dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 2,675 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h := <a>congr_arg</a> (fun x => <a>LucasLehmer.X.ω</a> ^ 2 ^ p' * x) h | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' + ωb ^ 2 ^ p' = ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : (fun x => ω ^ 2 ^ p' * x) (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = (fun x => ω ^ 2 ^ p' * x) ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HAdd.hAdd) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"replace","sourceEnd":17268,"sourceStart":17261,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":17270,"sourceStart":17269,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":17270,"sourceStart":17269,"tag":"no... | [] | [{"source":"congr_arg (fun x => ω ^ 2 ^ p' * x) h","source_end":17312,"source_start":17274,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 19 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6d3d3f495b348e79d9b40fe3bfea8eb4a2397806a101475b5f7d6e3e9f65c01 | 12f8021e3e22cb5cfb346035a51112d630e7536f7a54630c6763a69d33e4e199 | 5328d681cc00f878522a8c297fc426426bc3532c1cb5da0de6647796dcb0c297 | 17c3d468621a24d5d3b3738b3aca93f960997c564732ac39c31fcd9eefe60efb |
cat-searcher/leandojo-benchmark-4-random | test | 2,676 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at h | case h
p' : ℕ
k : ℤ
h : (fun x => ω ^ 2 ^ p' * x) (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = (fun x => ω ^ 2 ^ p' * x) ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' * (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:lambda x ((:c... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"dsimp","sourceEnd":17320,"sourceStart":17315,"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":[{"ch... | [] | [{"source":"h","source_end":17325,"source_start":17324,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 20 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a0b8bdcf31b7eb1b049f2e114605c02130f761221c72b14d9b66015b2ad6c4f | 17c3d468621a24d5d3b3738b3aca93f960997c564732ac39c31fcd9eefe60efb | 77a3f35897bdf6b787da21ef08ddf8dafef80050e286f9c04243531c1e998d85 | 83a18e6b65b88d5f535ddc1898e962afb26361fd246409112f5b8626ffa8c6c1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,677 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1) := by ring | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' * (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' * (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HMul.hMul) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"have","sourceEnd":17332,"sourceStart":17328,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t","sourceEnd":17334,"sourceStart":17333,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"t","sourceEnd":17334,"sourceStart":17333,"tag":"node"... | [] | [{"source":"2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)","source_end":17367,"source_start":17337,"syntax_kind":"«term_=_»"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 21 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 21846b173506106e30890c052eb6edc208fb8e7a54c677325b1c9e99e7343b09 | 83a18e6b65b88d5f535ddc1898e962afb26361fd246409112f5b8626ffa8c6c1 | 363a6da3222135cb0bad00965392d9ab3ceaaa47b500c1d9c8543d4577b7502d | 7d4b6d654ed598d7b77f8caa6bafb2d46efe5b8d8b16ef48c6398d1db361239a |
cat-searcher/leandojo-benchmark-4-random | test | 2,678 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_add</a>, ← <a>pow_add</a> <a>LucasLehmer.X.ω</a>, t, ← <a>mul_pow</a> <a>LucasLehmer.X.ω</a> <a>LucasLehmer.X.ωb</a> (2 ^ p'), <a>LucasLehmer.X.ω_mul_ωb</a>, <a>one_pow</a>] at h | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' * (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HMul.hMul) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"rw","sourceEnd":17383,"sourceStart":17381,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17385,"sourceStart":17384,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_add","semant... | [] | [{"source":"mul_add","source_end":17392,"source_start":17385,"syntax_kind":"ident"},{"source":"h","source_end":17467,"source_start":17466,"syntax_kind":"ident"},{"source":"pow_add ω","source_end":17408,"source_start":17398,"syntax_kind":"Lean.Parser.Term.app"},{"source":"t","source_end":17411,"source_start":17410,"synt... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 24 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6456b7d4c70c9ff0825695052c5aed58543cddd6577de7ba85e76eb3408c8e8 | 7d4b6d654ed598d7b77f8caa6bafb2d46efe5b8d8b16ef48c6398d1db361239a | c2454c663f6978b53bc66d4cd973ea71f87d0349c4e29c221417c02fe12329fb | 3d1e53690c60b7a7eb5e27bada3e3b1565becd4c4d699a92601a350d826afa36 |
cat-searcher/leandojo-benchmark-4-random | test | 2,679 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a>, <a>LucasLehmer.X.coe_mul</a>] at h | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ↑(2 ^ (p' + 2) - 1) * ↑k * ω ^ 2 ^ p'
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HAdd.hAdd) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"rw","sourceEnd":17472,"sourceStart":17470,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17474,"sourceStart":17473,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_comm","seman... | [] | [{"source":"mul_comm","source_end":17482,"source_start":17474,"syntax_kind":"ident"},{"source":"h","source_end":17497,"source_start":17496,"syntax_kind":"ident"},{"source":"coe_mul","source_end":17491,"source_start":17484,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 32 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a41a4114f8be9f29db487df00047311e350114b3b0f4176a794b0cd280481b69 | 3d1e53690c60b7a7eb5e27bada3e3b1565becd4c4d699a92601a350d826afa36 | d4d96dbef9eca87c6614f8cc9a90ed4a4d842f4e40c0ad9a6331229a1688bcc1 | feaa12882758c14ace41f3f695588dd55ea0ad88fbfc4c9e71baf8b31c866737 |
cat-searcher/leandojo-benchmark-4-random | test | 2,680 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_comm</a> _ (k : <a>LucasLehmer.X</a> (<a>LucasLehmer.q</a> (p' + 2)))] at h | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ↑(2 ^ (p' + 2) - 1) * ↑k * ω ^ 2 ^ p'
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p'
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HAdd.hAdd) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"rw","sourceEnd":17502,"sourceStart":17500,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17504,"sourceStart":17503,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"mul... | [] | [{"source":"h","source_end":17541,"source_start":17540,"syntax_kind":"ident"},{"source":"mul_comm _ (k : X (q (p' + 2)))","source_end":17535,"source_start":17504,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 36 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb8c292f1b220a2a13f7caa85a1ddf938c6ddd2c6da064b63d542969bfc02a94 | feaa12882758c14ace41f3f695588dd55ea0ad88fbfc4c9e71baf8b31c866737 | d6d12f92327672e52f9fbbeb8a5816939c5249fcaddb7bb4ba693d5701a68568 | 60c2b6e4d9e5417ad85544cb3ab0d5d7570d2e994210093baea762b45c51f87f |
cat-searcher/leandojo-benchmark-4-random | test | 2,681 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h := <a>eq_sub_of_add_eq</a> h | case h
p' : ℕ
k : ℤ
h : ω ^ 2 ^ (p' + 1) + 1 = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p'
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
h : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HAdd.hAdd) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"replace","sourceEnd":17551,"sourceStart":17544,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":17553,"sourceStart":17552,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":17553,"sourceStart":17552,"tag":"no... | [] | [{"source":"eq_sub_of_add_eq h","source_end":17575,"source_start":17557,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 39 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f2881399f74e73cd550189eb254d30a4b8ef59bd4c988f30ccc79be73b778b64 | 60c2b6e4d9e5417ad85544cb3ab0d5d7570d2e994210093baea762b45c51f87f | fa7d711fbfb231fd55720e3b5a483ff9b3ea8d1bacf6774f61dd9365301bae9b | 3500583f0fb64a4dab07680728ab794a6c88abe92b69cca42dc1bd90c248e04d |
cat-searcher/leandojo-benchmark-4-random | test | 2,682 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : 1 ≤ 2 ^ (p' + 2) := <a>Nat.one_le_pow</a> _ _ (by decide) | case h
p' : ℕ
k : ℤ
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
h : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | case h
p' : ℕ
k : ℤ
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
h : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1
this : 1 ≤ 2 ^ (p' + 2)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"t","sexp":"((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"have","sourceEnd":17582,"sourceStart":17578,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":17583,"sourceStart":17583,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":17583,"sourceStart":17583,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"1 ≤ 2 ^ (p' + 2)","source_end":17603,"source_start":17585,"syntax_kind":"«term_≤_»"},{"source":"Nat.one_le_pow _ _ (by decide)","source_end":17637,"source_start":17607,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 40 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f849b4645729e2c7aee9a344f7534f12a0ca6aa4709784aba8e6277fdd8dd007 | 3500583f0fb64a4dab07680728ab794a6c88abe92b69cca42dc1bd90c248e04d | e69104a807ed9f3f4fdbc12870f537123ea927ea53793fef08625dc7934a3492 | 1d86ad3188a90bc4a47ee0d09d37bba7f8a7386b4470f24f525e14ac021e9286 |
cat-searcher/leandojo-benchmark-4-random | test | 2,683 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact mod_cast h | case h
p' : ℕ
k : ℤ
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
h : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1
this : 1 ≤ 2 ^ (p' + 2)
⊢ ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) (... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"t","sexp":"((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"exact","sourceEnd":17645,"sourceStart":17640,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":17654,"sourceStart":17646,"tag":"atom"},{"contextIndex":4,"semanticRole":"local","source":"h","sourceEnd":17656,"sourceStart":17655,"tag":"identifier"}],"kind":"Lean.modCast","source":"mod_ca... | [] | [{"source":"mod_cast h","source_end":17656,"source_start":17646,"syntax_kind":"Lean.modCast"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 46 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c4b8cc3efdd2b4ffd3baf06bd50cb22ea31c80d0f3f8f3b9f105ddd247de8cb6 | 1d86ad3188a90bc4a47ee0d09d37bba7f8a7386b4470f24f525e14ac021e9286 | 7d40d3db64d7c1be0fcc75a4a5f15f1f7ed9a43c85318f50fa0b965866890c11 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,684 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>add_tsub_cancel_right</a>, <a>ZMod.intCast_zmod_eq_zero_iff_dvd</a>, <a>Nat.ofNat_pos</a>, <a>pow_pos</a>, <a>Nat.cast_pred</a>, <a>Nat.cast_pow</a>, <a>Nat.cast_ofNat</a>] at h | p' : ℕ
h : ↑(s (p' + 2 - 2)) = 0
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | p' : ℕ
h : 2 ^ (p' + 2) - 1 ∣ s p'
⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1 | ((:c Exists) (:c Int) (:lambda k (:c Int) ((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HPow.hPow) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"h","sexp":"((:c Eq) ((:c ZMod) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c OfNat.ofNat) (:c Nat) (:lit 2... | (:app (:c Exists) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:lambda k :explicit (:c Int) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LucasLehmer.X) (:arg :explicit 0 (:app (:c LucasLehmer.q) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impl... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87798","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:app (:c ZM... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":16970,"sourceStart":16966,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16975,"sourceStart":16971,"tag":"atom"}],"kind"... | [] | [{"source":"add_tsub_cancel_right","source_end":16998,"source_start":16977,"syntax_kind":"ident"},{"source":"ZMod.intCast_zmod_eq_zero_iff_dvd","source_end":17033,"source_start":17000,"syntax_kind":"ident"},{"source":"ofNat_pos","source_end":17044,"source_start":17035,"syntax_kind":"ident"},{"source":"pow_pos","source_... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.87798","is_instance":false,"is_let":false,"user_name":"h"}] | 137 | 9 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a6f7339995d9d15548019f1be979586ebecb6d4a144674d55533f81cc4c47bd | 4569f781b3a8488e94594705c7020ff10ffe0e6751378ba718f2ef9cbbfcffb6 | daf6a16c1e225b87c023fe463816adbdd4ba196b081c055f72e96589fea9987c | eddf0396018619cd8ec4c75845fb81bf15d5826a71873942c297fe155dfff68c |
