset) (:fv _uniq.23378)) 1 0))) (:fv _uniq.23563)) ((:c Exists) (:fv _uniq.23561) (:lambda i ... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Not) (:arg :explicit 0 (:forall hdt :explicit (:app (:c Directed) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"push_neg","sourceEnd":16143,"sourceStart":16135,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.PushNeg.tacticPush_neg_","source":"push_neg","sourceEnd":16143,"sourceStart":16135,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 13 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c1af7b47331df6c0789aabccebea89adf4a519a4bd1881d21c136d6d23ef25d | d0e01e9187f5e38e401707dde1a0f80aa20e5e22d98b5bf7facff767d0a2813c | b0ca1774ed2e892f05294629909df3ac01eea8fadab4999a2254832ded4e7412 | 3b45b3c4276b1a29690dde995ac8e991ac9234aa078fdcf3a176863fc7149eb6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,305 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Set.nonempty_iff_ne_empty</a>] at htn ⊢ | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), t i ≠ ∅
⊢ Directed (fun x x_1 => x... | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
⊢ Directed (fun x x... | ((:c And) ((:c Directed) ((:c Set) (:fv _uniq.23378)) (:fv _uniq.23561) (:lambda _ ((:c Set) (:fv _uniq.23378)) (:lambda _ ((:c Set) (:fv _uniq.23378)) ((:c Superset) ((:c Set) (:fv _uniq.23378)) ((:c Set.instHasSubset) (:fv _uniq.23378)) 1 0))) (:fv _uniq.23563)) (:forall i (:fv _uniq.23561) ((:c Set.Nonempty) (:fv _u... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c And) (:arg :explicit 0 (:app (:c Directed) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c Supe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":16150,"sourceStart":16146,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16155,"sourceStart":16151,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":161... | [] | [{"source":"nonempty_iff_ne_empty","source_end":16182,"source_start":16161,"syntax_kind":"ident"},{"source":"htn","source_end":16190,"source_start":16187,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 14 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08a89d3807664dc78dad6c0341f2bae20b4c878e7dcb802dba9362d3d06bbcfc | 3b45b3c4276b1a29690dde995ac8e991ac9234aa078fdcf3a176863fc7149eb6 | 39d7a41a4f26cfe52244963e5f73885a533d5d08730dd903337e5f800e2ad71d | e81aff6ac2c87c4bb9afd76cecd4340e7efe81b34d669bd35419017bf20d8447 |
cat-searcher/leandojo-benchmark-4-random | test | 2,306 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨htd, fun i => ?_⟩ | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
⊢ Directed (fun x x... | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
i : ι
⊢ (t i₀ ∩ t i... | ((:c And) ((:c Directed) ((:c Set) (:fv _uniq.23378)) (:fv _uniq.23561) (:lambda _ ((:c Set) (:fv _uniq.23378)) (:lambda _ ((:c Set) (:fv _uniq.23378)) ((:c Superset) ((:c Set) (:fv _uniq.23378)) ((:c Set.instHasSubset) (:fv _uniq.23378)) 1 0))) (:fv _uniq.23563)) (:forall i (:fv _uniq.23561) ((:c Set.Nonempty) (:fv _u... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c And) (:arg :explicit 0 (:app (:c Directed) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:lambda _ :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c Supe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":16203,"sourceStart":16197,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":16207,"sourceStart":16204,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"htd","sourceEnd":16210,"sourceStart":16207,"tag":"identifier"},{"source":",","sourceEnd":162... | [] | [{"source":"⟨htd, fun i => ?_⟩","source_end":16226,"source_start":16204,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 15 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d93c7ed839f4c925f3d35f338231aac139a70ce81d9696dad9512f62d9bf57d | e81aff6ac2c87c4bb9afd76cecd4340e7efe81b34d669bd35419017bf20d8447 | 232fa98f2ec9f64b6147085c610c114c5eb6630345936d56e83d222f83302aac | b3e95578a0649454280b8577b4560232999fd9bada74cd6bb3cb0a193c604fa7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,307 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases htd i₀ i with ⟨j, hji₀, hji⟩ | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
i : ι
⊢ (t i₀ ∩ t i... | case intro.intro
X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
i ... | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Inter.inter) ((:c Set) (:fv _uniq.23378)) ((:c Set.instInter) (:fv _uniq.23378)) ((:fv _uniq.23563) (:fv _uniq.23579)) ((:fv _uniq.23563) (:fv _uniq.24071)))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:fv FV10) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":16235,"sourceStart":16229,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"htd","sourceEnd":16239,"sourceStart":16236,"tag":"identifier"},{"children":[{"contextIndex... | [] | [{"source":"htd i₀ i","source_end":16246,"source_start":16236,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨j, hji₀, hji⟩","source_end":16272,"source_start":16252,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 16 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63b6fa9cad1b9ad9ea0b5baccc13e4bda226d53cb534823132d7ca4b6a982a71 | b3e95578a0649454280b8577b4560232999fd9bada74cd6bb3cb0a193c604fa7 | a9465e495f237e9bf9d051b4b9066b0cef0a392ea6dae5dde4e1bf78e4c88319 | 0fa9a9fe52519c9985fab89dbfa392cd367306db777b97549fcb246512e84045 |
cat-searcher/leandojo-benchmark-4-random | test | 2,308 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (htn j).<a>Set.Nonempty.mono</a> (<a>Set.subset_inter</a> hji₀ hji) | case intro.intro
X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
htn : ∀ (i : ι), (t i).Nonempty
i ... | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Inter.inter) ((:c Set) (:fv _uniq.23378)) ((:c Set.instInter) (:fv _uniq.23378)) ((:fv _uniq.23563) (:fv _uniq.23579)) ((:fv _uniq.23563) (:fv _uniq.24071)))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:fv FV10) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":16280,"sourceStart":16275,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":16282,"sourceStart":16281,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"htn","sourceEnd":16285,"sourceStart":16282,"tag":"identifier"},{"ch... | [] | [{"source":"(htn j).mono (subset_inter hji₀ hji)","source_end":16319,"source_start":16281,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 17 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7133ef4fae666bd4e394b6c753904a8cdd09af8cf0b38cdfebcfec5832105b8d | 0fa9a9fe52519c9985fab89dbfa392cd367306db777b97549fcb246512e84045 | 5c80c9c27ea67f9308159bb61270578ac512dad5de834875d6d1243309d2e702 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,309 | IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed | Mathlib/Topology/Compactness/Compact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [inter_eq_right.mpr (<a>Set.iInter_subset</a> _ i₀)] at this | X : Type u
Y : Type v
ι✝ : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t✝ : Set X
ι : Type v
hι : Nonempty ι
t : ι → Set X
htd : Directed (fun x x_1 => x ⊇ x_1) t
htn : ∀ (i : ι), (t i).Nonempty
htc : ∀ (i : ι), IsCompact (t i)
htcl : ∀ (i : ι), IsClosed (t i)
i₀ : ι := hι.some
this : (t i₀ ∩ ⋂ i,... | ((:c Set.Nonempty) (:fv _uniq.23378) ((:c Set.iInter) (:fv _uniq.23378) (:fv _uniq.23561) (:lambda i (:fv _uniq.23561) ((:fv _uniq.23563) 0)))) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.23378))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.23380))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.23378))"},{"name":"t✝","... | (:app (:c Set.Nonempty) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set.iInter) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV8)) (:arg :explicit 2 (:lambda i :explicit (:fv FV8) (:app (:fv FV10) (:arg :explicit 0 0))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":15974,"sourceStart":15971,"tag":"atom"},{"children":[{"source":"[","sourceEnd":15976,"sourceStart":15975,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"inter_eq_right.m... | [] | [{"source":"this","source_end":16026,"source_start":16022,"syntax_kind":"ident"},{"source":"inter_eq_right.mpr (iInter_subset _ i₀)","source_end":16017,"source_start":15976,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23378","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23380","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 58 | 6 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a2be680cb53962c3b2cb1634c02401c78a8b49d97fe5225d894c1bbcfdcf7f81 | dca06ce926c9c878e1631eeb42f52136d3c6db0dcc66b5ea04ba5c43667d0b6d | d61bbeccf8d6b4880e270f22e3368ed62248c7f04a49f907138c00eb35f6a2b6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,310 | Function.IsFixedPt.apply | Mathlib/Dynamics/FixedPoints/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert hx | α : Type u
β : Type v
f fa g : α → α
x✝ y : α
fb : β → β
m n k : ℕ
e : Perm α
x : α
hx : IsFixedPt f x
⊢ IsFixedPt f (f x) | ((:c Function.IsFixedPt) (:fv _uniq.1042) (:fv _uniq.1048) ((:fv _uniq.1048) (:fv _uniq.1092))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.1042) (:fv _uniq.1042))"},{"name":"fa","sexp":"(:forall _ (:fv _uniq.1042) (:fv _uniq.1042))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.1042) (:fv _uniq.1042))"},{"name":"x✝","sexp":"(:fv _uniq.1042)"... | (:app (:c Function.IsFixedPt) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:app (:fv FV2) (:arg :explicit 0 (:fv FV13))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1042","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1044","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"convert","sourceEnd":3158,"sourceStart":3151,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"semanticRole":"local","source":"hx","sourceEnd":3161,"sourceStart":3... | [] | [{"source":"hx","source_end":3161,"source_start":3159,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1042","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1044","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 25 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fc2e4f92aef542ab0bae91f2e7b3ae384eead32427f39bfebb60699af6d92e7 | 2a27934b248db6adbf55973d744e36f6cb27f02474a3b420f9a459cb2e6fb6a1 | 3f40f6436cb02bcb142fbe9d6d879ccb14910e888ef14b5063ba9a2de4a4312c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,311 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let f₁ := hf.toL1 f | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:fv _uniq.790282) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.toNormedSpace) (:c Real) (:c Real.normedField)) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:fv _uniq.793419) 0))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"let","sourceEnd":54759,"sourceStart":54756,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"f₁","sourceEnd":54764,"sourceStart":54760,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},... | [] | [{"source":"hf.toL1 f\n -- Go to the `L¹` space","source_end":54777,"source_start":54768,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2736b195cb53af7191d028d18da42085f8fa492568ca960c27fe5158b27d1c96 | a842df6fa8a92dd890ac6483b803de7511ee3a897049d5f0807f6c781b625a7a | 33007507a5380bf1e1c0b6a42df56090db8f8e09354efff59d465d0061b694b1 | daf47cd9392dc8d591498de81f80e39273195f95d01dd1873ed9ad4ec5c071b3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,312 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have eq₁ : <a>ENNReal.toReal</a> (∫⁻ a, <a>ENNReal.ofReal</a> (f a) ∂μ) = ‖<a>MeasureTheory.Lp.posPart</a> f₁‖ := by rw [<a>MeasureTheory.L1.norm_def</a>] congr 1 apply <a>MeasureTheory.lintegral_congr_ae</a> filter_upwards [<a>MeasureTheory.Lp.coeFn_posPart</a> f₁, hf.coeFn_toL1] with _ h₁ h₂ rw [h₁, h₂, <a>ENNReal.of... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:fv _uniq.790282) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.toNormedSpace) (:c Real) (:c Real.normedField)) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:fv _uniq.793419) 0))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":54811,"sourceStart":54807,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"eq₁","sourceEnd":54817,"sourceStart":54812,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"eq₁","sourceEnd":54817,"sourceStart":54812,"tag":"n... | [] | [{"source":"ENNReal.toReal (∫⁻ a, ENNReal.ofReal (f a) ∂μ) = ‖Lp.posPart f₁‖","source_end":54897,"source_start":54820,"syntax_kind":"«term_=_»"},{"source":"L1.norm_def","source_end":54923,"source_start":54912,"syntax_kind":"ident"},{"source":"lintegral_congr_ae","source_end":54965,"source_start":54947,"syntax_kind":"id... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 5 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ccacfa7b3924d1cbebbd389ab932472018839a1270f414d2bf0a399ed8bbfaf | daf47cd9392dc8d591498de81f80e39273195f95d01dd1873ed9ad4ec5c071b3 | e4421a41c3d0918f262c7dd35d8a8e4fbe46f48af830fc8e1f6d45b86088cffa | 9c1d8619e1186f4b1be495661b715fe9f01306a90e6babf0f12f91656d1e8a85 |
cat-searcher/leandojo-benchmark-4-random | test | 2,313 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have eq₂ : <a>ENNReal.toReal</a> (∫⁻ a, <a>ENNReal.ofReal</a> (-f a) ∂μ) = ‖<a>MeasureTheory.Lp.negPart</a> f₁‖ := by rw [<a>MeasureTheory.L1.norm_def</a>] congr 1 apply <a>MeasureTheory.lintegral_congr_ae</a> filter_upwards [<a>MeasureTheory.Lp.coeFn_negPart</a> f₁, hf.coeFn_toL1] with _ h₁ h₂ rw [h₁, h₂, <a>ENNReal.o... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:fv _uniq.790282) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.toNormedSpace) (:c Real) (:c Real.normedField)) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:fv _uniq.793419) 0))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":55235,"sourceStart":55231,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"eq₂","sourceEnd":55241,"sourceStart":55236,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"eq₂","sourceEnd":55241,"sourceStart":55236,"tag":"n... | [] | [{"source":"ENNReal.toReal (∫⁻ a, ENNReal.ofReal (-f a) ∂μ) = ‖Lp.negPart f₁‖","source_end":55322,"source_start":55244,"syntax_kind":"«term_=_»"},{"source":"L1.norm_def","source_end":55348,"source_start":55337,"syntax_kind":"ident"},{"source":"lintegral_congr_ae","source_end":55390,"source_start":55372,"syntax_kind":"i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 27 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0992b2c0c0ac7ed655fae126eb23f48cf11006ba60d7f6c255b9198e75f046a9 | 9c1d8619e1186f4b1be495661b715fe9f01306a90e6babf0f12f91656d1e8a85 | 59b0d6ff3c574afe9357c22a7deb487c423973f4f4528fe64e92d4f49d7fb10f | 5f15f9ccdf1d086d08a5e7ab25d06d5b9f33c415de5456a11de1a13ae490e502 |
cat-searcher/leandojo-benchmark-4-random | test | 2,314 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [eq₁, eq₂, <a>MeasureTheory.integral</a>, <a>dif_pos</a>, <a>dif_pos</a>] | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c MeasureTheory.integral) (:fv _uniq.790282) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.toNormedSpace) (:c Real) (:c Real.normedField)) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:fv _uniq.793419) 0))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instH... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55672,"sourceStart":55670,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55674,"sourceStart":55673,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":27,"seman... | [] | [{"source":"eq₁","source_end":55679,"source_start":55674,"syntax_kind":"ident"},{"source":"eq₂","source_end":55686,"source_start":55681,"syntax_kind":"ident"},{"source":"integral","source_end":55696,"source_start":55688,"syntax_kind":"ident"},{"source":"dif_pos","source_end":55705,"source_start":55698,"syntax_kind":"id... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 48 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8db485a84df5843026eb8b6e49f7eb040dc760033f1c99520437c1936c7aa1f3 | 5f15f9ccdf1d086d08a5e7ab25d06d5b9f33c415de5456a11de1a13ae490e502 | 14cf878d2a52a9bea0e389cb70c9e7b16387165da9f2affe230d15128d9c3480 | 56c26b33260977a1b87b421fbbd7cebc5fb431d05dc57bf18ad5761fc4a0475b |
cat-searcher/leandojo-benchmark-4-random | test | 2,316 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.L1.norm_def</a>] | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:fv _uniq.793419) 0))))) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.790282) (:c Real) (:fv _uniq.793177) ((:c Unif... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":54910,"sourceStart":54908,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":54912,"sourceStart":54911,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.L1... | [] | [{"source":"L1.norm_def","source_end":54923,"source_start":54912,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 7 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93ffc31ef05ed2d4ab92dcf567c1ac3bf792913cd140e9aded7045aec0d7cfbd | 127ac480409d2795d7f359499778ec26f0e23383846c5bb0aff9ff9e447a363e | d362376c6a68dce8c669ff28f5fd0eee628c28cb5d4cf62f881d86313d58a5bd | b1ea7cb71d1ea8e7cc3e8c611124589d5fb488c4108a5bcb5ba7788e79e36d24 |
cat-searcher/leandojo-benchmark-4-random | test | 2,317 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 1 | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | case e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type... | ((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:fv _uniq.793419) 0))))) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":54934,"sourceStart":54929,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":54936,"sourceStart":54935,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":54936,"sourceStart":54935,"tag":"node"}],"kind":"null","source":"1","sourceEnd":54936,"sourceStart":54935,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 10 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c63afe415090e6b4d7c4ada87c1ad5e10d4fc9431ee8b80903447cd178358a19 | b1ea7cb71d1ea8e7cc3e8c611124589d5fb488c4108a5bcb5ba7788e79e36d24 | 8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b | f1334fcb2854aa1a9b217765517376f3cb02ded805a8b602eccd1be0f2e0a035 |
cat-searcher/leandojo-benchmark-4-random | test | 2,318 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.lintegral_congr_ae</a> | case e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type... | case e_a.h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:fv _uniq.793419) 0)))) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofNN... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 0))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":54946,"sourceStart":54941,"tag":"atom"},{"name":"MeasureTheory.lintegral_congr_ae","semanticRole":"global","source":"lintegral_congr_ae","sourceEnd":54965,"sourceStart":54947,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply lintegral_congr_ae","sourceEnd"... | [] | [{"source":"lintegral_congr_ae","source_end":54965,"source_start":54947,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 11 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 472363780dc940727aa6e7bd755443dd7d7cfc78f90d735adc1fde20d07ba23a | f1334fcb2854aa1a9b217765517376f3cb02ded805a8b602eccd1be0f2e0a035 | 347990bb4b204df5f5b92de76438fba1c7810756d1f3ff2bc15f19690fd43bfb | 19fead3d02c8cced4a9441185be964fae05b770e3db091ce61a756f1fa545bab |
cat-searcher/leandojo-benchmark-4-random | test | 2,319 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [<a>MeasureTheory.Lp.coeFn_posPart</a> f₁, hf.coeFn_toL1] with _ h₁ h₂ | case e_a.h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | ((:c Filter.EventuallyEq) (:fv _uniq.790282) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.790282) ((:c MeasureTheory.Measure) (:fv _uniq.790282) (:fv _uniq.793177)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.790282) (:fv _uniq.793177)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.790282) (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"filter_upwards","sourceEnd":54984,"sourceStart":54970,"tag":"atom"},{"children":[{"source":"[","sourceEnd":54986,"sourceStart":54985,"tag":"atom"},{"children":[{"children":[{"name":"MeasureTheory.Lp.coeFn_posPart","semanticRole":"global","source":"Lp.coeFn_posPart","sourceEnd":55002,"sourceStart... | [] | [{"source":"hf.coeFn_toL1","source_end":55022,"source_start":55009,"syntax_kind":"ident"},{"source":"Lp.coeFn_posPart f₁","source_end":55007,"source_start":54986,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 12 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1a757aa756c7098ed2366d1e661dc951b0b938e52ee7834d5a7d2637c11f65e | 19fead3d02c8cced4a9441185be964fae05b770e3db091ce61a756f1fa545bab | 70b26b0837e0472683639cf55070c9501914c8a13a8ef6acad0f63b3fdcc6a7a | 0631fb76ffed0e7d2a26a0b976d781a22ddaaa9bfb3e8be6fdfaa0fd4f03b291 |
cat-searcher/leandojo-benchmark-4-random | test | 2,320 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h₁, h₂, <a>ENNReal.ofReal</a>] | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:fv _uniq.793419) (:fv _uniq.794073))) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Real) (:c Real.normedAddC... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 (:fv FV27)))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55047,"sourceStart":55045,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55049,"sourceStart":55048,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":28,"seman... | [] | [{"source":"h₁","source_end":55053,"source_start":55049,"syntax_kind":"ident"},{"source":"h₂","source_end":55059,"source_start":55055,"syntax_kind":"ident"},{"source":"ENNReal.ofReal","source_end":55075,"source_start":55061,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 13 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 530d2985d20b5f1c0294fd5d77a28b183e79dcab1527b914c47b9edbf5f4c942 | 0631fb76ffed0e7d2a26a0b976d781a22ddaaa9bfb3e8be6fdfaa0fd4f03b291 | 8f16c25a28ff103029502936d5004c1bf304fa59f656c6651580a8419b89abdc | be356f7594b47f4f8ea5a3b0095c6886e9c8c2787647df829b5a685f5a3e425d |