cat-searcher/leandojo-benchmark-4-random | test | 2,685 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | p' : ℕ
k : ℤ
h : ω ^ 2 ^ p' * (ω ^ 2 ^ p' + ωb ^ 2 ^ p') = ω ^ 2 ^ p' * ↑((2 ^ (p' + 2) - 1) * k)
⊢ 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1) | ((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) (:fv _uniq.87780)) ((:c... | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"h","sexp":"((:c Eq) ((:c LucasLehmer.X) ((:c LucasLehmer.q) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.87780) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))))) ((:c HMul.hMul) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"source":"ring","sourceEnd":17378,"sourceStart":17374,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":17378,"sourceStart":17374,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 23 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8921c1cb50052904e6350f0c04def8d032470d1d68a0ba7c9e5a0d5f5e70155f | 0c2ac49b3978f3dc5f938aa1d13f9c64b47416dd0dfd133509802998ef5bb77c | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,686 | LucasLehmer.ω_pow_formula | Mathlib/NumberTheory/LucasLehmer.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | p' : ℕ
k : ℤ
t : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)
h : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1
⊢ 0 < 2 | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) | [{"name":"p'","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Int)"},{"name":"t","sexp":"((:c Eq) (:c Nat) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c HPow.hPow) (:c Nat) (:c Nat) (:c Nat) ((:c instHPow) (:c Nat) (:c Nat) ((:c Monoid.toNatPow) (:c Nat) (:c Nat.instMonoid))) ((:c ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explici... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"name":"p'","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Int)"},{"binder_role":":explicit","context_in... | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":17636,"sourceStart":17630,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":17636,"sourceStart":17630,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":17636,"sourceStart":17630,"tag":"node"}],"kind... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.87780","is_instance":false,"is_let":false,"user_name":"p'"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.88987","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 137 | 43 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ef5db63d2ed39c69cd793ae7286222d1d9c491a7976209e82ca5ac71ac363ea | 77a29dd081dcb65a2f1793b468e206371ef5b74e5a33cf0099d97590945eb9ea | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,687 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>MeasurableSpace.generateFrom_induction</a> (p := fun t : <a>Set</a> s => <a>MeasureTheory.NullMeasurableSet</a> ((↑) '' t) μ) { t : <a>Set</a> s | ∃ s' : <a>Set</a> α, <a>MeasurableSet</a> s' ∧ (↑) ⁻¹' s' = t } ?_ ?_ ?_ ?_ ht | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ NullMeasurableSet (Subtype.val '' t) μ | case refine_1
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ ∀ t ∈ {t | ∃ s', MeasurableSet s' ∧ Subty... | ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _uniq.148041)) ((:c Set.instMembe... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":45064,"sourceStart":45058,"tag":"atom"},{"children":[{"name":"MeasurableSpace.generateFrom_induction","semanticRole":"global","source":"generateFrom_induction","sourceEnd":45091,"sourceStart":45069,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":45093,... | [] | [{"source":"generateFrom_induction (p := fun t : Set s => NullMeasurableSet ((↑) '' t) μ)\n { t : Set s | ∃ s' : Set α, MeasurableSet s' ∧ (↑) ⁻¹' s' = t } ?_ ?_ ?_ ?_ ht","source_end":45244,"source_start":45069,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 8 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef13a43df9eebe8f659748e693c0b5b11c9638315b7f8b1fe02d25f0f76e6efa | 0761821a5fd3961f27aeb7ef41f7ebdfe11d542f348ef6bae10adf935c7d2e78 | 5c90207ca20436679f6433da2db5cb0dcc0093c7a4d96a3e86ab032e879709cc | 2bb1b5f8e6b207eb4c0e64f2e0d12ced343af23775ab438523ec935f10741abe |
cat-searcher/leandojo-benchmark-4-random | test | 2,688 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro t' ⟨s', hs', rfl⟩ | case refine_1
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ ∀ t ∈ {t | ∃ s', MeasurableSet s' ∧ Subty... | case refine_1.intro.intro
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s'✝ t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
s' : Set α
hs' : MeasurableSet... | (:forall t ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) (:forall _ ((:c Membership.mem) ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) ((:c Set) ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)))) ((:c Set.instMembership) ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rintro","sourceEnd":45256,"sourceStart":45250,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"t'","sourceEnd":45259,"sourceStart":45257,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"t'","sourceEnd":45259,"sourceStart":45257... | [{"role":"fresh_name","source":"s'","source_end":45265,"source_start":45263,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs'","source_end":45270,"source_start":45267,"syntax_kind":"ident"}] | [{"source":"⟨s', hs', rfl⟩","source_end":45278,"source_start":45260,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 13 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ad1a4e6f72067b03a9f5f5ff8f548f22f363021144a0bfddf0d871414d703a9 | 7444552747b83dc392a3abfd4b94b02b4280cfbe0cad995d624c20dbe8fd7a0b | fd0b612251503b7a64d75dc5c4b26f4427304f6e050810d6371f32eb854c5b81 | 3ad09a34795a335dd3ccab12ec18dc2340a819611bb65b8db5e313fa450ebcf8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,689 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Subtype.image_preimage_coe</a>] | case refine_1.intro.intro
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s'✝ t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
s' : Set α
hs' : MeasurableSet... | case refine_1.intro.intro
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s'✝ t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
s' : Set α
hs' : MeasurableSet... | ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _uniq.148041)) ((:c Set.instMembe... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":45285,"sourceStart":45283,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45287,"sourceStart":45286,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Subtype.image_pr... | [] | [{"source":"Subtype.image_preimage_coe","source_end":45313,"source_start":45287,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 14 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48ac54651b22cc28053aef7e482b6f5aa6f95671627ca7b2adaef61194e0fa7f | 3ad09a34795a335dd3ccab12ec18dc2340a819611bb65b8db5e313fa450ebcf8 | a362c185ac9150f768b38cb6cfce6133af90c070c08a07857200c466db472741 | 3f0b527b13acf4bba1227efed2cae36b2111418e86f915870059568a16851281 |
cat-searcher/leandojo-benchmark-4-random | test | 2,690 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hs.inter (hs'.nullMeasurableSet) | case refine_1.intro.intro
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s'✝ t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
s' : Set α
hs' : MeasurableSet... | ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Inter.inter) ((:c Set) (:fv _uniq.148041)) ((:c Set.instInter) (:fv _uniq.148041)) (:fv _uniq.148101) (:fv _uniq.149971)) (:fv _uniq.148070)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":45324,"sourceStart":45319,"tag":"atom"},{"children":[{"source":"hs.inter","sourceEnd":45333,"sourceStart":45325,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":45335,"sourceStart":45334,"tag":"atom"},{"name":"MeasurableSet.nullMeasurableSet","semanticRo... | [] | [{"source":"hs.inter (hs'.nullMeasurableSet)","source_end":45357,"source_start":45325,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 17 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01e5d7825c6b312fe13fc88bca422ae5fd3a636cb3aae0756e093c9ee581a2ab | 3f0b527b13acf4bba1227efed2cae36b2111418e86f915870059568a16851281 | 9b6c32fddbbc4faea6dd5ab573e18712a897dffe19b79fcaefc4bdbf1d9a4054 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,691 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.image_empty</a>, <a>MeasureTheory.nullMeasurableSet_empty</a>] | case refine_2
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ (fun t => NullMeasurableSet (Subtype.val ... | ((:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Member... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:app (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17))))) (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":45367,"sourceStart":45363,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":45372,"sourceStart":45368,"tag":"atom"}],"kind"... | [] | [{"source":"image_empty","source_end":45385,"source_start":45374,"syntax_kind":"ident"},{"source":"nullMeasurableSet_empty","source_end":45410,"source_start":45387,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 20 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fddb303fdbefe359cb84a29f1dd13f70fe90ac014cc4f78552f4e4e285b117c7 | debec6d8549f86cb1c99c330f2e71c820f10fb0d9236f2111322dd7bbbcc50ee | 210766dc9d937e4723bc6e058e1891a980ea7e7bdc2eb707120a452339f55980 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,692 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro t' | case refine_3
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ ∀ (t : Set ↑s),
(fun t => NullMeasura... | case refine_3
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
t' : Set ↑s
⊢ (fun t => NullMeasurableSet (... | (:forall t ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) (:forall _ ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17))))) (:forall _ :explicit (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":45422,"sourceStart":45417,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"t'","sourceEnd":45425,"sourceStart":45423,"tag":"identifier"}],"kind":"null","source":"t'","sourceEnd":45425,"sourceStart":45423,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","sour... | [{"role":"fresh_name","source":"t'","source_end":45425,"source_start":45423,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 27 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b13f4f48b8940f339f94e260fbda8e4688614994ac62f35324f0a343fd9934c | db2fa3f9981706a84bee65820a89d193646a9118338d42016719f2db8477924a | 09847014f8ec144e0b7f1a6c9ae309d2a10fc8785dc61bbb06e6a989941a3227 | fdee7f38c7e99b061865c4f5b72c80296eee7bc6371d2d9e036b43872749e089 |
cat-searcher/leandojo-benchmark-4-random | test | 2,693 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Set.range_diff_image</a> <a>Subtype.coe_injective</a>, <a>Subtype.range_coe_subtype</a>, <a>Set.setOf_mem_eq</a>] | case refine_3
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
t' : Set ↑s
⊢ (fun t => NullMeasurableSet (... | case refine_3
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
t' : Set ↑s
⊢ NullMeasurableSet (Subtype.va... | (:forall _ ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _uniq.148041)) ((:c Se... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall _ :explicit (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":45434,"sourceStart":45430,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":45439,"sourceStart":45435,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":454... | [] | [{"source":"range_diff_image Subtype.coe_injective","source_end":45483,"source_start":45445,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Subtype.range_coe_subtype","source_end":45510,"source_start":45485,"syntax_kind":"ident"},{"source":"setOf_mem_eq","source_end":45524,"source_start":45512,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 28 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7a3e4a291eaf711acfe7bfe1a33752d61476fa95e54efaf6e0ffd65ac85ed74 | fdee7f38c7e99b061865c4f5b72c80296eee7bc6371d2d9e036b43872749e089 | dfee549ede2fb1fb1979f3e29e242b50a2f51913632e091d783d32a9dfa9f627 | 8a2a154ac04fd116c39bd4fd2148cad2f19d0e5d75a668328315f0e6cf7dda17 |
cat-searcher/leandojo-benchmark-4-random | test | 2,694 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hs.diff | case refine_3
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
t' : Set ↑s
⊢ NullMeasurableSet (Subtype.va... | (:forall _ ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _uniq.148041)) ((:c Se... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall _ :explicit (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":45535,"sourceStart":45530,"tag":"atom"},{"name":"MeasureTheory.NullMeasurableSet.diff","semanticRole":"global","source":"hs.diff","sourceEnd":45543,"sourceStart":45536,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hs.diff","sourceEnd":45543,"sourceStar... | [] | [{"source":"hs.diff","source_end":45543,"source_start":45536,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 29 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4e39a95b6dac116f271de5c46ab00df2e55e6262f5ddc425a545d9207094389c | 8a2a154ac04fd116c39bd4fd2148cad2f19d0e5d75a668328315f0e6cf7dda17 | b1b18742f62bbf30adff8076bc741e282d5494719ca85423644fb0f64ea0b7fc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,695 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro f | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
⊢ ∀ (f : ℕ → Set ↑s),
(∀ (n : ℕ), (fun ... | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), (fun t => Null... | (:forall f (:forall _ (:c Nat) ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)))) (:forall _ (:forall n (:c Nat) ((:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall f :explicit (:forall _ :explicit (:c Nat) (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17)))))) (:forall _ :explicit (:forall n :explicit (:c Nat) (:app (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-t... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":45554,"sourceStart":45549,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"f","sourceEnd":45556,"sourceStart":45555,"tag":"identifier"}],"kind":"null","source":"f","sourceEnd":45556,"sourceStart":45555,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"f","source_end":45556,"source_start":45555,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 34 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29159b074c6077f0db237ad957deda847e8f9ea488766aca94d19ad31b6bfc9d | 2ef9b91371f4f562c82b4b55c91416897e95b3413fceb780c74594dfd71693e0 | 1b6adeb7609491c9394bb306e96476a63e76a33485b960b718905e46990895c7 | 8816c263731eb809998dfa8fcfcf57c62a01170763bd47c6f3ff6508c9434ae8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,696 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [] | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), (fun t => Null... | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), NullMeasurable... | (:forall _ (:forall n (:c Nat) ((:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101))) ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall _ :explicit (:forall n :explicit (:c Nat) (:app (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV17))))) (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Mea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"dsimp","sourceEnd":45566,"sourceStart":45561,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":45571,"sourceStart":45567,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":45... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 35 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a8d24de27aec59b257622951a3da1cab48132cc3788c0243f12d388dcb4f8584 | 8816c263731eb809998dfa8fcfcf57c62a01170763bd47c6f3ff6508c9434ae8 | 6292ddfed51e73e4410178db16604865c8bef2306a4bd0c08784ecba139e8af0 | 0e1ecd2eef5d6ab289ca3715989d8d44f01450deef793e420f9a6ccc9338fbd0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,697 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.image_iUnion</a>] | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), NullMeasurable... | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), NullMeasurable... | (:forall _ (:forall n (:c Nat) ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall _ :explicit (:forall n :explicit (:c Nat) (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":45581,"sourceStart":45579,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45583,"sourceStart":45582,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.image_iUnion... | [] | [{"source":"image_iUnion","source_end":45595,"source_start":45583,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 36 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bf714f6bd9dcf6e5e7aed57b06c74a4a8658fe2402572d6284c8dd1cdbe15a3 | 0e1ecd2eef5d6ab289ca3715989d8d44f01450deef793e420f9a6ccc9338fbd0 | a8b9c3b19f1438d71c1dacef3c5047e4cdb8df682294529d048ac8a49bde648f | e3da8f337de3182375d17601f4a1c55125f2504e2bf00e0000dbf760c0796b81 |
cat-searcher/leandojo-benchmark-4-random | test | 2,698 | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.NullMeasurableSet.iUnion</a> | case refine_4
R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s s' t✝ : Set α
t : Set ↑s
hs : NullMeasurableSet s μ
ht : MeasurableSet t
f : ℕ → Set ↑s
⊢ (∀ (n : ℕ), NullMeasurable... | (:forall _ (:forall n (:c Nat) ((:c MeasureTheory.NullMeasurableSet) (:fv _uniq.148041) (:fv _uniq.148056) ((:c Set.image) ((:c Set.Elem) (:fv _uniq.148041) (:fv _uniq.148101)) (:fv _uniq.148041) ((:c Subtype.val) (:fv _uniq.148041) (:lambda x (:fv _uniq.148041) ((:c Membership.mem) (:fv _uniq.148041) ((:c Set) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.148041))"},{"name":"inst✝... | (:forall _ :explicit (:forall n :explicit (:c Nat) (:app (:c MeasureTheory.NullMeasurableSet) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":45606,"sourceStart":45601,"tag":"atom"},{"name":"MeasureTheory.NullMeasurableSet.iUnion","semanticRole":"global","source":"NullMeasurableSet.iUnion","sourceEnd":45631,"sourceStart":45607,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact NullMeasurableSet.i... | [] | [{"source":"NullMeasurableSet.iUnion","source_end":45631,"source_start":45607,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.148038","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.148041","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 248 | 39 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e8013f5574d571681103df64feb040e1668ad97737555ac86d09447ac9e7b3e | e3da8f337de3182375d17601f4a1c55125f2504e2bf00e0000dbf760c0796b81 | 6788a059e3b80f9dc14b8905523fdc6873f90005da1bf3da3a7e1fe91062eabc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,699 | MeasureTheory.Measure.integral_comp_mul_left | Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>smul_eq_mul</a>, <a>MeasureTheory.Measure.integral_comp_smul</a>, <a>FiniteDimensional.finrank_self</a>, <a>pow_one</a>] | E : Type u_1
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : MeasurableSpace E
inst✝⁴ : BorelSpace E
inst✝³ : FiniteDimensional ℝ E
μ : Measure E
inst✝² : μ.IsAddHaarMeasure
F : Type u_2
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
s : Set E
g : ℝ → F
a : ℝ
⊢ ∫ (x : ℝ), g (a * x) = |a⁻¹| • ∫ (y... | ((:c Eq) (:fv _uniq.89211) ((:c MeasureTheory.integral) (:c Real) (:fv _uniq.89211) (:fv _uniq.89214) (:fv _uniq.89323) ((:c MeasureTheory.MeasureSpace.toMeasurableSpace) (:c Real) (:c Real.measureSpace)) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace)) (:lambda x (:c Real) ((:fv _uniq.91099) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.88335))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.88335) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.88335) (:fv _uniq.88338)))"},{"name":"inst✝⁵","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:app (:c MeasureTheory.integral) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV8)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 3 (:instance-of (:app (:c NormedSpace) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88335","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.88338","is_instance":true,"is_let":false,"name":"inst✝⁷","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":7220,"sourceStart":7213,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7222,"sourceStart":7221,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{... | [] | [{"source":"smul_eq_mul","source_end":7237,"source_start":7226,"syntax_kind":"ident"},{"source":"Measure.integral_comp_smul","source_end":7265,"source_start":7239,"syntax_kind":"ident"},{"source":"FiniteDimensional.finrank_self","source_end":7297,"source_start":7267,"syntax_kind":"ident"},{"source":"pow_one","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88335","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.88338","is_instance":true,"is_let":false,"user_name":"inst✝⁷"},{"binder_role":":instance-implicit","context_index":... | 31 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7a111bd547970aedc50d76785736ba12c068590acc30f2f804f0ee7f773bcea4 | 07edcfa7df1ef5db8c029894d689d28a50dad1f0a360c3330bc6a980a8bde208 | 1626adbcf48c16f4bd3d9ef1bcfadee6cfef6b115be19add0b8d72ffe3efa8ba | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,700 | WeierstrassCurve.Jacobian.Point.toAffine_of_equiv | Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h with ⟨u, rfl⟩ | R : Type u
inst✝¹ : CommRing R
W' : Jacobian R
F : Type v
inst✝ : Field F
W : Jacobian F
P Q : Fin 3 → F
h : P ≈ Q
⊢ toAffine W P = toAffine W Q | case intro
R : Type u
inst✝¹ : CommRing R
W' : Jacobian R
F : Type v
inst✝ : Field F
W : Jacobian F
Q : Fin 3 → F
u : Fˣ
⊢ toAffine W ((fun m => m • Q) u) = toAffine W Q | ((:c Eq) ((:c WeierstrassCurve.Affine.Point) (:fv _uniq.1032659) ((:c EuclideanDomain.toCommRing) (:fv _uniq.1032659) ((:c Field.toEuclideanDomain) (:fv _uniq.1032659) (:fv _uniq.1032662))) ((:c WeierstrassCurve.Jacobian.toAffine) (:fv _uniq.1032659) (:fv _uniq.1032665))) ((:c WeierstrassCurve.Jacobian.Point.toAffine) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.1032651))"},{"name":"W'","sexp":"((:c WeierstrassCurve.Jacobian) (:fv _uniq.1032651))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.1032659))"},{"name":"W","sexp":"((:c WeierstrassCurve.Jac... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WeierstrassCurve.Affine.Point) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c WeierstrassCurve.Jacobian.toAffine) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:fv FV5... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1032651","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1032654","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :ex... | {"children":[{"source":"rcases","sourceEnd":72517,"sourceStart":72511,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRole":"local","source":"h","sourceEnd":72519,"sourceStart":72518,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"h","source_end":72519,"source_start":72518,"syntax_kind":"ident"},{"source":"⟨u, rfl⟩","source_end":72537,"source_start":72525,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1032651","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1032654","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"in... | 283 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff831b755117e9cb096dab099ecfe5424f651c7685a51a04d0cffe1575bb3bde | 8e09e23927cca1bb9557c22b5c434202dab0ae6a54d4038e9da38d15a3c9dd14 | 1241ffe3451e69eb0b8afe0dbccbad8f1b2978163df2e5d314a9b3409fec9f15 | 5b0a54052c286095f2a12159f0ef537c8cca8e1f1bb52e6adf855f1feebfba06 |