cat-searcher/leandojo-benchmark-4-random | test | 2,321 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 1 | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | case h.e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofNNReal) ((:c Real.toNNReal) ((:fv _uniq.793419) (:fv _uniq.794073)))) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 (:fv FV27)))))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":55086,"sourceStart":55081,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":55088,"sourceStart":55087,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":55088,"sourceStart":55087,"tag":"node"}],"kind":"null","source":"1","sourceEnd":55088,"sourceStart":55087,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 18 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 83db0ef8be8f6a9a74669ba28330d77c23b81398bfb683283ce903e5139227d6 | be356f7594b47f4f8ea5a3b0095c6886e9c8c2787647df829b5a685f5a3e425d | 8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b | a2dc375b81dd365cf89bc3ab0b4f40f1a5b9fe725836e0e0872a3be5f203bf73 |
cat-searcher/leandojo-benchmark-4-random | test | 2,322 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>NNReal.eq</a> | case h.e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c NNReal) ((:c Real.toNNReal) ((:fv _uniq.793419) (:fv _uniq.794073))) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Real) (:c Real.normedAddCommGroup)))) ((:c Max.max... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 (:fv FV27)))))) (:arg :explicit 2 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":55098,"sourceStart":55093,"tag":"atom"},{"name":"NNReal.eq","semanticRole":"global","source":"NNReal.eq","sourceEnd":55108,"sourceStart":55099,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply NNReal.eq","sourceEnd":55108,"sourceStart":55093,"tag":"node"} | [] | [{"source":"NNReal.eq","source_end":55108,"source_start":55099,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 19 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77fc9d4e08d982c629e191412859c6f1d9cdb34f1c8f4d6344553971b68573cc | a2dc375b81dd365cf89bc3ab0b4f40f1a5b9fe725836e0e0872a3be5f203bf73 | 40586911d7b66ce2a846e8d04c9f4a9d5f1f2a2e800c10bae7d03c1fc85b2e51 | 23a0b87f73e1437536a7f35838a43076b445032492d7294c6f0bd1656006be02 |
cat-searcher/leandojo-benchmark-4-random | test | 2,323 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.nnnorm_of_nonneg</a> (<a>le_max_right</a> _ _)] | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c Real) ((:c NNReal.toReal) ((:c Real.toNNReal) ((:fv _uniq.793419) (:fv _uniq.794073)))) ((:c NNReal.toReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Real) (:c R... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 (:fv FV27)))))))) (:arg :explicit 2 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:c Re... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55115,"sourceStart":55113,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55117,"sourceStart":55116,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Rea... | [] | [{"source":"Real.nnnorm_of_nonneg (le_max_right _ _)","source_end":55157,"source_start":55117,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 20 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9495a010c0462d154ea4e1b35637ec5fc039e537023ae09adab1c0435c4a360b | 23a0b87f73e1437536a7f35838a43076b445032492d7294c6f0bd1656006be02 | 5554e099ee2790ffe853cc6cb227ab0b580891fc794433b5ba8fab973a7e84d6 | 14fdd036d6a8c009c1c90734f4f42ccf7834b48cdc9557b5a0dc497ffce7b46d |
cat-searcher/leandojo-benchmark-4-random | test | 2,324 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.coe_toNNReal'</a>, <a>NNReal.coe_mk</a>] | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c Real) ((:c NNReal.toReal) ((:c Real.toNNReal) ((:fv _uniq.793419) (:fv _uniq.794073)))) ((:c NNReal.toReal) ((:c Subtype.mk) (:c Real) (:lambda r (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) 0)) ((:c Max.max) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:fv FV24) (:arg :explicit 0 (:fv FV27)))))))) (:arg :explicit 2 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c Subtype.mk) (:arg :implicit-type 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55165,"sourceStart":55163,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55167,"sourceStart":55166,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Real.coe_toNNRea... | [] | [{"source":"Real.coe_toNNReal'","source_end":55185,"source_start":55167,"syntax_kind":"ident"},{"source":"NNReal.coe_mk","source_end":55200,"source_start":55187,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 23 | exact | true | 1 | 29 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52dc1cce34d08b2255c06883c79c9867bba3bdf0523b5a54fa37ba4d9e83576d | 14fdd036d6a8c009c1c90734f4f42ccf7834b48cdc9557b5a0dc497ffce7b46d | 495034182b6266da76ffe9a5676b4628f140a68bfb87e8a9c1de9ed36d1b34ef | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,325 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.L1.norm_def</a>] | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | ((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) 0)))))) ((:c Norm.norm) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.790... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55335,"sourceStart":55333,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55337,"sourceStart":55336,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.L1... | [] | [{"source":"L1.norm_def","source_end":55348,"source_start":55337,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 29 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08877f15746c2dfdb18fc234efbeb37426e65a8a23bb662046661f89dedfe89b | a5667d4dcf4ecefa30b2e96414ef79147893520bfd1c79197d8fa64c8a6d4032 | d362376c6a68dce8c669ff28f5fd0eee628c28cb5d4cf62f881d86313d58a5bd | 0805e63cb582507b145d564dab1c6ff8b70c4170d6ff9b5aa3727facf27b706f |
cat-searcher/leandojo-benchmark-4-random | test | 2,326 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 1 | α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u_5
inst... | case e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type... | ((:c Eq) (:c Real) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) 0)))))) ((:c ENNReal.toReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":55359,"sourceStart":55354,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":55361,"sourceStart":55360,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":55361,"sourceStart":55360,"tag":"node"}],"kind":"null","source":"1","sourceEnd":55361,"sourceStart":55360,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 32 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 45bebd97926fe130f2f709f3d4436ee1d4c955db01b51f91ee1be627b4c33fb9 | 0805e63cb582507b145d564dab1c6ff8b70c4170d6ff9b5aa3727facf27b706f | 8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b | f0e4e99f285f9a2329adcf71c757fb6323a61439dfecefd690674d9f456aa349 |
cat-searcher/leandojo-benchmark-4-random | test | 2,327 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.lintegral_congr_ae</a> | case e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type... | case e_a.h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:lambda a (:fv _uniq.790282) ((:c ENNReal.ofReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) 0))))) ((:c MeasureTheory.lintegral) (:fv _uniq.790282) (:fv _uniq.793177) (:fv _uniq.793186) (:la... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV19)) (:arg :explicit 3 (:lambda a :explicit (:fv FV0) (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":55371,"sourceStart":55366,"tag":"atom"},{"name":"MeasureTheory.lintegral_congr_ae","semanticRole":"global","source":"lintegral_congr_ae","sourceEnd":55390,"sourceStart":55372,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply lintegral_congr_ae","sourceEnd"... | [] | [{"source":"lintegral_congr_ae","source_end":55390,"source_start":55372,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 33 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ca785dee98ae7b15273bc7f0e2e54ec7ccb5ba1af3755d45571cbf32bbac684 | f0e4e99f285f9a2329adcf71c757fb6323a61439dfecefd690674d9f456aa349 | 347990bb4b204df5f5b92de76438fba1c7810756d1f3ff2bc15f19690fd43bfb | 70519e701770b8ac72b7284fac740e9a9be436f8ea531bbe0e35df7af1239358 |
cat-searcher/leandojo-benchmark-4-random | test | 2,328 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [<a>MeasureTheory.Lp.coeFn_negPart</a> f₁, hf.coeFn_toL1] with _ h₁ h₂ | case e_a.h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | ((:c Filter.EventuallyEq) (:fv _uniq.790282) (:c ENNReal) ((:c MeasureTheory.ae) (:fv _uniq.790282) ((:c MeasureTheory.Measure) (:fv _uniq.790282) (:fv _uniq.793177)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.790282) (:fv _uniq.793177)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.790282) (:fv ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"filter_upwards","sourceEnd":55409,"sourceStart":55395,"tag":"atom"},{"children":[{"source":"[","sourceEnd":55411,"sourceStart":55410,"tag":"atom"},{"children":[{"children":[{"name":"MeasureTheory.Lp.coeFn_negPart","semanticRole":"global","source":"Lp.coeFn_negPart","sourceEnd":55427,"sourceStart... | [] | [{"source":"hf.coeFn_toL1","source_end":55447,"source_start":55434,"syntax_kind":"ident"},{"source":"Lp.coeFn_negPart f₁","source_end":55432,"source_start":55411,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 34 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 241a1968ee2acf41c35051890f9b610ea8926fd33a9e9f3ced00705c144c463c | 70519e701770b8ac72b7284fac740e9a9be436f8ea531bbe0e35df7af1239358 | 1e17471ca772e77d436e71f0c793546492033dd0175004fcc7f315cacdc057b3 | e50c939a5f5bf12abad9eda207e89f0e68cf8e037e2e1ffb8358c7833d46d996 |
cat-searcher/leandojo-benchmark-4-random | test | 2,329 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h₁, h₂, <a>ENNReal.ofReal</a>] | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) (:fv _uniq.794933)))) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormed... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofReal) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV24) (:arg :explicit 0 (:fv FV28)))))))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55472,"sourceStart":55470,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55474,"sourceStart":55473,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":29,"seman... | [] | [{"source":"h₁","source_end":55478,"source_start":55474,"syntax_kind":"ident"},{"source":"h₂","source_end":55484,"source_start":55480,"syntax_kind":"ident"},{"source":"ENNReal.ofReal","source_end":55500,"source_start":55486,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 35 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53ce4e2da086eb83d76c845135ba5a8b5461e5200af9f1291342a41296f581dc | e50c939a5f5bf12abad9eda207e89f0e68cf8e037e2e1ffb8358c7833d46d996 | 8f16c25a28ff103029502936d5004c1bf304fa59f656c6651580a8419b89abdc | 6a5e5aa76e546f41c626de9ce3f453288807e55256ff710818d7e86e9376aea9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,330 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 1 | case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Type u... | case h.e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | ((:c Eq) (:c ENNReal) ((:c ENNReal.ofNNReal) ((:c Real.toNNReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) (:fv _uniq.794933))))) ((:c ENNReal.ofNNReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":55511,"sourceStart":55506,"tag":"atom"},{"children":[{"children":[{"source":"1","sourceEnd":55513,"sourceStart":55512,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":55513,"sourceStart":55512,"tag":"node"}],"kind":"null","source":"1","sourceEnd":55513,"sourceStart":55512,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 40 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1dd1a85fd6d239cfc564da89d5ac0312212617e745bad45c4e98d2cb994f8756 | 6a5e5aa76e546f41c626de9ce3f453288807e55256ff710818d7e86e9376aea9 | 8f6f3e102b5370312cdd673cdfe3acc12b0ae98d6a7b45eb025d5bd0bb778a5b | 47ecdfbb480db3c39b4cdd58ca60efd527847053a636f07cdb47612f6b814e3e |
cat-searcher/leandojo-benchmark-4-random | test | 2,331 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>NNReal.eq</a> | case h.e_a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : Ty... | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c NNReal) ((:c Real.toNNReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) (:fv _uniq.794933)))) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:c Real) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c NNReal)) (:arg :explicit 1 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV24) (:arg :explicit 0 (:fv FV28)))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":55523,"sourceStart":55518,"tag":"atom"},{"name":"NNReal.eq","semanticRole":"global","source":"NNReal.eq","sourceEnd":55533,"sourceStart":55524,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply NNReal.eq","sourceEnd":55533,"sourceStart":55518,"tag":"node"} | [] | [{"source":"NNReal.eq","source_end":55533,"source_start":55524,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 41 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1862a0f67ec9a082fc168256342971af1a5f4fae386b3dc99faf57130cfdc78 | 47ecdfbb480db3c39b4cdd58ca60efd527847053a636f07cdb47612f6b814e3e | 40586911d7b66ce2a846e8d04c9f4a9d5f1f2a2e800c10bae7d03c1fc85b2e51 | a656d65bfb3b19b2a251817f69913b80d7f547e646594e36c043ac13366ed70d |
cat-searcher/leandojo-benchmark-4-random | test | 2,332 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Real.coe_toNNReal'</a>, <a>coe_nnnorm</a>, <a>nnnorm_neg</a>] | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c Real) ((:c NNReal.toReal) ((:c Real.toNNReal) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) (:fv _uniq.794933))))) ((:c NNReal.toReal) ((:c NNNorm.nnnorm) (:c Real) ((:c SeminormedAddGroup.toNNNorm) (:c Real) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:c Real) ((:c NormedAddCommGrou... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c Real.toNNReal) (:arg :explicit 0 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV24) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":55542,"sourceStart":55538,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":55547,"sourceStart":55543,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":555... | [] | [{"source":"Real.coe_toNNReal'","source_end":55567,"source_start":55549,"syntax_kind":"ident"},{"source":"coe_nnnorm","source_end":55579,"source_start":55569,"syntax_kind":"ident"},{"source":"nnnorm_neg","source_end":55591,"source_start":55581,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 42 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe462d452c45f485624f249895ca7138c9e0cd6e226637adde95b0fdc54ad9ec | a656d65bfb3b19b2a251817f69913b80d7f547e646594e36c043ac13366ed70d | 4f141200f4f278bfcf3501a03e185c5980c8e19b4c92d9578c94cd2149071b9c | ad58b81384630328946a9c1015802396cfd9038f0bdc828d736b893e32593d63 |
cat-searcher/leandojo-benchmark-4-random | test | 2,333 | MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part | Mathlib/MeasureTheory/Integral/Bochner.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.norm_of_nonpos</a> (<a>min_le_right</a> _ _), ← <a>max_neg_neg</a>, <a>neg_zero</a>] | case h.e_a.a
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁹ : NontriviallyNormedField 𝕜
inst✝⁸ : NormedSpace 𝕜 E
inst✝⁷ : SMulCommClass ℝ 𝕜 E
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace ℝ F
inst✝⁴ : CompleteSpace F
G : ... | ((:c Eq) (:c Real) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:fv _uniq.793419) (:fv _uniq.794933))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Norm.norm) (:c Real) ((:c S... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.790285))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.790285) (:c Real.nor... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":55599,"sourceStart":55597,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55601,"sourceStart":55600,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Rea... | [] | [{"source":"Real.norm_of_nonpos (min_le_right _ _)","source_end":55639,"source_start":55601,"syntax_kind":"Lean.Parser.Term.app"},{"source":"max_neg_neg","source_end":55656,"source_start":55645,"syntax_kind":"ident"},{"source":"neg_zero","source_end":55666,"source_start":55658,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.790282","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.790285","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 294 | 43 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b89b8e1c77bffe0b4257528db542fce0d7fec32cb0e814cb6d17aac1a4494e4 | ad58b81384630328946a9c1015802396cfd9038f0bdc828d736b893e32593d63 | 4dd162a4c6133d704613c7cc1352ae241838cb43e2a5a9ca39b7ec24f8f7064f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,334 | HomogeneousLocalization.val_sub | Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_eq_add_neg</a>, ← <a>HomogeneousLocalization.val_neg</a>, ← <a>HomogeneousLocalization.val_add</a>] | ι : Type u_1
R : Type u_2
A : Type u_3
inst✝⁵ : AddCommMonoid ι
inst✝⁴ : DecidableEq ι
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Algebra R A
𝒜 : ι → Submodule R A
inst✝ : GradedAlgebra 𝒜
x : Submonoid A
y1 y2 : HomogeneousLocalization 𝒜 x
⊢ (y1 - y2).val = y1.val - y2.val | ι : Type u_1
R : Type u_2
A : Type u_3
inst✝⁵ : AddCommMonoid ι
inst✝⁴ : DecidableEq ι
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Algebra R A
𝒜 : ι → Submodule R A
inst✝ : GradedAlgebra 𝒜
x : Submonoid A
y1 y2 : HomogeneousLocalization 𝒜 x
⊢ (y1 - y2).val = (y1 + -y2).val | ((:c Eq) ((:c Localization) (:fv _uniq.275566) ((:c CommRing.toCommMonoid) (:fv _uniq.275566) (:fv _uniq.275584)) (:fv _uniq.277671)) ((:c HomogeneousLocalization.val) (:fv _uniq.275560) (:fv _uniq.275563) (:fv _uniq.275566) (:fv _uniq.275581) (:fv _uniq.275584) (:fv _uniq.275901) (:fv _uniq.276430) (:fv _uniq.277671) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c AddCommMonoid) (:fv _uniq.275560))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.275560))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.275563))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Localization) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c HomogeneousLocalization.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275560","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275563","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":18368,"sourceStart":18366,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18370,"sourceStart":18369,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sub_eq_add_neg",... | [] | [{"source":"sub_eq_add_neg","source_end":18384,"source_start":18370,"syntax_kind":"ident"},{"source":"val_neg","source_end":18397,"source_start":18390,"syntax_kind":"ident"},{"source":"val_add","source_end":18410,"source_start":18403,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275560","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275563","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 131 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44383b7fa10f5db0b1b4c12ac0e0ed3f278d5a51616f851cb82a0991ffef125e | ee8e92e03b98ec193baf1281da17768431c6acd06d3c3a929d688b9aaff10744 | d4227849de7782839c1f7b5b9e263edfceb026d7520719e8a2e1267b836e6670 | a9fb819bd3e2f833647c8d7580d2c3275c3fe382d85110fc9af7649140cc15a0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,335 | HomogeneousLocalization.val_sub | Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | ι : Type u_1
R : Type u_2
A : Type u_3
inst✝⁵ : AddCommMonoid ι
inst✝⁴ : DecidableEq ι
inst✝³ : CommRing R
inst✝² : CommRing A
inst✝¹ : Algebra R A
𝒜 : ι → Submodule R A
inst✝ : GradedAlgebra 𝒜
x : Submonoid A
y1 y2 : HomogeneousLocalization 𝒜 x
⊢ (y1 - y2).val = (y1 + -y2).val | ((:c Eq) ((:c Localization) (:fv _uniq.275566) ((:c CommRing.toCommMonoid) (:fv _uniq.275566) (:fv _uniq.275584)) (:fv _uniq.277671)) ((:c HomogeneousLocalization.val) (:fv _uniq.275560) (:fv _uniq.275563) (:fv _uniq.275566) (:fv _uniq.275581) (:fv _uniq.275584) (:fv _uniq.275901) (:fv _uniq.276430) (:fv _uniq.277671) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"A","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c AddCommMonoid) (:fv _uniq.275560))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.275560))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.275563))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Localization) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c HomogeneousLocalization.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275560","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275563","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":18416,"sourceStart":18413,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":18416,"sourceStart":18413,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.275560","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.275563","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 131 | 10 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a154e9ed46e9f08c07788f2a57a4ef87e37a08e7f8aad14a83462798d0e557a | a9fb819bd3e2f833647c8d7580d2c3275c3fe382d85110fc9af7649140cc15a0 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,336 | Set.preimage_const_add_Icc | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← <a>Set.Ici_inter_Iic</a>] | α : Type u_1
inst✝ : OrderedAddCommGroup α
a b c : α
⊢ (fun x => a + x) ⁻¹' Icc b c = Icc (b - a) (c - a) | ((:c Eq) ((:c Set) (:fv _uniq.21116)) ((:c Set.preimage) (:fv _uniq.21116) (:fv _uniq.21116) (:lambda x (:fv _uniq.21116) ((:c HAdd.hAdd) (:fv _uniq.21116) (:fv _uniq.21116) (:fv _uniq.21116) ((:c instHAdd) (:fv _uniq.21116) ((:c AddCommMagma.toAdd) (:fv _uniq.21116) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.211... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c OrderedAddCommGroup) (:fv _uniq.21116))"},{"name":"a","sexp":"(:fv _uniq.21116)"},{"name":"b","sexp":"(:fv _uniq.21116)"},{"name":"c","sexp":"(:fv _uniq.21116)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.preimage) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21116","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21119","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c OrderedAddCommGroup) (:a... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5416,"sourceStart":5412,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"Ici_inter_Iic","source_end":5435,"source_start":5422,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21116","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.21119","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 36 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 229086059b6c2cce6be5d9dabd67613eb332d3ec5013997fa9d08aa66ac08cf4 | 4ebc3feb1ed0e7296a11df1f05f0a66870c462d8853d143e6f0c7ed878106a8e | 6a277dc25e137b27e9241575ea2053c5c2628212f21f04f987f9df4b6a4b109c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,337 | Nat.floor_eq_iff | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Nat.le_floor_iff</a> ha, ← <a>Nat.cast_one</a>, ← <a>Nat.cast_add</a>, ← <a>Nat.floor_lt</a> ha, <a>Nat.lt_add_one_iff</a>, <a>le_antisymm_iff</a>, <a>and_comm</a>] | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedSemiring α