cat-searcher/leandojo-benchmark-4-random | test | 2,701 | WeierstrassCurve.Jacobian.Point.toAffine_of_equiv | Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>WeierstrassCurve.Jacobian.Point.toAffine_smul</a> Q u.isUnit | case intro
R : Type u
inst✝¹ : CommRing R
W' : Jacobian R
F : Type v
inst✝ : Field F
W : Jacobian F
Q : Fin 3 → F
u : Fˣ
⊢ toAffine W ((fun m => m • Q) u) = toAffine W Q | ((:c Eq) ((:c WeierstrassCurve.Affine.Point) (:fv _uniq.1032659) ((:c EuclideanDomain.toCommRing) (:fv _uniq.1032659) ((:c Field.toEuclideanDomain) (:fv _uniq.1032659) (:fv _uniq.1032662))) ((:c WeierstrassCurve.Jacobian.toAffine) (:fv _uniq.1032659) (:fv _uniq.1032665))) ((:c WeierstrassCurve.Jacobian.Point.toAffine) ... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.1032651))"},{"name":"W'","sexp":"((:c WeierstrassCurve.Jacobian) (:fv _uniq.1032651))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝","sexp":"((:c Field) (:fv _uniq.1032659))"},{"name":"W","sexp":"((:c WeierstrassCurve.Jac... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WeierstrassCurve.Affine.Point) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c WeierstrassCurve.Jacobian.toAffine) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:fv FV5... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1032651","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1032654","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :ex... | {"children":[{"source":"exact","sourceEnd":72545,"sourceStart":72540,"tag":"atom"},{"children":[{"name":"WeierstrassCurve.Jacobian.Point.toAffine_smul","semanticRole":"global","source":"toAffine_smul","sourceEnd":72559,"sourceStart":72546,"tag":"identifier"},{"children":[{"contextIndex":7,"semanticRole":"local","source... | [] | [{"source":"toAffine_smul Q u.isUnit","source_end":72570,"source_start":72546,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1032651","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1032654","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":2,"in... | 283 | 5 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af531a723571c6a80efa2085aee18d1066ad541985713090fae68b6d555f4953 | 5b0a54052c286095f2a12159f0ef537c8cca8e1f1bb52e6adf855f1feebfba06 | a191f2def029d2026611361bde20be96cb72fe9b83a260a168613a254033e4d6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,702 | Finsupp.sigma_support | Mathlib/Data/Finsupp/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finset.ext_iff</a>, <a>Finsupp.splitSupport</a>, <a>Finsupp.split</a>, <a>Finsupp.comapDomain</a>, @<a>Finset.mem_image</a> _ _ (<a>Classical.decEq</a> _), <a>Finset.mem_preimage</a>, <a>Sigma.forall</a>, <a>Finset.mem_sigma</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
M : Type u_5
M' : Type u_6
N : Type u_7
P : Type u_8
G : Type u_9
H : Type u_10
R : Type u_11
S : Type u_12
αs : ι → Type u_13
inst✝ : Zero M
l : (i : ι) × αs i →₀ M
⊢ l.support = l.splitSupport.sigma fun i => (l.split i).support | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
M : Type u_5
M' : Type u_6
N : Type u_7
P : Type u_8
G : Type u_9
H : Type u_10
R : Type u_11
S : Type u_12
αs : ι → Type u_13
inst✝ : Zero M
l : (i : ι) × αs i →₀ M
⊢ ∀ (a : ι) (b : αs a), ⟨a, b⟩ ∈ l.support ↔ (∃ a_1 ∈ l.support, a_1.fst = a) ∧ ⟨a, b⟩ ∈ l.support | ((:c Eq) ((:c Finset) ((:c Sigma) (:fv _uniq.549141) (:lambda i (:fv _uniq.549141) ((:fv _uniq.549170) 0)))) ((:c Finsupp.support) ((:c Sigma) (:fv _uniq.549141) (:lambda i (:fv _uniq.549141) ((:fv _uniq.549170) 0))) (:fv _uniq.549144) (:fv _uniq.549173) (:fv _uniq.549201)) ((:c Finset.sigma) (:fv _uniq.549141) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M'","sexp":"(:sort (+ u_6 1))"},{"name":"N","sexp":"(:sort (+ u_7 1))"},{"name":"P","sexp":"(:sort (+ u_8 1))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda i :explicit (:fv FV3) (:app (:fv FV12) (:arg :explicit 0 0)))))))) (:arg :explicit 1 (:app (:c Finsupp.support) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-t... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.549132","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.549135","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":76360,"sourceStart":76356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":76365,"sourceStart":76361,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":763... | [] | [{"source":"Finset.ext_iff","source_end":76381,"source_start":76367,"syntax_kind":"ident"},{"source":"splitSupport","source_end":76395,"source_start":76383,"syntax_kind":"ident"},{"source":"split","source_end":76402,"source_start":76397,"syntax_kind":"ident"},{"source":"comapDomain","source_end":76415,"source_start":76... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.549132","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.549135","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 566 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c20fc0f096970174b5a5453e9bf2b114a8bd63cfa4220d68ed49ac1a11acc4c | e32746e91f703ed327d8909c412a853043c6ef74d22a0a0419db0772513b9635 | d737e1467cc1cd8b34d12c989df0624813ccebd7742036b0d5d77e096afa7959 | 9bd62f86a8a63f73f44a85761323d22ebef8d2d35d6ecef768ef813a17892563 |
cat-searcher/leandojo-benchmark-4-random | test | 2,703 | Finsupp.sigma_support | Mathlib/Data/Finsupp/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | tauto | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Type u_4
M : Type u_5
M' : Type u_6
N : Type u_7
P : Type u_8
G : Type u_9
H : Type u_10
R : Type u_11
S : Type u_12
αs : ι → Type u_13
inst✝ : Zero M
l : (i : ι) × αs i →₀ M
⊢ ∀ (a : ι) (b : αs a), ⟨a, b⟩ ∈ l.support ↔ (∃ a_1 ∈ l.support, a_1.fst = a) ∧ ⟨a, b⟩ ∈ l.support | (:forall a (:fv _uniq.549141) (:forall b ((:fv _uniq.549170) 0) ((:c Iff) ((:c Membership.mem) ((:c Sigma) (:fv _uniq.549141) (:lambda i (:fv _uniq.549141) ((:fv _uniq.549170) 0))) ((:c Finset) ((:c Sigma) (:fv _uniq.549141) (:lambda i (:fv _uniq.549141) ((:fv _uniq.549170) 0)))) ((:c Finset.instMembership) ((:c Sigma)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort (+ u_4 1))"},{"name":"M","sexp":"(:sort (+ u_5 1))"},{"name":"M'","sexp":"(:sort (+ u_6 1))"},{"name":"N","sexp":"(:sort (+ u_7 1))"},{"name":"P","sexp":"(:sort (+ u_8 1))"... | (:forall a :explicit (:fv FV3) (:forall b :explicit (:app (:fv FV12) (:arg :explicit 0 0)) (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda i :explicit (:fv FV3) (:app (:fv FV12) (:arg :explicit 0 0)))))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.549132","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.549135","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"tauto","sourceEnd":76582,"sourceStart":76577,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.Tauto.tauto","source":"tauto","sourceEnd":76582,"sourceStart":76577,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.549132","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.549135","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 566 | 5 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b7bfafc1243312d9228cfd26d601bb9afcf3eac08b75804ceee12e0eb602d0b | 9bd62f86a8a63f73f44a85761323d22ebef8d2d35d6ecef768ef813a17892563 | 78175d0e14580017b7abde3d46f7acc510808867e2ea0a22535e39b5dff68317 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,704 | List.Nat.mem_antidiagonalTuple | Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases n | case h0
k n : ℕ
⊢ Fin.elim0 ∈ antidiagonalTuple 0 n ↔ ∑ i : Fin 0, i.elim0 = n | ((:c Iff) ((:c Membership.mem) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat)) ((:c List) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat))) ((:c List.instMembership) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0... | [{"name":"k","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1013","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":2716,"sourceStart":2711,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":2,"semanticRole":"local","source":"n","sourceEnd":2718,"sourceStart":2717,"tag":"identifier"}],"kind":"... | [] | [{"source":"n","source_end":2718,"source_start":2717,"syntax_kind":"ident"},{"source":"eq_comm","source_end":2753,"source_start":2746,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1013","is_instance":false,"is_let":false,"user_name":"n"}] | 10 | 7 | branch_opener | false | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0f248a415499df89c45d8a534fbb76a338f9bca8655fb07e61c563ed19943c0 | 49f6986042c5884e6a558e3afc55e127864b79fffa89013b53fb97294188121b | 587af0ace40623dade91be1b78e831facc5de085c3c720b59185b89ff09878a4 | 6d1a63e02c9eaa700788c6f28bf2912ada9832a8ab81acc2e83e368e11ee39bf | |
cat-searcher/leandojo-benchmark-4-random | test | 2,705 | List.Nat.mem_antidiagonalTuple | Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | case h0.zero
k : ℕ
⊢ Fin.elim0 ∈ antidiagonalTuple 0 0 ↔ ∑ i : Fin 0, i.elim0 = 0 | ((:c Iff) ((:c Membership.mem) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat)) ((:c List) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat))) ((:c List.instMembership) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0... | [{"name":"k","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":2732,"sourceStart":2726,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":2732,"sourceStart":2726,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":2732,"sourceStart":2726,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"user_name":"k"}] | 10 | 12 | exact | true | 1 | 1 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87ac32b6a149047ec04d6fed5b196247be42dfe01013c125b8945c5ae98241d4 | 4c4c7f620700ce2d7d858a422691107ddd898bfb07f496213f7064e67574823d | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,706 | List.Nat.mem_antidiagonalTuple | Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>eq_comm</a>] | case h0.succ
k n✝ : ℕ
⊢ Fin.elim0 ∈ antidiagonalTuple 0 (n✝ + 1) ↔ ∑ i : Fin 0, i.elim0 = n✝ + 1 | ((:c Iff) ((:c Membership.mem) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat)) ((:c List) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:c Nat))) ((:c List.instMembership) (:forall _ ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 0... | [{"name":"k","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1050","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2744,"sourceStart":2740,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"eq_comm","source_end":2753,"source_start":2746,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.1050","is_instance":false,"is_let":false,"user_name":"n✝"}] | 10 | 17 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ebaecfc61093762aa1427b40de02454d114735743ccb4cf69eba6b69e32c504 | 9b572847bb54c712727f2332c7ea2e0bff19548f4128fcadc6f7faf0f005d0f5 | b523db2eb4897bcd9112c9a963bf55dc6a94039ddfa7a71e8d970f576369f1f4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,707 | List.Nat.mem_antidiagonalTuple | Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Fin.sum_cons</a>, <a>List.Nat.antidiagonalTuple</a>, <a>List.mem_bind</a>, <a>List.mem_map</a>, <a>List.Nat.mem_antidiagonal</a>, <a>Fin.cons_eq_cons</a>, <a>exists_eq_right_right</a>, ih, @<a>eq_comm</a> _ _ (<a>Prod.snd</a> _), <a>and_comm</a> (a := <a>Prod.snd</a> _ = _), ← <a>Prod.mk.inj_iff</a> (a₁ := ... | case h
k n✝ x₀ : ℕ
x : Fin n✝ → ℕ
ih : ∀ {n : ℕ}, x ∈ antidiagonalTuple n✝ n ↔ ∑ i : Fin n✝, x i = n
n : ℕ