inst✝ : FloorSemiring α
a : α
n : ℕ
ha : 0 ≤ a
⊢ ⌊a⌋₊ = n ↔ ↑n ≤ a ∧ a < ↑n + 1 | ((:c Iff) ((:c Eq) (:c Nat) ((:c Nat.floor) (:fv _uniq.30600) ((:c StrictOrderedSemiring.toOrderedSemiring) (:fv _uniq.30600) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.30600) (:fv _uniq.30606))) (:fv _uniq.30687) (:fv _uniq.30689)) (:fv _uniq.30691)) ((:c And) ((:c LE.le) (:fv _uniq.30600) ((:c Pre... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedSemiring) (:fv _uniq.30600))"},{"name":"inst✝","sexp":"((:c FloorSemiring) (:fv _uniq.30600) ((:c StrictOrderedSemiring.toOrderedSemiring) (:fv _uniq.30600)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Nat.floor) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c OrderedSemiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c FloorSemiring) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30597","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30600","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":8314,"sourceStart":8312,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8316,"sourceStart":8315,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"le_floor_iff ha","source_end":8335,"source_start":8320,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Nat.cast_one","source_end":8353,"source_start":8341,"syntax_kind":"ident"},{"source":"Nat.cast_add","source_end":8371,"source_start":8359,"syntax_kind":"ident"},{"source":"floor_lt ha","source_end":8388,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30597","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30600","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 73 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | feccfa3d7051da256b6c32cbb686d482710882bce1e0f15275e98b69188e4adb | 5768e0f2ea675c67154b8ba41071218f3022ed241f4cc296aae00013df902546 | 354eeb1d9fd88a9d52d121fe737c8ec9225eed0319b57d104b25c4bf47d7c140 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,338 | List.IsPrefix.ne_nil | Mathlib/Data/List/Infix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | α : Type u_1
β : Type u_2
l l₁ l₂ l₃ : List α
a b : α
m n : ℕ
x y : List α
h : x <+: y
hx : x ≠ []
⊢ y ≠ [] | α : Type u_1
β : Type u_2
l l₁ l₂ l₃ : List α
a b : α
m n : ℕ
x : List α
hx : x ≠ []
h : x <+: []
⊢ False | ((:c Ne) ((:c List) (:fv _uniq.27513)) (:fv _uniq.27566) ((:c List.nil) (:fv _uniq.27513))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₃","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"a","sexp":"(:fv _un... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c List.nil) (:arg :implicit-type 0 (:fv FV0))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27513","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27516","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rintro","sourceEnd":21184,"sourceStart":21178,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":21188,"sourceStart":21185,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":21188,"sourceStart":211... | [] | [{"source":"rfl","source_end":21188,"source_start":21185,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27513","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27516","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 212 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5ac99000587fa94b05969879578ea57d9a771f1e55171a77a20b26477380031 | 851a381c54fd1f8d4c309be12ba881b15b409b39ec443a54b1d9f9a961828d52 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 187c9a55c58e8ed668a2c94c09460fa14a110661edfcca67b8122e12aeb6a20e |
cat-searcher/leandojo-benchmark-4-random | test | 2,339 | List.IsPrefix.ne_nil | Mathlib/Data/List/Infix.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hx <| List.prefix_nil.mp h | α : Type u_1
β : Type u_2
l l₁ l₂ l₃ : List α
a b : α
m n : ℕ
x : List α
hx : x ≠ []
h : x <+: []
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"l₃","sexp":"((:c List) (:fv _uniq.27513))"},{"name":"a","sexp":"(:fv _un... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27513","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27516","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":21195,"sourceStart":21190,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hx","sourceEnd":21198,"sourceStart":21196,"tag":"identifier"},{"source":"<|","sourceEnd":21201,"sourceStart":21199,"tag":"atom"},{"children":[{"source":"List.prefix_nil.mp"... | [] | [{"source":"hx <| List.prefix_nil.mp h","source_end":21222,"source_start":21196,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27513","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.27516","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 212 | 6 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8117f64c7da186a2c2977814ddb55cdc68c35f9152ed532ca1412557422846b7 | 187c9a55c58e8ed668a2c94c09460fa14a110661edfcca67b8122e12aeb6a20e | b9f312fa498584599a047c14d14d3458ddb8048624bf937c90061521ec40c4d2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,340 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' x with r₁ s₁ | R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
x y z : OreLocalization S X
⊢ x + y + z = x + (y + z) | case c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
y z : OreLocalization S X
r₁ : X
s₁ : ↥S
⊢ r₁ /ₒ s₁ + y + z = r₁ /ₒ s₁ + (y + z) | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"induction'","sourceEnd":31442,"sourceStart":31432,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"x","sourceEnd":31444,"sourceStart":31443,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget... | [] | [{"source":"x","source_end":31444,"source_start":31443,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8446232585b841ccb803f502a6a521068778fafc715c64d79debb1dc3dab359a | 72d873fb4e97b329540a838803a0af8818e3da544669580b1a1558bb791c0212 | 513766368e90e80440b6428785fa1fa837244c45ef2129f2949fde2a29726784 | 636f15967509430280a24f639a7e8aa24c828d0cf5cad8579c53c486571db5a4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,341 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' y with r₂ s₂ | case c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
y z : OreLocalization S X
r₁ : X
s₁ : ↥S
⊢ r₁ /ₒ s₁ + y + z = r₁ /ₒ s₁ + (y + z) | case c.c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
z : OreLocalization S X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ + z = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + z) | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"induction'","sourceEnd":31472,"sourceStart":31462,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"y","sourceEnd":31474,"sourceStart":31473,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget... | [] | [{"source":"y","source_end":31474,"source_start":31473,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 085556b1f3195ba2716a837946a0530b5184f7669d800d225211e5d67a4ba876 | 636f15967509430280a24f639a7e8aa24c828d0cf5cad8579c53c486571db5a4 | 5da958cf4822dde03fe93e18fa0e328b882537e765622aba1ef5fecc377c858a | cc96af38fc1ce0796f9a6378ad609b62e535a86e8a7b681f3d1af337f37a44c3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,342 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' z with r₃ s₃ | case c.c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
z : OreLocalization S X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ + z = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + z) | case c.c.c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ + r₃ /ₒ s₃ = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + r₃ /ₒ s₃) | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"induction'","sourceEnd":31502,"sourceStart":31492,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"z","sourceEnd":31504,"sourceStart":31503,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget... | [] | [{"source":"z","source_end":31504,"source_start":31503,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f0e4d55a786243a8f2e8f082af84246e44ec45121d83c1b350aea7b6a2f9744 | cc96af38fc1ce0796f9a6378ad609b62e535a86e8a7b681f3d1af337f37a44c3 | 41a4f53cabfb35256ed7f03e1a302ebec605f60df3da927cf91a5e1d72a1d5ee | 5093a4b886134b4ad8989058b4b8f4845ac820066e098b86477c11b26ded235f |
cat-searcher/leandojo-benchmark-4-random | test | 2,343 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>OreLocalization.oreDivAddChar'</a> r₁ r₂ s₁ s₂ with ⟨ra, sa, ha, ha'⟩ | case c.c.c
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ + r₃ /ₒ s₃ = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + r₃ /ₒ s₃) | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
ha' : r₁ /ₒ s₁ + r₂ /ₒ s₂ = (sa • r₁ + ra • r₂) /ₒ (sa * s₁)
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ ... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rcases","sourceEnd":31528,"sourceStart":31522,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"OreLocalization.oreDivAddChar'","semanticRole":"global","source":"oreDivAddChar'","sourceEnd":31543,"sourceStart":31529,"tag":"identi... | [] | [{"source":"oreDivAddChar' r₁ r₂ s₁ s₂","source_end":31563,"source_start":31529,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨ra, sa, ha, ha'⟩","source_end":31590,"source_start":31569,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55b05d7253d0cb39600deaade1cc48c97683193e09c127be95e6f0024af5c545 | 5093a4b886134b4ad8989058b4b8f4845ac820066e098b86477c11b26ded235f | f31bbe7d41247264dfe3113a93c940a788091a6534ddbcbdf0412fe3567e1694 | 6ba4db436bd4f2da455d278aa43d370a252112b9ebe90855f895ca43a9b15ceb |
cat-searcher/leandojo-benchmark-4-random | test | 2,344 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [ha'] | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
ha' : r₁ /ₒ s₁ + r₂ /ₒ s₂ = (sa • r₁ + ra • r₂) /ₒ (sa * s₁)
⊢ r₁ /ₒ s₁ + r₂ /ₒ s₂ ... | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
ha' : r₁ /ₒ s₁ + r₂ /ₒ s₂ = (sa • r₁ + ra • r₂) /ₒ (sa * s₁)
⊢ (sa • r₁ + ra • r₂) ... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":31594,"sourceStart":31592,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31596,"sourceStart":31595,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"seman... | [] | [{"source":"ha'","source_end":31599,"source_start":31596,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 9 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3eaa8fc0f8b1b7bbe10d16e484a3d0ab730107c4f255f41980afae7845fb0945 | 6ba4db436bd4f2da455d278aa43d370a252112b9ebe90855f895ca43a9b15ceb | 386aa1ea0f0ee7ab4601ebef24044ff092d2b819c6af636fe4006f6d8ad96ab5 | c29967c1fca990af923b1553af8d0192d1107a53520970d14ae8af530b9ecaab |