⊢ Fin.cons x₀ x ∈ antidiagonalTuple (n✝ + 1) n ↔ ∑ i : Fin (n✝ + 1), Fin.cons x₀ x i = n | ((:c Iff) ((:c Membership.mem) (:forall _ ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.1757) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) (:c Nat)) ((:c List) (:forall _ ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd)... | [{"name":"k","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"x₀","sexp":"(:c Nat)"},{"name":"x","sexp":"(:forall _ ((:c Fin) (:fv _uniq.1757)) (:c Nat))"},{"name":"ih","sexp":"(:forall n (:c Nat) ((:c Iff) ((:c Membership.mem) (:forall _ ((:c Fin) (:fv _uniq.1757)) (:c Nat)) ((:c List) (:forall _ ((:c Fin) ... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"name":"k","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1757","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":2785,"sourceStart":2778,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2787,"sourceStart":2786,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":""... | [] | [{"source":"Fin.sum_cons","source_end":2799,"source_start":2787,"syntax_kind":"ident"},{"source":"antidiagonalTuple","source_end":2818,"source_start":2801,"syntax_kind":"ident"},{"source":"List.mem_bind","source_end":2833,"source_start":2820,"syntax_kind":"ident"},{"source":"List.mem_map","source_end":2847,"source_star... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.980","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1757","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 10 | 21 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d2d1667082d89ea8b450a5ded7dadd417760953d3ff465a84121103885f3fe8 | 63c20d198e5a356d5587bb0d84c8af23b3805ea51e878bfc85fe48ada516803e | 73dd0e296772ecb9f09b8c6b9fafbf73fabb22d096ce3cac0ec4ebec2167b40e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,708 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hm : m ≤ m0 | α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs gs : ℕ... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":21621,"sourceStart":21613,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hm","sourceEnd":21624,"sourceStart":21622,"tag":"identifier"},{"source":":","sourceEnd":21626,"sourceStart":21625,"tag":"atom"}],"kind":"null","source":"hm :","sourceEnd":21626,"so... | [] | [{"source":"m ≤ m0","source_end":21635,"source_start":21627,"syntax_kind":"«term_≤_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 4 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ad9ebd601987983663ea833b166a9feb7d7bc6f7f2f595a7894739359dcc1fc | e419de689ab2fb55d4672e544bf07bee742eee78c6ea5326192c97ca9165e3b6 | 730cccc3c11ddfce0a7ceb70ed0381eb226fd8d7f0c6e86a6aa177966e209d97 | dad30eed562a79d270936cf868f3c17cc8a8533824c93cef23bdbf3dcb2f01e8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,710 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hμm : <a>MeasureTheory.SigmaFinite</a> (μ.trim hm) | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":21692,"sourceStart":21684,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hμm","sourceEnd":21697,"sourceStart":21693,"tag":"identifier"},{"source":":","sourceEnd":21699,"sourceStart":21698,"tag":"atom"}],"kind":"null","source":"hμm :","sourceEnd":21699,"... | [] | [{"source":"SigmaFinite (μ.trim hm)","source_end":21724,"source_start":21700,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 17 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8f5e20365431c6ba988663f471381873173537cbf3944dabab90e48763fed92 | 8f074e01d737cee6d1fc7584cf15bebe6ade1dbed5f76a17da3930337912ed25 | ae0198e6b12373380b46a9219d858c7d7ae763eeea37f445b85ebca49c0cb4a0 | 2251f7a9158478fa2cace17991883d677f824ef14b42f7ed57b3670bb40e9fb0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,712 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI : <a>MeasureTheory.SigmaFinite</a> (μ.trim hm) := hμm | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"haveI","sourceEnd":21792,"sourceStart":21787,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":21793,"sourceStart":21793,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":21793,"sourceStart":21793,"tag":"node"}],"kind":"Lean.Parser.Term.ha... | [] | [{"source":"SigmaFinite (μ.trim hm)","source_end":21819,"source_start":21795,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hμm","source_end":21827,"source_start":21823,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 30 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 14aea7cb56301f179c33742efe960bfce6e168cb5551eff21f5cbb15c9caefe0 | 427d1ebafc1e6ab24f1eef148f6fcbb45d1b8a53d44f1ea150df52b01fb079e3 | f84c44ef294bd36805d1f6ecae1f9d5e6acc74f0c18f2ebdebefaec683b767ae | 9776c219135b973ffb4e2f77fcb8f986c7c70e2a95477ed440300f641bec356d |
cat-searcher/leandojo-benchmark-4-random | test | 2,713 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm f).<a>Filter.EventuallyEq.trans</a> ((<a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm g).<a>Filter.EventuallyEq.trans</a> ?_).<a>Filter.EventuallyEq.symm</a> | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":21836,"sourceStart":21830,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":21838,"sourceStart":21837,"tag":"atom"},{"children":[{"name":"MeasureTheory.condexp_ae_eq_condexpL1","semanticRole":"global","source":"condexp_ae_eq_condexpL1","sourceEnd"... | [] | [{"source":"(condexp_ae_eq_condexpL1 hm f).trans ((condexp_ae_eq_condexpL1 hm g).trans ?_).symm","source_end":21920,"source_start":21837,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 31 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2db23ae8134e68583fba71ca3fd0fab9a95f38087e01259104830aba908c7cb | 9776c219135b973ffb4e2f77fcb8f986c7c70e2a95477ed440300f641bec356d | d3a208c0d8de84dcc5dc5ed72e4d5a6e05f04878f40bac192b063a13001f2f7c | 1152151997b4e167f52f5cb82c55af3cd10a319fcbae89accfa8f33df98ab5cc |
cat-searcher/leandojo-benchmark-4-random | test | 2,714 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.Lp.ext_iff</a>] | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":21925,"sourceStart":21923,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21927,"sourceStart":21926,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":21930,"sourceSt... | [] | [{"source":"Lp.ext_iff","source_end":21941,"source_start":21931,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 32 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 99b754c786c32d72186bd8efc67720496a32437660cad2a01361388af3b8cbca | 1152151997b4e167f52f5cb82c55af3cd10a319fcbae89accfa8f33df98ab5cc | 07fc7689b739fb527e9710eed45cfa8d7574bb31da12d9660d54582f849fc8d3 | cfeeaaee45a0b1a138013ce78633cd8ee129bc49cc35a8d90248ca7f6451371e |
cat-searcher/leandojo-benchmark-4-random | test | 2,715 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hn_eq : ∀ n, <a>MeasureTheory.condexpL1</a> hm μ (gs n) = <a>MeasureTheory.condexpL1</a> hm μ (fs n) := by intro n ext1 refine (<a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm (gs n)).symm.trans ((hfg n).symm.trans ?_) exact <a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm (fs n) | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c NormedAddCommGroup.toSem... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":21949,"sourceStart":21945,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hn_eq","sourceEnd":21955,"sourceStart":21950,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hn_eq","sourceEnd":21955,"sourceStart":21950,"tag... | [] | [{"source":"∀ n, condexpL1 hm μ (gs n) = condexpL1 hm μ (fs n)","source_end":22012,"source_start":21958,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"(condexp_ae_eq_condexpL1 hm (gs n)).symm.trans ((hfg n).symm.trans ?_)","source_end":22121,"source_start":22051,"syntax_kind":"Lean.Parser.Term.app"},{"source":"con... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 35 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 757e48b088fd998635ddf92acf7cd7e1f238fb2662b9dcae4300c7403a169f8f | cfeeaaee45a0b1a138013ce78633cd8ee129bc49cc35a8d90248ca7f6451371e | f8f2dcd26cb08763ba95246c0308f41dc3054210e55d0cec7df08ed15f92faf7 | 41acc400991211589b77d852e01daba60c0d53d781098df976d590231d0fbf29 |
cat-searcher/leandojo-benchmark-4-random | test | 2,716 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hcond_fs : <a>Filter.Tendsto</a> (fun n => <a>MeasureTheory.condexpL1</a> hm μ (fs n)) <a>Filter.atTop</a> (𝓝 (<a>MeasureTheory.condexpL1</a> hm μ f)) := <a>MeasureTheory.tendsto_condexpL1_of_dominated_convergence</a> hm _ (fun n => (hfs_int n).1) h_int_bound_fs hfs_bound hfs | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c NormedAddCommGroup.toSem... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":22172,"sourceStart":22168,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hcond_fs","sourceEnd":22181,"sourceStart":22173,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hcond_fs","sourceEnd":22181,"sourceStart":2217... | [] | [{"source":"Tendsto (fun n => condexpL1 hm μ (fs n)) atTop (𝓝 (condexpL1 hm μ f))","source_end":22258,"source_start":22184,"syntax_kind":"Lean.Parser.Term.app"},{"source":"tendsto_condexpL1_of_dominated_convergence hm _ (fun n => (hfs_int n).1) h_int_bound_fs\n hfs_bound hfs","source_end":22373,"source_start":222... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 41 | exact | true | 1 | 37 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9966c4e7b3f92c9ddc2ebae25a50ac3d44eeabf201df21f583a246ef28bf6c91 | 41acc400991211589b77d852e01daba60c0d53d781098df976d590231d0fbf29 | 0e96562c83f0162373a4fcab025d033296706dc9f97232ed4d20db259b6cb01b | 097566e706264cb28137c66e491e36d50646995ae34fcfa0c9c2ad93bae0b702 |
cat-searcher/leandojo-benchmark-4-random | test | 2,717 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hcond_gs : <a>Filter.Tendsto</a> (fun n => <a>MeasureTheory.condexpL1</a> hm μ (gs n)) <a>Filter.atTop</a> (𝓝 (<a>MeasureTheory.condexpL1</a> hm μ g)) := <a>MeasureTheory.tendsto_condexpL1_of_dominated_convergence</a> hm _ (fun n => (hgs_int n).1) h_int_bound_gs hgs_bound hgs | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c NormedAddCommGroup.toSem... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"have","sourceEnd":22380,"sourceStart":22376,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hcond_gs","sourceEnd":22389,"sourceStart":22381,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hcond_gs","sourceEnd":22389,"sourceStart":2238... | [] | [{"source":"Tendsto (fun n => condexpL1 hm μ (gs n)) atTop (𝓝 (condexpL1 hm μ g))","source_end":22466,"source_start":22392,"syntax_kind":"Lean.Parser.Term.app"},{"source":"tendsto_condexpL1_of_dominated_convergence hm _ (fun n => (hgs_int n).1) h_int_bound_gs\n hgs_bound hgs","source_end":22581,"source_start":224... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 42 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88f9bbaf7debc9f3b29c109edd2cd83e7b59b433103f244a28301a5a3a8a59c6 | 097566e706264cb28137c66e491e36d50646995ae34fcfa0c9c2ad93bae0b702 | a6510e5b2c621eff18be78ff7ec0af67d8fb8808cb7c3de0adecfa794333c8fa | 9bf7c06c331fd818d692de4246d8556ffe5eeab11b7b589248109026f9991470 |
cat-searcher/leandojo-benchmark-4-random | test | 2,718 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>tendsto_nhds_unique_of_eventuallyEq</a> hcond_gs hcond_fs (<a>Filter.eventually_of_forall</a> hn_eq) | case pos
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c NormedAddCommGroup.toSem... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":22589,"sourceStart":22584,"tag":"atom"},{"children":[{"name":"tendsto_nhds_unique_of_eventuallyEq","semanticRole":"global","source":"tendsto_nhds_unique_of_eventuallyEq","sourceEnd":22625,"sourceStart":22590,"tag":"identifier"},{"children":[{"contextIndex":39,"semanticRole":"l... | [] | [{"source":"tendsto_nhds_unique_of_eventuallyEq hcond_gs hcond_fs (eventually_of_forall hn_eq)","source_end":22672,"source_start":22590,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 43 | exact | true | 1 | 39 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94815bd281d5c90736b6815e09e925313755d276c7a7af7207748f671ed73eea | 9bf7c06c331fd818d692de4246d8556ffe5eeab11b7b589248109026f9991470 | 93e9e0050afae8fb7bb349d4623ab9bddff313bcf1ea38dd8b39bd11db2000b8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,719 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.condexp_of_not_le</a> hm] | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":21653,"sourceStart":21646,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21655,"sourceStart":21654,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name"... | [] | [{"source":"condexp_of_not_le hm","source_end":21675,"source_start":21655,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 12 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8855c1ece93d6afb37d211a62a924b788e022d04aea2322f2016965b3f8a8c38 | c3be12c85f5a46a23d0ed32d1e34daffa5c0cf6019051eace11a0030a6e49c49 | b6d4caa00dad2e9fb689b83130e6f0b7c1a6433dd83c4a5a175e7cb8e47f3d14 | 2f749397d18b368bdc8b1df80372ceff5aa63c6e3008dd80b3bbdf5ff882a79a |