cat-searcher/leandojo-benchmark-4-random | test | 2,345 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear ha' | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
ha' : r₁ /ₒ s₁ + r₂ /ₒ s₂ = (sa • r₁ + ra • r₂) /ₒ (sa * s₁)
⊢ (sa • r₁ + ra • r₂) ... | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
⊢ (sa • r₁ + ra • r₂) /ₒ (sa * s₁) + r₃ /ₒ s₃ = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + r₃ /ₒ s₃) | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"clear","sourceEnd":31607,"sourceStart":31602,"tag":"atom"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"ha'","sourceEnd":31611,"sourceStart":31608,"tag":"identifier"}],"kind":"null","source":"ha'","sourceEnd":31611,"sourceStart":31608,"tag":"node"}],"kind":"Lean.Parser.Tactic... | [] | [{"source":"ha'","source_end":31611,"source_start":31608,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 13 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53742c6410756b22cef74efd52e49165911765f3692610a0626648abba525dd7 | c29967c1fca990af923b1553af8d0192d1107a53520970d14ae8af530b9ecaab | c0cbc1fb62d5ce50b15121429243c980b49f642c567d67945d80fd88c6257353 | 67dba382ccb27e4eda762078083085ca18419c7e7e9ef8f507de3650435e0144 |
cat-searcher/leandojo-benchmark-4-random | test | 2,346 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>OreLocalization.oreDivAddChar'</a> (sa • r₁ + ra • r₂) r₃ (sa * s₁) s₃ with ⟨rc, sc, hc, q⟩ | case c.c.c.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
⊢ (sa • r₁ + ra • r₂) /ₒ (sa * s₁) + r₃ /ₒ s₃ = r₁ /ₒ s₁ + (r₂ /ₒ s₂ + r₃ /ₒ s₃) | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
q : (sa • r₁ + ra • r₂)... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rcases","sourceEnd":31620,"sourceStart":31614,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"OreLocalization.oreDivAddChar'","semanticRole":"global","source":"oreDivAddChar'","sourceEnd":31635,"sourceStart":31621,"tag":"identi... | [] | [{"source":"oreDivAddChar' (sa • r₁ + ra • r₂) r₃ (sa * s₁) s₃","source_end":31685,"source_start":31621,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨rc, sc, hc, q⟩","source_end":31710,"source_start":31691,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 14 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8497f82cfb8ac0e71f5d29dfd2c6f298e72a5ebe1cbe57d942bd906aac76e70c | 67dba382ccb27e4eda762078083085ca18419c7e7e9ef8f507de3650435e0144 | 2543118774b3b57a44c1bb52bde1d0dd12a09dc389df435a3fc4954602acd9e6 | 457f8d58fcf56fc584851097cc46bc70412a5f007b6489fed6977ae75fdde27e |
cat-searcher/leandojo-benchmark-4-random | test | 2,347 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [q] | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
q : (sa • r₁ + ra • r₂)... | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
q : (sa • r₁ + ra • r₂)... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":31714,"sourceStart":31712,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31716,"sourceStart":31715,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":20,"seman... | [] | [{"source":"q","source_end":31717,"source_start":31716,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 16 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb9284e4ae28576f32b65bd8eef1c649e8abed9f522509e863b6c419e9719e11 | 457f8d58fcf56fc584851097cc46bc70412a5f007b6489fed6977ae75fdde27e | 3332c5e33844d18213dafd3d6b26a270549278f04a74bc8bfa8da84ddc09b540 | 1073748610b0b59ab313ec07c897b0892ea6c6b9bc2b6671fa8501931586d4f3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,348 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | clear q | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
q : (sa • r₁ + ra • r₂)... | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ (sc • (sa • r₁ + ra •... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"clear","sourceEnd":31725,"sourceStart":31720,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"q","sourceEnd":31727,"sourceStart":31726,"tag":"identifier"}],"kind":"null","source":"q","sourceEnd":31727,"sourceStart":31726,"tag":"node"}],"kind":"Lean.Parser.Tactic.cle... | [] | [{"source":"q","source_end":31727,"source_start":31726,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 20 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7a43528ec355700e5139a89762a518cb1c6cd010a4d5a8a6932b09c29353dab | 1073748610b0b59ab313ec07c897b0892ea6c6b9bc2b6671fa8501931586d4f3 | 8a5f98e04a06b4cde7858801accb27d86c09e2d48246a2a759dd4a0c1bc5fd46 | c506f04570042f6f7d68e9c3f491757c165dea14fbca8b01177ff8c9061a732a |
cat-searcher/leandojo-benchmark-4-random | test | 2,349 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>smul_add</a>, <a>mul_assoc</a>, <a>add_assoc</a>] | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ (sc • (sa • r₁ + ra •... | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ (sc • sa • r₁ + (sc •... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"simp","sourceEnd":31734,"sourceStart":31730,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":31739,"sourceStart":31735,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":317... | [] | [{"source":"smul_add","source_end":31749,"source_start":31741,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":31760,"source_start":31751,"syntax_kind":"ident"},{"source":"add_assoc","source_end":31771,"source_start":31762,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 21 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1325e8e5007d40cb7ae1d2fc0062fa1eb3632ccabcc49a65144990b0920d730d | c506f04570042f6f7d68e9c3f491757c165dea14fbca8b01177ff8c9061a732a | f5a56294c544570607916ba3a300a38dc5e71599eb85aa9ed348b58ed7e197c6 | 22594a6e19977b71528d89d9a77146771f96e7ea3275d659d17855ced3907e6f |
cat-searcher/leandojo-benchmark-4-random | test | 2,350 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>OreLocalization.add_oreDiv</a>, ← <a>OreLocalization.expand'</a>] | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ (sc • sa • r₁ + (sc •... | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ r₁ /ₒ s₁ + (ra • r₂ /... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"simp_rw","sourceEnd":31782,"sourceStart":31775,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31784,"sourceStart":31783,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31787,"sou... | [] | [{"source":"add_oreDiv","source_end":31798,"source_start":31788,"syntax_kind":"ident"},{"source":"OreLocalization.expand'","source_end":31827,"source_start":31804,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 22 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 98bfeb414d766ffd55eb6b24084e8df06731784f33ec0f19a2a15781eaedd94c | 22594a6e19977b71528d89d9a77146771f96e7ea3275d659d17855ced3907e6f | ab31c26473ee893b36a6d31c8d4661e63cebbdd00a52ffbb39565c542b2ce5cf | 244dfc1ad0994f79a7135f98c99dec3da99beb81493486fc2690df028f871f5b |
cat-searcher/leandojo-benchmark-4-random | test | 2,351 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 2 | case c.c.c.mk.mk.intro.mk.mk.intro
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ r₁ /ₒ s₁ + (ra • r₂ /... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ra • r₂ /ₒ (s... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c HAdd.hAdd) ((:c OreLocalization) (:fv _uniq.188249) (:fv ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"congr","sourceEnd":31836,"sourceStart":31831,"tag":"atom"},{"children":[{"children":[{"source":"2","sourceEnd":31838,"sourceStart":31837,"tag":"atom"}],"kind":"num","source":"2","sourceEnd":31838,"sourceStart":31837,"tag":"node"}],"kind":"null","source":"2","sourceEnd":31838,"sourceStart":31837,... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 26 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20f3b2f6e0b58c4c47bf0bcb38f40af5f76e42ed39f301e21b1af62c659aa76e | 244dfc1ad0994f79a7135f98c99dec3da99beb81493486fc2690df028f871f5b | 216dbc98bbb24e1a0fab2dbe9996a78800e7e700a272495ba61387ecc465ca0e | 4194076fdd1c6851141cc8c5a8cf912082141d0e97ff952956860ffa77cd4da0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,352 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>OreLocalization.expand</a> r₂ s₂ ra (ha.symm ▸ (sa * s₁).2)] | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ra • r₂ /ₒ (s... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ra • r₂ /ₒ (s... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":31846,"sourceStart":31844,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31848,"sourceStart":31847,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Ore... | [] | [{"source":"OreLocalization.expand r₂ s₂ ra (ha.symm ▸ (sa * s₁).2)","source_end":31911,"source_start":31848,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 31 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 547aab8b7a328d2990acc800b2919e83d17a7d2acfc39b55f3f3e8954cf8e0cf | b7a62955bcb349a7e416af7c3c3ae6cff2eb3e83b0981145a00d7bf4c01d65ad | 208add84e46a84ced9e63c502380158f986fbfa35509a2636711287544245168 | 5e8e628416b1c07f3ab827073623ef31a52c116e514d6ab79d2d3729819eb580 |
cat-searcher/leandojo-benchmark-4-random | test | 2,353 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ra • r₂ /ₒ (s... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ sa * s₁ =... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"congr","sourceEnd":31919,"sourceStart":31914,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":31919,"sourceStart":31914,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 35 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 799555d1adb3cd251aae3873b0bf359b32e37545e3bf1d9b2dcbacd28a65b7f0 | 5e8e628416b1c07f3ab827073623ef31a52c116e514d6ab79d2d3729819eb580 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | d107b6aa8cdeeedcec627a5737ac882340f5917ebd1e3394e974972bcaa9909b |
cat-searcher/leandojo-benchmark-4-random | test | 2,354 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ sa * s₁ =... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s.a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ↑(sa * ... | ((:c Eq) ((:c Subtype) (:fv _uniq.188249) (:lambda x (:fv _uniq.188249) ((:c Membership.mem) (:fv _uniq.188249) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252))) ((:c SetLike.instMembership) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.1882... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submonoid) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MulOne... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"ext","sourceEnd":31924,"sourceStart":31921,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":31924,"sourceStart":31921,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 37 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ad0da34b9fb162efd3b67c3ce471e68ef130e235427c967529d802315e63c47b | d107b6aa8cdeeedcec627a5737ac882340f5917ebd1e3394e974972bcaa9909b | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 3d980f9d35798a18d417cc2cb1a1020e5a472a0f97f35a3e05cd9dcdfe9a999a |
cat-searcher/leandojo-benchmark-4-random | test | 2,355 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s.a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ↑(sa * ... | ((:c Eq) (:fv _uniq.188249) ((:c Subtype.val) (:fv _uniq.188249) (:lambda x (:fv _uniq.188249) ((:c Membership.mem) (:fv _uniq.188249) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252))) ((:c SetLike.instMembership) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOn... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Memb... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":31931,"sourceStart":31926,"tag":"atom"},{"contextIndex":16,"semanticRole":"local","source":"ha","sourceEnd":31934,"sourceStart":31932,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha","sourceEnd":31934,"sourceStart":31926,"tag":"node"} | [] | [{"source":"ha","source_end":31934,"source_start":31932,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 39 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ace77654e66708426b7bc8a2cb2b84fc513a84c50c30111cb93c87e10f6d9c9d | 3d980f9d35798a18d417cc2cb1a1020e5a472a0f97f35a3e05cd9dcdfe9a999a | ed7b20bfa58750585795fc60c8364f3d8cfaa54d8e6d316fdcf777f9aa77d07b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,356 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>OreLocalization.expand</a> r₃ s₃ rc (hc.symm ▸ (sc * (sa * s₁)).2)] | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ rc • r₃ /ₒ (s... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ rc • r₃ /ₒ (s... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":31942,"sourceStart":31940,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31944,"sourceStart":31943,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Ore... | [] | [{"source":"OreLocalization.expand r₃ s₃ rc (hc.symm ▸ (sc * (sa * s₁)).2)","source_end":32014,"source_start":31944,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 44 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fd9a4a0c3febc13a0cdcb0c39de6d4327aedbd35a4009b455906ea47c568b900 | 8f39f44c2cd70e5c47e505fc9dec171b1e67bee364a7883dbd77a00b4fed3fe4 | 1be70f559a1369fb6b3d315c93effe68f7abd6c7040a84ae28d339eb031bdee9 | 09f41cf0f67a170dfca9067b9d62d27d3f35a79471b81b6fd4630641d2df5bc2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,357 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ rc • r₃ /ₒ (s... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ sc * (sa ... | ((:c Eq) ((:c OreLocalization) (:fv _uniq.188249) (:fv _uniq.188252) (:fv _uniq.188363) (:fv _uniq.188402) (:fv _uniq.188405) ((:c DistribMulAction.toMulAction) (:fv _uniq.188249) (:fv _uniq.188405) (:fv _uniq.188252) (:fv _uniq.188408) (:fv _uniq.188428))) ((:c OreLocalization.oreDiv) (:fv _uniq.188249) (:fv _uniq.188... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"congr","sourceEnd":32022,"sourceStart":32017,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":32022,"sourceStart":32017,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 48 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0714be22a7b117d7eb57538fda17d367e01f3d4f04d3847736c2e87423d244e | 09f41cf0f67a170dfca9067b9d62d27d3f35a79471b81b6fd4630641d2df5bc2 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | 92d66de1794ddef95d84a1641806313e2458503f43ee159f8b5915688d61e18f |
cat-searcher/leandojo-benchmark-4-random | test | 2,358 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ sc * (sa ... | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s.a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ↑(sc * ... | ((:c Eq) ((:c Subtype) (:fv _uniq.188249) (:lambda x (:fv _uniq.188249) ((:c Membership.mem) (:fv _uniq.188249) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252))) ((:c SetLike.instMembership) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.1882... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submonoid) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MulOne... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"ext","sourceEnd":32027,"sourceStart":32024,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":32027,"sourceStart":32024,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 50 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b8ebf8a511b24db881341ff4722a1fb1cee0a0ebfe55c44aa50aed9ff45cffa7 | 92d66de1794ddef95d84a1641806313e2458503f43ee159f8b5915688d61e18f | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 0c83b1842c27a7191290223adda0410d3e88bd13c282ac7e4e2d670925f18df5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,359 | OreLocalization.add_assoc | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hc | case c.c.c.mk.mk.intro.mk.mk.intro.e_a.e_a.e_s.a
R : Type u_1
inst✝³ : Monoid R
S : Submonoid R
inst✝² : OreSet S
X : Type u_2
inst✝¹ : AddMonoid X
inst✝ : DistribMulAction R X
r₁ : X
s₁ : ↥S
r₂ : X
s₂ : ↥S
r₃ : X
s₃ : ↥S
ra : R
sa : ↥S
ha : ↑sa * ↑s₁ = ra * ↑s₂
rc : R
sc : ↥S
hc : ↑sc * ↑(sa * s₁) = rc * ↑s₃
⊢ ↑(sc * ... | ((:c Eq) (:fv _uniq.188249) ((:c Subtype.val) (:fv _uniq.188249) (:lambda x (:fv _uniq.188249) ((:c Membership.mem) (:fv _uniq.188249) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252))) ((:c SetLike.instMembership) ((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOn... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c Monoid) (:fv _uniq.188249))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.188249) ((:c Monoid.toMulOneClass) (:fv _uniq.188249) (:fv _uniq.188252)))"},{"name":"inst✝²","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.188249) (:fv _uniq.188252) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Memb... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":32034,"sourceStart":32029,"tag":"atom"},{"contextIndex":19,"semanticRole":"local","source":"hc","sourceEnd":32037,"sourceStart":32035,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hc","sourceEnd":32037,"sourceStart":32029,"tag":"node"} | [] | [{"source":"hc","source_end":32037,"source_start":32035,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.188249","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.188252","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":implicit","context_index":2,"inte... | 140 | 52 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29bf4b153b625cc24ddde13271840fd59ce3f93f38d9508788b9c33636525a53 | 0c83b1842c27a7191290223adda0410d3e88bd13c282ac7e4e2d670925f18df5 | 1844206188efd35ca5b537f85956e635e822402f1d37d2ffc78d25a5a9873d6b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,360 | ENNReal.toReal_le_toReal | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | lift a to ℝ≥0 using ha | a b c d : ℝ≥0∞
r p q : ℝ≥0
ha : a ≠ ⊤
hb : b ≠ ⊤
⊢ a.toReal ≤ b.toReal ↔ a ≤ b | case intro
b c d : ℝ≥0∞
r p q : ℝ≥0
hb : b ≠ ⊤
a : ℝ≥0
⊢ (↑a).toReal ≤ b.toReal ↔ ↑a ≤ b | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) (:fv _uniq.5852)) ((:c ENNReal.toReal) (:fv _uniq.5854))) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemirin... | [{"name":"a","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c NNReal)"},{"name":"q","sexp":"(:c NNReal)"},{"name":"ha","sexp":"((:c Ne) (:c ENNReal) (:fv _uniq.5852) ((:c Top.top) (:c... | (:app (:c Iff) (:arg :explicit 0 (: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 ENNReal.toReal) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c ENNReal.toReal) (:arg :explicit 0 (:fv FV1)))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5852","is_instance":false,"is_let":false,"name":"a","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5854","is_instance":false,"is_let":false,"name":"b","sexp":"(:c ENNReal)"},{"binder_role":":implicit","conte... | {"children":[{"source":"lift","sourceEnd":3181,"sourceStart":3177,"tag":"atom"},{"contextIndex":0,"semanticRole":"local","source":"a","sourceEnd":3183,"sourceStart":3182,"tag":"identifier"},{"source":"to","sourceEnd":3186,"sourceStart":3184,"tag":"atom"},{"children":[{"source":"ℝ≥0","sourceEnd":3194,"sourceStart":3187,... | [] | [{"source":"a","source_end":3183,"source_start":3182,"syntax_kind":"ident"},{"source":"ℝ≥0","source_end":3194,"source_start":3187,"syntax_kind":"NNReal.«termℝ≥0»"},{"source":"ha","source_end":3203,"source_start":3201,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5852","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5854","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 18 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37349699294092005cf4fd9983783e9940d7c0daf896cc36f196463007f861c3 | fdf93a2f4977c0fca13c80f8a09622d312bc5c4f2e9a2751dfed5d90d8a1db8c | 2c177b3958178f23147c34a0fe1bbb3b9dc14586155ae749bd84e13f575a2818 | 05354c041e9a2d5f65eed3615f7c0362107777e17fba478fd9d1cbc67768cc95 |
cat-searcher/leandojo-benchmark-4-random | test | 2,361 | ENNReal.toReal_le_toReal | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | lift b to ℝ≥0 using hb | case intro
b c d : ℝ≥0∞
r p q : ℝ≥0
hb : b ≠ ⊤
a : ℝ≥0
⊢ (↑a).toReal ≤ b.toReal ↔ ↑a ≤ b | case intro.intro
c d : ℝ≥0∞
r p q a b : ℝ≥0
⊢ (↑a).toReal ≤ (↑b).toReal ↔ ↑a ≤ ↑b | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c ENNReal.ofNNReal) (:fv _uniq.6158))) ((:c ENNReal.toReal) (:fv _uniq.5854))) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommS... | [{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c NNReal)"},{"name":"q","sexp":"(:c NNReal)"},{"name":"hb","sexp":"((:c Ne) (:c ENNReal) (:fv _uniq.5854) ((:c Top.top) (:c ENNReal) ((:c CompleteLattice.toTo... | (:app (:c Iff) (:arg :explicit 0 (: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 ENNReal.toReal) (:arg :explicit 0 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:fv FV7)))))) (:arg :explicit 3 (:app (:c ENNReal... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5854","is_instance":false,"is_let":false,"name":"b","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5856","is_instance":false,"is_let":false,"name":"c","sexp":"(:c ENNReal)"},{"binder_role":":implicit","conte... | {"children":[{"source":"lift","sourceEnd":3210,"sourceStart":3206,"tag":"atom"},{"contextIndex":0,"semanticRole":"local","source":"b","sourceEnd":3212,"sourceStart":3211,"tag":"identifier"},{"source":"to","sourceEnd":3215,"sourceStart":3213,"tag":"atom"},{"children":[{"source":"ℝ≥0","sourceEnd":3223,"sourceStart":3216,... | [] | [{"source":"b","source_end":3212,"source_start":3211,"syntax_kind":"ident"},{"source":"ℝ≥0","source_end":3223,"source_start":3216,"syntax_kind":"NNReal.«termℝ≥0»"},{"source":"hb","source_end":3232,"source_start":3230,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5854","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5856","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 18 | 5 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7256a0057232b4727cedc203a72072e3620e41e16f4668674cb0c6d019945ab5 | 05354c041e9a2d5f65eed3615f7c0362107777e17fba478fd9d1cbc67768cc95 | 29b91aa57ff49c82f0f67e1a38c2ee6b6246a2b8b2219b19b37602dc7ec6c491 | 99ac12be54de7d63d2628b2f779a16377da055f920f3c21e0cd61e3a421aaf00 |
cat-searcher/leandojo-benchmark-4-random | test | 2,362 | ENNReal.toReal_le_toReal | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | case intro.intro