cat-searcher/leandojo-benchmark-4-random | test | 2,720 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":21681,"sourceStart":21678,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":21681,"sourceStart":21678,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 16 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 070471dd50e955af79bd4503e46d0f6089b4e6698b549dd94030211a84fb3286 | 2f749397d18b368bdc8b1df80372ceff5aa63c6e3008dd80b3bbdf5ff882a79a | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,721 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.condexp_of_not_sigmaFinite</a> hm hμm] | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp_rw","sourceEnd":21742,"sourceStart":21735,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21744,"sourceStart":21743,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name"... | [] | [{"source":"condexp_of_not_sigmaFinite hm hμm","source_end":21778,"source_start":21744,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 25 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dba4c2a3cb9eb7b0ac5129982a8c87f792f6d23ddd560597736570feecca311a | 2a9c582c5e6cf3dfdc04cddda24c871d6df0ef7613ad6fa416609201da536de5 | 4a0595923b418fc0613514516986d12990f579777d517d91c113c6ba223055e1 | ce6300e4812f64a3b65fd44c4d1887784cc1f889dc786e71958d9cc940269f9c |
cat-searcher/leandojo-benchmark-4-random | test | 2,722 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case neg
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":21784,"sourceStart":21781,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":21784,"sourceStart":21781,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 29 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c82174fe934b7e1232de7406d187edde92022f26bb3f271cd04443d68cf868e | ce6300e4812f64a3b65fd44c4d1887784cc1f889dc786e71958d9cc940269f9c | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,723 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro n | α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs gs : ℕ... | α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs gs : ℕ... | (:forall n (:c Nat) ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c Norm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:forall n :explicit (:c Nat) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":22028,"sourceStart":22023,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":22030,"sourceStart":22029,"tag":"identifier"}],"kind":"null","source":"n","sourceEnd":22030,"sourceStart":22029,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"n","source_end":22030,"source_start":22029,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 37 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b14fde5fed5206345a49ac5fd6f231d161d27e50041ae7cd13ba2bfb7460bf33 | c622ea35db662b915a96df664ebb6f6160b2f88123fda95e61b2adf2786fc713 | 552b0263d5d2dc23e39f080d99d92b8331d063041140b7e6312fecfaba2b5392 | 639a44325f1514cfcf69ae20351d0a7ccbc32681db00196fd192ad25c09c3b3b |
cat-searcher/leandojo-benchmark-4-random | test | 2,724 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 | α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs gs : ℕ... | case h
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs... | ((:c Eq) ((:c Subtype) ((:c MeasureTheory.AEEqFun) (:fv _uniq.138216) (:fv _uniq.138222) (:fv _uniq.138672) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.138222) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.138222) ((:c SeminormedAddCommGroup.toPseudoMetricSpace) (:fv _uniq.138222) ((:c NormedAddCommGroup.toSem... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c MeasureTheory.AEEqFun) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext1","sourceEnd":22039,"sourceStart":22035,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1","sourceEnd":22039,"sourceStart":22035,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 38 | exact | true | 1 | 37 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab2f4bf72fba05d2f90a3941c919b7cdc7878ce98c4def71e23b95cf7f5ea883 | 639a44325f1514cfcf69ae20351d0a7ccbc32681db00196fd192ad25c09c3b3b | e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b | bcd3a252838cd740ba4eb7d411afe838522c8c2677974a094a943512bec9aacd |
cat-searcher/leandojo-benchmark-4-random | test | 2,725 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm (gs n)).symm.trans ((hfg n).symm.trans ?_) | case h
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs... | case h
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":22050,"sourceStart":22044,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":22052,"sourceStart":22051,"tag":"atom"},{"children":[{"name":"MeasureTheory.condexp_ae_eq_condexpL1","semanticRole":"global","source":"condexp_ae_eq_condexpL1","sourceEnd"... | [] | [{"source":"(condexp_ae_eq_condexpL1 hm (gs n)).symm.trans ((hfg n).symm.trans ?_)","source_end":22121,"source_start":22051,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 39 | exact | true | 1 | 37 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f513e814cdc4cd3a3c5a1d097ee06aaa3cfd5e0037a290b2d82c2561fbc40ab | bcd3a252838cd740ba4eb7d411afe838522c8c2677974a094a943512bec9aacd | 915cf45acb67d724378dc10c7b2641e422fc60b7fe2cf069790ce1d5a6f1f9a2 | 12d2b684d9aa02c4570bd58e27f23de3b39dbb4851ccabb324398ac332c660eb |
cat-searcher/leandojo-benchmark-4-random | test | 2,726 | MeasureTheory.tendsto_condexp_unique | Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.condexp_ae_eq_condexpL1</a> hm (fs n) | case h
α : Type u_1
F : Type u_2
F' : Type u_3
𝕜 : Type u_4
p : ℝ≥0∞
inst✝⁶ : RCLike 𝕜
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace 𝕜 F'
inst✝¹ : NormedSpace ℝ F'
inst✝ : CompleteSpace F'
m m0 : MeasurableSpace α
μ : Measure α
f✝ g✝ : α → F'
s : Set α
fs... | ((:c Filter.EventuallyEq) (:fv _uniq.138216) (:fv _uniq.138222) ((:c MeasureTheory.ae) (:fv _uniq.138216) ((:c MeasureTheory.Measure) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.138216) (:fv _uniq.138672)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.138216)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"F","sexp":"(:sort (+ u_2 1))"},{"name":"F'","sexp":"(:sort (+ u_3 1))"},{"name":"𝕜","sexp":"(:sort (+ u_4 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁶","sexp":"((:c RCLike) (:fv _uniq.138225))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (: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 MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":22131,"sourceStart":22126,"tag":"atom"},{"children":[{"name":"MeasureTheory.condexp_ae_eq_condexpL1","semanticRole":"global","source":"condexp_ae_eq_condexpL1","sourceEnd":22155,"sourceStart":22132,"tag":"identifier"},{"children":[{"contextIndex":34,"semanticRole":"local","sou... | [] | [{"source":"condexp_ae_eq_condexpL1 hm (fs n)","source_end":22165,"source_start":22132,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138216","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138219","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 72 | 40 | exact | true | 1 | 37 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60164872cca911025633424222a04b1c8a39b25ab60fce7222483bb46768c0b1 | 12d2b684d9aa02c4570bd58e27f23de3b39dbb4851ccabb324398ac332c660eb | b4161dcfc368f8e5db2172edb2f07578096b3ffaa7e6c0617e64db4f6368be97 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,727 | RingHom.codomain_trivial_iff_map_one_eq_zero | Mathlib/Algebra/Ring/Hom/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>map_one</a>, <a>eq_comm</a>] | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
x✝¹ : NonAssocSemiring α
x✝ : NonAssocSemiring β
f : α →+* β
x y : α
⊢ 0 = 1 ↔ f 1 = 0 | ((:c Iff) ((:c Eq) (:fv _uniq.48446) ((:c OfNat.ofNat) (:fv _uniq.48446) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.48446) ((:c MulZeroOneClass.toZero) (:fv _uniq.48446) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.48446) (:fv _uniq.48455))))) ((:c OfNat.ofNat) (:fv _uniq.48446) (:lit 1) ((:c One.toOfNat1) (:fv _un... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"x✝¹","sexp":"((:c NonAssocSemiring) (:fv _uniq.48443))"},{"name":"x✝","sexp":"((:c NonAssocSemiring) (:fv _uniq.48446))"},{"name":"f","sexp":"((:c Rin... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:lit 0))))))) (:arg :explicit 2 (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48440","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48443","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":21391,"sourceStart":21389,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21393,"sourceStart":21392,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"map_one","source_end":21400,"source_start":21393,"syntax_kind":"ident"},{"source":"eq_comm","source_end":21409,"source_start":21402,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48440","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48443","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 195 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b74873608c324a1dfd35795ef7bcda7028dacb48f4181ab66831cfafe8848760 | f1abbc73298b4a1d35c12e63bf282a8185c552b32b8153ae6f36bc15fd28f04d | d08871176bdc023e5346fd489cc6c62f6389f5e03ffda7bad36774d0942969c8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,728 | cfc_nonpos | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hf : <a>ContinuousOn</a> f (<a>spectrum</a> R a) | R : Type u_1
A : Type u_2
p : A → Prop
inst✝¹⁵ : OrderedCommSemiring R
inst✝¹⁴ : StarRing R
inst✝¹³ : StarOrderedRing R
inst✝¹² : MetricSpace R
inst✝¹¹ : TopologicalSemiring R
inst✝¹⁰ : ContinuousStar R
inst✝⁹ : ∀ (α : Type ?u.684485) [inst : TopologicalSpace α], StarOrderedRing C(α, R)
inst✝⁸ : TopologicalSpace A
inst... | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝¹⁵ : OrderedCommSemiring R
inst✝¹⁴ : StarRing R
inst✝¹³ : StarOrderedRing R
inst✝¹² : MetricSpace R
inst✝¹¹ : TopologicalSemiring R
inst✝¹⁰ : ContinuousStar R
inst✝⁹ : ∀ (α : Type ?u.684485) [inst : TopologicalSpace α], StarOrderedRing C(α, R)
inst✝⁸ : TopologicalSpa... | ((:c LE.le) (:fv _uniq.682891) ((:c Preorder.toLE) (:fv _uniq.682891) ((:c PartialOrder.toPreorder) (:fv _uniq.682891) (:fv _uniq.685536))) ((:c cfc) (:fv _uniq.682888) (:fv _uniq.682891) (:fv _uniq.682895) ((:c OrderedCommSemiring.toCommSemiring) (:fv _uniq.682888) (:fv _uniq.682898)) (:fv _uniq.683218) (:fv _uniq.683... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.682891) (:sort 0))"},{"name":"inst✝¹⁵","sexp":"((:c OrderedCommSemiring) (:fv _uniq.682888))"},{"name":"inst✝¹⁴","sexp":"((:c StarRing) (:fv _uniq.682888) ((:c NonAssocSemiring.toNonUnitalNonAssocS... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":37009,"sourceStart":37001,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":37012,"sourceStart":37010,"tag":"identifier"},{"source":":","sourceEnd":37014,"sourceStart":37013,"tag":"atom"}],"kind":"null","source":"hf :","sourceEnd":37014,"so... | [] | [{"source":"ContinuousOn f (spectrum R a)","source_end":37044,"source_start":37015,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 125 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ceedc4433cb889459ee6c06eed35c079e9b3b4457018c614db06e7a0fbbecc82 | 8b6d6929539c6c15b6baf60a73197de70db89eebb7116237eafc1d63b8ac272d | 9093b01ad3d0ab6e672c34cbeb72885f025e45af76f5f8ef2d4e1f5340561415 | 2d1d85761f0608cf89ccd1c8cf13560af7a09d831df99ae76f60583eaa0d929f |
cat-searcher/leandojo-benchmark-4-random | test | 2,729 | cfc_nonpos | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>cfc_mono</a> h | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝¹⁵ : OrderedCommSemiring R
inst✝¹⁴ : StarRing R
inst✝¹³ : StarOrderedRing R
inst✝¹² : MetricSpace R
inst✝¹¹ : TopologicalSemiring R
inst✝¹⁰ : ContinuousStar R
inst✝⁹ : ∀ (α : Type ?u.684485) [inst : TopologicalSpace α], StarOrderedRing C(α, R)
inst✝⁸ : TopologicalSpa... | ((:c LE.le) (:fv _uniq.682891) ((:c Preorder.toLE) (:fv _uniq.682891) ((:c PartialOrder.toPreorder) (:fv _uniq.682891) (:fv _uniq.685536))) ((:c cfc) (:fv _uniq.682888) (:fv _uniq.682891) (:fv _uniq.682895) ((:c OrderedCommSemiring.toCommSemiring) (:fv _uniq.682888) (:fv _uniq.682898)) (:fv _uniq.683218) (:fv _uniq.683... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.682891) (:sort 0))"},{"name":"inst✝¹⁵","sexp":"((:c OrderedCommSemiring) (:fv _uniq.682888))"},{"name":"inst✝¹⁴","sexp":"((:c StarRing) (:fv _uniq.682888) ((:c NonAssocSemiring.toNonUnitalNonAssocS... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":37055,"sourceStart":37050,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"cfc_mono h","source_end":37072,"source_start":37062,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 125 | 7 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 577253f1206ad934f82e803e1debac6e713d3d8ef73928e1dfd6721a51e5f3ca | 469107c21a513a3e9932e891ff6390ce97e35af5799a9cad2abdd624a2e56aec | 3dd0933860d9a486493e5243142abeb4e17f406e3579bc0deff6e427677c0870 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,730 | cfc_nonpos | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>cfc_apply_of_not_continuousOn</a> _ hf, <a>le_rfl</a>] | case neg
R : Type u_1
A : Type u_2
p : A → Prop
inst✝¹⁵ : OrderedCommSemiring R
inst✝¹⁴ : StarRing R
inst✝¹³ : StarOrderedRing R
inst✝¹² : MetricSpace R
inst✝¹¹ : TopologicalSemiring R
inst✝¹⁰ : ContinuousStar R
inst✝⁹ : ∀ (α : Type u_1) [inst : TopologicalSpace α], StarOrderedRing C(α, R)
inst✝⁸ : TopologicalSpace A
i... | ((:c LE.le) (:fv _uniq.682891) ((:c Preorder.toLE) (:fv _uniq.682891) ((:c PartialOrder.toPreorder) (:fv _uniq.682891) (:fv _uniq.685536))) ((:c cfc) (:fv _uniq.682888) (:fv _uniq.682891) (:fv _uniq.682895) ((:c OrderedCommSemiring.toCommSemiring) (:fv _uniq.682888) (:fv _uniq.682898)) (:fv _uniq.683218) (:fv _uniq.683... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.682891) (:sort 0))"},{"name":"inst✝¹⁵","sexp":"((:c OrderedCommSemiring) (:fv _uniq.682888))"},{"name":"inst✝¹⁴","sexp":"((:c StarRing) (:fv _uniq.682888) ((:c NonAssocSemiring.toNonUnitalNonAssocS... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":37082,"sourceStart":37078,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":37087,"sourceStart":37083,"tag":"atom"}],"kind"... | [] | [{"source":"cfc_apply_of_not_continuousOn _ hf","source_end":37123,"source_start":37089,"syntax_kind":"Lean.Parser.Term.app"},{"source":"le_rfl","source_end":37131,"source_start":37125,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.682888","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.682891","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 125 | 12 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 045b0a1b931b909214d87a4e879bf4ba3fa8a7e77356b47f7c616ead885f6cd4 | bfa24788fd204e384ec3a36d84f587d34d90580307c9657786722e1ff49b3c79 | 630c7e81d9225aa894b1e71fadc6c4b821220cfca84bd2723510fc7fa054efab | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,731 | RelEmbedding.exists_not_acc_lt_of_not_acc | Mathlib/Order/OrderIsoNat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | contrapose! h | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ¬Acc r a
⊢ ∃ b, ¬Acc r b ∧ r b a | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
⊢ Acc r a | ((:c Exists) (:fv _uniq.1178) (:lambda b (:fv _uniq.1178) ((:c And) ((:c Not) ((:c Acc) (:fv _uniq.1178) (:fv _uniq.1222) 0)) ((:fv _uniq.1222) 0 (:fv _uniq.1221))))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uniq.1178) (:sort 0)))"},{"name":"inst✝","sexp":"((:c IsStrictOrder) (:fv _uniq.1178) (:fv _uniq.1184))"},{"name":"a","sexp":"(:fv _uniq.1178)"},{"name":"r","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uni... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda b :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Not) (:arg :explicit 0 (:app (:c Acc) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 0))))) (:arg :explicit 1 (:app (:fv FV5) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"name":"r✝","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expl... | {"children":[{"source":"contrapose!","sourceEnd":2190,"sourceStart":2179,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"h","sourceEnd":2192,"sourceStart":2191,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"h","sourceEnd":2192,"sourceSta... | [] | [{"source":"h","source_end":2192,"source_start":2191,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"user_name":"r✝"},{"binder_role":":instance-implicit","context_index":2,"internal_na... | 13 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ee27d36617a5b04536053089325bb39a5719d86fe81a2c310fe2b65615e991a | 66095d15339cea444e1223721353c1828f9133f2ebfc8592c76660dd46c2c899 | f1c344e3174b14056331ea226f3666d6eca3c3126f1a2fbc18a81a0fe4db0cf9 | 6c81e0b80f2581ee946f355534cfd2f1351faf3b54cd215fd3e47e50ffa1093e |
cat-searcher/leandojo-benchmark-4-random | test | 2,732 | RelEmbedding.exists_not_acc_lt_of_not_acc | Mathlib/Order/OrderIsoNat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨_, fun b hr => ?_⟩ | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
⊢ Acc r a | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
b : α
hr : r b a
⊢ Acc r b | ((:c Acc) (:fv _uniq.1178) (:fv _uniq.1222) (:fv _uniq.1221)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uniq.1178) (:sort 0)))"},{"name":"inst✝","sexp":"((:c IsStrictOrder) (:fv _uniq.1178) (:fv _uniq.1184))"},{"name":"a","sexp":"(:fv _uniq.1178)"},{"name":"r","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uni... | (:app (:c Acc) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"name":"r✝","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expl... | {"children":[{"source":"refine","sourceEnd":2201,"sourceStart":2195,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2205,"sourceStart":2202,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":2206,"sourceStart":2205,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":2206,"sourceSt... | [] | [{"source":"⟨_, fun b hr => ?_⟩","source_end":2225,"source_start":2202,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"user_name":"r✝"},{"binder_role":":instance-implicit","context_index":2,"internal_na... | 13 | 5 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e7b86ec8540ca884d154cea2d918d75a1fd29cd097271f73c5cc37af67e3dd6 | 6c81e0b80f2581ee946f355534cfd2f1351faf3b54cd215fd3e47e50ffa1093e | bb5daa7186568af16462dcfb80a9f7106006f384f3825c1ed0c80cce3ea205c5 | 50ebead9daee97d7a412a4729482181a1ffe97f54325c8ae14007e7353c8ce01 |
cat-searcher/leandojo-benchmark-4-random | test | 2,733 | RelEmbedding.exists_not_acc_lt_of_not_acc | Mathlib/Order/OrderIsoNat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_contra hb | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
b : α
hr : r b a
⊢ Acc r b | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
b : α
hr : r b a
hb : ¬Acc r b
⊢ False | ((:c Acc) (:fv _uniq.1178) (:fv _uniq.1222) (:fv _uniq.1305)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uniq.1178) (:sort 0)))"},{"name":"inst✝","sexp":"((:c IsStrictOrder) (:fv _uniq.1178) (:fv _uniq.1184))"},{"name":"a","sexp":"(:fv _uniq.1178)"},{"name":"r","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uni... | (:app (:c Acc) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:fv FV7))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"name":"r✝","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expl... | {"children":[{"source":"by_contra","sourceEnd":2237,"sourceStart":2228,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"hb","sourceEnd":2240,"sourceStart":2238,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"hb","sourceEnd":2240,"sourceStart":2238,"tag":"node"}],"kind":"null","s... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"user_name":"r✝"},{"binder_role":":instance-implicit","context_index":2,"internal_na... | 13 | 6 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 330050611a2099f97be837f7bfdb4bef2e446d4bfb509aceae8b09ea18e9671d | 50ebead9daee97d7a412a4729482181a1ffe97f54325c8ae14007e7353c8ce01 | ac14e2d1c02eaaaefeb5a96d3b993dc2a081dbf904b5268583fbc12f1fbba553 | ca4cbe993be367dce724595776d1c0b4f0374c6b0b84101ec11c59c3f3c10c3e |
cat-searcher/leandojo-benchmark-4-random | test | 2,734 | RelEmbedding.exists_not_acc_lt_of_not_acc | Mathlib/Order/OrderIsoNat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h b hb hr | α : Type u_1
r✝ : α → α → Prop
inst✝ : IsStrictOrder α r✝
a : α
r : α → α → Prop
h : ∀ (b : α), ¬Acc r b → ¬r b a
b : α
hr : r b a
hb : ¬Acc r b
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"r✝","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uniq.1178) (:sort 0)))"},{"name":"inst✝","sexp":"((:c IsStrictOrder) (:fv _uniq.1178) (:fv _uniq.1184))"},{"name":"a","sexp":"(:fv _uniq.1178)"},{"name":"r","sexp":"(:forall _ (:fv _uniq.1178) (:forall _ (:fv _uni... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"name":"r✝","sexp":"(:forall _ :explicit (:fv FV0) (:forall _ :expl... | {"children":[{"source":"exact","sourceEnd":2248,"sourceStart":2243,"tag":"atom"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"h","sourceEnd":2250,"sourceStart":2249,"tag":"identifier"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"b","sourceEnd":2252,"sourceStart":2251,"tag":"identi... | [] | [{"source":"h b hb hr","source_end":2258,"source_start":2249,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1178","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1184","is_instance":false,"is_let":false,"user_name":"r✝"},{"binder_role":":instance-implicit","context_index":2,"internal_na... | 13 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce72139b646b937fc1cf419b69bd25a2d59f332eeb9f114c7b5484227c959e69 | ca4cbe993be367dce724595776d1c0b4f0374c6b0b84101ec11c59c3f3c10c3e | 814072f9e6aaa26f897ecb728a7e5e7c83463ddc6583bf7b079e93a55d59c026 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,735 | Set.image_prod_mk_subset_prod_left | Mathlib/Data/Set/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨a, ha, rfl⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
s s₁ s₂ : Set α
t t₁ t₂ : Set β
a : α
b : β
hb : b ∈ t
⊢ (fun a => (a, b)) '' s ⊆ s ×ˢ t | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
s s₁ s₂ : Set α
t t₁ t₂ : Set β
a✝ : α
b : β
hb : b ∈ t
a : α
ha : a ∈ s
⊢ (fun a => (a, b)) a ∈ s ×ˢ t | ((:c HasSubset.Subset) ((:c Set) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818))) ((:c Set.instHasSubset) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818))) ((:c Set.image) (:fv _uniq.62815) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818)) (:lambda a (:fv _uniq.62815) ((:c Prod.mk) (:fv _uniq.62815) (:fv _uniq.62818) 0 (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.62815))"},{"name":"s₁","sexp":"((:c Set) (:fv _uniq.62815))"},{"name":"s₂","sexp":"((:c Set) (:fv _uniq.62815))"},{"na... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62815","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62818","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rintro","sourceEnd":13782,"sourceStart":13776,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":13784,"sourceStart":13783,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":13784,"sourceStart":13783,"tag":"node"}],"kind":"Lean.Parser... | [{"role":"fresh_name","source":"a","source_end":13789,"source_start":13788,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":13793,"source_start":13791,"syntax_kind":"ident"}] | [{"source":"⟨a, ha, rfl⟩","source_end":13801,"source_start":13785,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62815","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62818","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 120 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c49d8853f26d485d9a05a5b2f5dd1478e7fab851c4e22052fa6b22be9b75b05 | dfd822935118cdc175a712f8fe36ed59014bb060a510527533cb410228829c9d | af5ce6f2f10081b2733a69bcc5f8c4b38f91a25a1bc154a97346657ce815e4d7 | eeaedac05f76757c63ead072016ad9736add8263a87d13add023264c613e93ec |