c d : ℝ≥0∞
r p q a b : ℝ≥0
⊢ (↑a).toReal ≤ (↑b).toReal ↔ ↑a ≤ ↑b | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c ENNReal.toReal) ((:c ENNReal.ofNNReal) (:fv _uniq.6158))) ((:c ENNReal.toReal) ((:c ENNReal.ofNNReal) (:fv _uniq.6213)))) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c EN... | [{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","sexp":"(:c NNReal)"},{"name":"p","sexp":"(:c NNReal)"},{"name":"q","sexp":"(:c NNReal)"},{"name":"a","sexp":"(:c NNReal)"},{"name":"b","sexp":"(:c NNReal)"}] | (:app (:c Iff) (:arg :explicit 0 (: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 ENNReal.toReal) (:arg :explicit 0 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:fv FV5)))))) (:arg :explicit 3 (:app (:c ENNReal... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5856","is_instance":false,"is_let":false,"name":"c","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5858","is_instance":false,"is_let":false,"name":"d","sexp":"(:c ENNReal)"},{"binder_role":":implicit","conte... | {"children":[{"source":"norm_cast","sourceEnd":3244,"sourceStart":3235,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":3244,"sourceStart":3235,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5856","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5858","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 18 | 6 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1b91f91ce7b46a0b17df583401046465b4462e962e666b8d09a1e7aff3ead51 | 99ac12be54de7d63d2628b2f779a16377da055f920f3c21e0cd61e3a421aaf00 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,363 | Subgroup.mem_ofUnits_iff_toUnits_mem | Mathlib/Algebra/Group/Submonoid/Units.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Subgroup.mem_ofUnits_iff</a>, toUnits.surjective.exists, <a>val_toUnits_apply</a>, <a>exists_eq_right</a>] | M : Type u_1
inst✝¹ : Monoid M
G : Type u_2
inst✝ : Group G
H : Subgroup Gˣ
x : G
⊢ x ∈ H.ofUnits ↔ toUnits x ∈ H | ((:c Iff) ((:c Membership.mem) (:fv _uniq.41972) ((:c Submonoid) (:fv _uniq.41972) ((:c Monoid.toMulOneClass) (:fv _uniq.41972) ((:c DivInvMonoid.toMonoid) (:fv _uniq.41972) ((:c Group.toDivInvMonoid) (:fv _uniq.41972) (:fv _uniq.41975))))) ((:c SetLike.instMembership) ((:c Submonoid) (:fv _uniq.41972) ((:c Monoid.toMu... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.41966))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.41972))"},{"name":"H","sexp":"((:c Subgroup) ((:c Units) (:fv _uniq.41972) ((:c DivInvMonoid.toMonoid) (:fv _uniq.41972) ((:c Group.t... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Submonoid) (:arg :explicit 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV2))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41966","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41969","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Monoid) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":12911,"sourceStart":12904,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12913,"sourceStart":12912,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"mem_ofUnits_iff","source_end":12928,"source_start":12913,"syntax_kind":"ident"},{"source":"toUnits.surjective.exists","source_end":12955,"source_start":12930,"syntax_kind":"ident"},{"source":"val_toUnits_apply","source_end":12974,"source_start":12957,"syntax_kind":"ident"},{"source":"exists_eq_right","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41966","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41969","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"intern... | 66 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a22d83df72548b7517547277dddde019849bfc0b0ad14390dc6a6b259c6e4026 | debffcfe13acf73cb2683845e50c3ef88007ed31e7fe098a27a6db8627b0dd5c | f790d8b1e7e8603f86b01690b7ddafb7293a67080de7f8d540bc85c7bba2fd07 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,364 | Equiv.Perm.card_cycleType_eq_zero | Mathlib/GroupTheory/Perm/Cycle/Type.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.card_eq_zero</a>, <a>Equiv.Perm.cycleType_eq_zero</a>] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
σ : Perm α
⊢ card σ.cycleType = 0 ↔ σ = 1 | ((:c Iff) ((:c Eq) (:c Nat) ((:c DFunLike.coe) ((:c AddMonoidHom) ((:c Multiset) (:c Nat)) (:c Nat) ((:c AddMonoid.toAddZeroClass) ((:c Multiset) (:c Nat)) ((:c AddCommMonoid.toAddMonoid) ((:c Multiset) (:c Nat)) ((:c OrderedAddCommMonoid.toAddCommMonoid) ((:c Multiset) (:c Nat)) ((:c CanonicallyOrderedAddCommMonoid.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.9564))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.9564))"},{"name":"σ","sexp":"((:c Equiv.Perm) (:fv _uniq.9564))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AddMonoidHom) (:arg :explicit 0 (:app (:c Multiset) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddZeroClass)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9564","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9567","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :explicit ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3174,"sourceStart":3172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3176,"sourceStart":3175,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"card_eq_zero","source_end":3188,"source_start":3176,"syntax_kind":"ident"},{"source":"cycleType_eq_zero","source_end":3207,"source_start":3190,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9564","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.9567","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,... | 19 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59d4af17b71c1ff86403f3bba7d99b0088de4cb8622541df6c7cdb8c44f03944 | 11a425999ab2940170411cbe56c08d1a7aed7fc74fb0d5d7263b1c902d929d58 | a59ca7daaf7184c693bbff73cf21e694ceb095efec94550928ed9ac29f0d37bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,365 | Finite.isDomain_to_isField | Mathlib/RingTheory/LittleWedderburn.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical cases <a>nonempty_fintype</a> D let _ := <a>Fintype.divisionRingOfIsDomain</a> D let _ := <a>littleWedderburn</a> D exact <a>Field.toIsField</a> D | D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
⊢ IsField D | ((:c IsField) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194))) | [{"name":"D","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Finite) (:fv _uniq.86192))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.86192))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194)))"}] | (:app (:c IsField) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1)))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Finite) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"classical","sourceEnd":7902,"sourceStart":7893,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":7910,"sourceStart":7905,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"no... | [] | [{"source":"nonempty_fintype D","source_end":7929,"source_start":7911,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Fintype.divisionRingOfIsDomain D","source_end":7973,"source_start":7941,"syntax_kind":"Lean.Parser.Term.app"},{"source":"littleWedderburn D","source_end":8003,"source_start":7985,"syntax_kind":"Lean.Pa... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 18 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f4ed475b626f915266eac601d804c232d40ee05cbd36c3c21faaa7af7891f814 | ae914bbc6caad0d7f9bce695611c9513513d617beca4f4fe8d0413425af5d0b3 | 267f7130e46f7f70e2847ae749a5891eef15ed5dc993e5febaa2b0b62966adbe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,366 | Finite.isDomain_to_isField | Mathlib/RingTheory/LittleWedderburn.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases <a>nonempty_fintype</a> D | D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
⊢ IsField D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
⊢ IsField D | ((:c IsField) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194))) | [{"name":"D","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Finite) (:fv _uniq.86192))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.86192))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194)))"}] | (:app (:c IsField) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1)))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Finite) (:arg :explicit... | {"children":[{"source":"cases","sourceEnd":7910,"sourceStart":7905,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"nonempty_fintype","semanticRole":"global","source":"nonempty_fintype","sourceEnd":7927,"sourceStart":7911,"tag":"identifier"},{"children... | [] | [{"source":"nonempty_fintype D","source_end":7929,"source_start":7911,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 18 | 7 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 714ffb41ccbd2bcd49b4f28f576c3c2614ab6179330936c566d084ee51684d5b | ae914bbc6caad0d7f9bce695611c9513513d617beca4f4fe8d0413425af5d0b3 | b2db8994a0a330171949c69f3da043429487e0a90060990cee2d7df8d852cea6 | 00783cfaa96599bb31031f59d3474299f422134e60f196e6d2b2e576bb1c8233 |
cat-searcher/leandojo-benchmark-4-random | test | 2,367 | Finite.isDomain_to_isField | Mathlib/RingTheory/LittleWedderburn.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let _ := <a>Fintype.divisionRingOfIsDomain</a> D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
⊢ IsField D | case intro
D : Type u_1
inst✝² : Finite D
inst✝¹ : Ring D
inst✝ : IsDomain D
val✝ : Fintype D
x✝ : DivisionRing D := divisionRingOfIsDomain D
⊢ IsField D | ((:c IsField) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194))) | [{"name":"D","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Finite) (:fv _uniq.86192))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.86192))"},{"name":"inst✝","sexp":"((:c IsDomain) (:fv _uniq.86192) ((:c Ring.toSemiring) (:fv _uniq.86192) (:fv _uniq.86194)))"},{"name":"val✝","sexp":"((:c Fintype) (:fv _u... | (:app (:c IsField) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1)))))) | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"name":"D","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Finite) (:arg :explicit... | {"children":[{"source":"let","sourceEnd":7935,"sourceStart":7932,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":7937,"sourceStart":7936,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":7937,"sourceStart":7936,"tag":"node"},{"children":[],"kind":"null","source":"","t... | [] | [{"source":"Fintype.divisionRingOfIsDomain D","source_end":7973,"source_start":7941,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.86192","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.86193","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 18 | 8 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eac5d028ef9ec25c4b9f3fa6a0c94247ef684ec4ab1f99d437aa51eb812fa74c | 00783cfaa96599bb31031f59d3474299f422134e60f196e6d2b2e576bb1c8233 | 139983d8e430423ccb1110678eb73d819bd0c4f48bd4db35d6f56ebcb3e93ce1 | 2bf0c5093a68299bf04e7be2f9f156b0714b58050103895e104574ba401062f3 |
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