cat-searcher/leandojo-benchmark-4-random | test | 2,736 | Set.image_prod_mk_subset_prod_left | Mathlib/Data/Set/Prod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨ha, hb⟩ | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
s s₁ s₂ : Set α
t t₁ t₂ : Set β
a✝ : α
b : β
hb : b ∈ t
a : α
ha : a ∈ s
⊢ (fun a => (a, b)) a ∈ s ×ˢ t | ((:c Membership.mem) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818)) ((:c Set) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.62815) (:fv _uniq.62818))) ((:lambda a (:fv _uniq.62815) ((:c Prod.mk) (:fv _uniq.62815) (:fv _uniq.62818) 0 (:fv _uniq.62846))) (:fv _uniq.62971... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.62815))"},{"name":"s₁","sexp":"((:c Set) (:fv _uniq.62815))"},{"name":"s₂","sexp":"((:c Set) (:fv _uniq.62815))"},{"na... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62815","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62818","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":13809,"sourceStart":13804,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13813,"sourceStart":13810,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"ha","sourceEnd":13815,"sourceStart":13813,"tag":"identifier"},{"source":",","sourceEnd":13816... | [] | [{"source":"⟨ha, hb⟩","source_end":13822,"source_start":13810,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62815","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.62818","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 120 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e03da2024a0b8e0f5f57b2a54ed101a3a63741a08489c082908ac805e3133044 | eeaedac05f76757c63ead072016ad9736add8263a87d13add023264c613e93ec | 986afee418e05014cfb80a77ea5beda904424f91d61ebd699a570c19a699193c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,737 | PMF.map_apply | Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>PMF.map</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
f : α → β
p : PMF α
b : β
⊢ (map f p) b = ∑' (a : α), if b = f a then p a else 0 | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c PMF) (:fv _uniq.193)) (:fv _uniq.193) (:lambda _ (:fv _uniq.193) (:c ENNReal)) ((:c PMF.instFunLike) (:fv _uniq.193)) ((:c PMF.map) (:fv _uniq.190) (:fv _uniq.193) (:fv _uniq.200) (:fv _uniq.203)) (:fv _uniq.205)) ((:c tsum) (:c ENNReal) ((:c NonUnitalNonAssocSemiring.toAdd... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.190) (:fv _uniq.193))"},{"name":"p","sexp":"((:c PMF) (:fv _uniq.190))"},{"name":"b","sexp":"(:fv _uniq.193)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c PMF) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c FunLike) (:arg :explicit 0 (:app (:c PMF) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":1703,"sourceStart":1699,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"map","source_end":1708,"source_start":1705,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.190","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.193","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.1... | 14 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 84116114257d71bba8c8c146e00d661c9ae5caf6132960965c92674630298c51 | ab147e78ee8d8dd2368a7bc63f6078a1459c86e0ec9f4095bbed76e0e0081973 | 1b407d88f3cd9bd8022994517c473148978fcf5b1bef94b10e12f3148ab5b537 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,738 | LieHom.mem_idealRange | Mathlib/Algebra/Lie/Submodule.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LieHom.idealRange_eq_map</a>] | R : Type u
L : Type v
L' : Type w₂
M : Type w
M' : Type w₁
inst✝¹² : CommRing R
inst✝¹¹ : LieRing L
inst✝¹⁰ : LieAlgebra R L
inst✝⁹ : LieRing L'
inst✝⁸ : LieAlgebra R L'
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup M'
inst✝² : Module R M'
inst✝¹ :... | R : Type u
L : Type v
L' : Type w₂
M : Type w
M' : Type w₁
inst✝¹² : CommRing R
inst✝¹¹ : LieRing L
inst✝¹⁰ : LieAlgebra R L
inst✝⁹ : LieRing L'
inst✝⁸ : LieAlgebra R L'
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup M'
inst✝² : Module R M'
inst✝¹ :... | ((:c Membership.mem) (:fv _uniq.595393) ((:c LieIdeal) (:fv _uniq.595389) (:fv _uniq.595393) (:fv _uniq.595400) (:fv _uniq.595422) (:fv _uniq.595436)) ((:c SetLike.instMembership) ((:c LieIdeal) (:fv _uniq.595389) (:fv _uniq.595393) (:fv _uniq.595400) (:fv _uniq.595422) (:fv _uniq.595436)) (:fv _uniq.595393) ((:c LieSu... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"L'","sexp":"(:sort (+ w₂ 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"M'","sexp":"(:sort (+ w₁ 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.595389))"},{"name":"inst✝¹¹","sexp":"((:c LieRing) (:fv _uniq.595391))"},... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.595389","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.595391","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":46494,"sourceStart":46492,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46496,"sourceStart":46495,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LieHom.idealRang... | [] | [{"source":"idealRange_eq_map","source_end":46513,"source_start":46496,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.595389","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.595391","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 379 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5010bfc7ea2a3ad5d11b52b0e6bd86108e45c31177ada2642b861828b7b88301 | a844cdb8882263dc2dcc2c161d6572248297c0c7d2bcad44affeb27d375e8ebb | 3b2b7a30e7659939cd2139d4059fae44160d0af76366f97f39a0f73182800f68 | d050b9b5f6466b1e7dd55c8b4a464766d396bc506e76a9230603ea58940bc162 |
cat-searcher/leandojo-benchmark-4-random | test | 2,739 | LieHom.mem_idealRange | Mathlib/Algebra/Lie/Submodule.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>LieIdeal.mem_map</a> (<a>LieSubmodule.mem_top</a> x) | R : Type u
L : Type v
L' : Type w₂
M : Type w
M' : Type w₁
inst✝¹² : CommRing R
inst✝¹¹ : LieRing L
inst✝¹⁰ : LieAlgebra R L
inst✝⁹ : LieRing L'
inst✝⁸ : LieAlgebra R L'
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup M'
inst✝² : Module R M'
inst✝¹ :... | ((:c Membership.mem) (:fv _uniq.595393) ((:c LieIdeal) (:fv _uniq.595389) (:fv _uniq.595393) (:fv _uniq.595400) (:fv _uniq.595422) (:fv _uniq.595436)) ((:c SetLike.instMembership) ((:c LieIdeal) (:fv _uniq.595389) (:fv _uniq.595393) (:fv _uniq.595400) (:fv _uniq.595422) (:fv _uniq.595436)) (:fv _uniq.595393) ((:c LieSu... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"L","sexp":"(:sort (+ v 1))"},{"name":"L'","sexp":"(:sort (+ w₂ 1))"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"M'","sexp":"(:sort (+ w₁ 1))"},{"name":"inst✝¹²","sexp":"((:c CommRing) (:fv _uniq.595389))"},{"name":"inst✝¹¹","sexp":"((:c LieRing) (:fv _uniq.595391))"},... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.595389","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.595391","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":46522,"sourceStart":46517,"tag":"atom"},{"children":[{"name":"LieIdeal.mem_map","semanticRole":"global","source":"LieIdeal.mem_map","sourceEnd":46539,"sourceStart":46523,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":46541,"sourceStart":46540,"tag":"at... | [] | [{"source":"LieIdeal.mem_map (LieSubmodule.mem_top x)","source_end":46564,"source_start":46523,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.595389","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.595391","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 379 | 7 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 94edbf506214c1ac69a6415df63b4681fd49f7fe6d8150f1973b0e26a13e78a2 | d050b9b5f6466b1e7dd55c8b4a464766d396bc506e76a9230603ea58940bc162 | 27d0e9fab23d5ac9dde9faf6c7280e49a7081ed9795fa5a0cf0fe364b529042a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,740 | SimpleGraph.map_singletonSubgraph | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext <;> simp only [<a>Relation.Map</a>, <a>SimpleGraph.Subgraph.map_adj</a>, <a>SimpleGraph.singletonSubgraph_adj</a>, <a>Pi.bot_apply</a>, <a>exists_and_left</a>, <a>and_iff_left_iff_imp</a>, <a>IsEmpty.forall_iff</a>, <a>SimpleGraph.Subgraph.map_verts</a>, <a>SimpleGraph.singletonSubgraph_verts</a>, <a>Set.image_sing... | ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
f : G →g G'
v : V
⊢ Subgraph.map f (G.singletonSubgraph v) = G'.singletonSubgraph (f v) | case Adj.h.h.a
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
f : G →g G'
v : V
x✝¹ x✝ : W
⊢ ⊥ → ∃ x, f x = x✝¹ ∧ ∃ x, f x = x✝ | ((:c Eq) ((:c SimpleGraph.Subgraph) (:fv _uniq.98211) (:fv _uniq.98217)) ((:c SimpleGraph.Subgraph.map) (:fv _uniq.98209) (:fv _uniq.98211) (:fv _uniq.98214) (:fv _uniq.98217) (:fv _uniq.98335) ((:c SimpleGraph.singletonSubgraph) (:fv _uniq.98209) (:fv _uniq.98214) (:fv _uniq.98336))) ((:c SimpleGraph.singletonSubgraph... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.98209))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.98211))"},{"name":"f","sexp":"((:c SimpleGraph.Hom) (:fv _uniq.98209) (:fv _uniq.98211) (:fv _uniq.9... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c SimpleGraph.Subgraph) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:fv FV4)))) (:arg :explicit 1 (:app (:c SimpleGraph.Subgraph.map) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:fv FV6... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98207","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98209","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"source":"ext","sourceEnd":35552,"sourceStart":35549,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":35552,"sourceStart":35549,"tag":"node"},{"source":"<;>... | [] | [{"source":"Relation.Map","source_end":35580,"source_start":35568,"syntax_kind":"ident"},{"source":"Subgraph.map_adj","source_end":35598,"source_start":35582,"syntax_kind":"ident"},{"source":"singletonSubgraph_adj","source_end":35621,"source_start":35600,"syntax_kind":"ident"},{"source":"Pi.bot_apply","source_end":3563... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98207","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98209","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 246 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bab23a8cc7df7450395bf1ceafa6226a02908d58bc8115199c38463dabc376a0 | aa98244f6e33fab73257c5469de025e2a0e063b8c6974708641c16e83be6eba4 | bac5356240f9f932a324615030251c2e2a7978214e71ea212ef82a8e8f00c0d8 | 3c121cd15d11b45f4f136ecfcd0bc680acf218839a25b858e13ab6e34c815fa6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,741 | SimpleGraph.map_singletonSubgraph | Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>False.elim</a> | case Adj.h.h.a
ι : Sort u_1
V : Type u
W : Type v
G : SimpleGraph V
G' : SimpleGraph W
f : G →g G'
v : V
x✝¹ x✝ : W
⊢ ⊥ → ∃ x, f x = x✝¹ ∧ ∃ x, f x = x✝ | (:forall _ ((:c Bot.bot) (:sort 0) ((:c CompleteLattice.toBot) (:sort 0) (:c Prop.instCompleteLattice))) ((:c Exists) (:fv _uniq.98209) (:lambda x (:fv _uniq.98209) ((:c And) ((:c Eq) (:fv _uniq.98211) ((:c DFunLike.coe) ((:c SimpleGraph.Hom) (:fv _uniq.98209) (:fv _uniq.98211) (:fv _uniq.98214) (:fv _uniq.98217)) (:fv... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"V","sexp":"(:sort (+ u 1))"},{"name":"W","sexp":"(:sort (+ v 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.98209))"},{"name":"G'","sexp":"((:c SimpleGraph) (:fv _uniq.98211))"},{"name":"f","sexp":"((:c SimpleGraph.Hom) (:fv _uniq.98209) (:fv _uniq.98211) (:fv _uniq.9... | (:forall _ :explicit (:app (:c Bot.bot) (:arg :implicit-type 0 (:sort Prop)) (:arg :instance 1 (:instance-of (:app (:c Bot) (:arg :explicit 0 (:sort Prop)))))) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :impli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98207","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98209","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":35777,"sourceStart":35772,"tag":"atom"},{"name":"False.elim","semanticRole":"global","source":"False.elim","sourceEnd":35788,"sourceStart":35778,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact False.elim","sourceEnd":35788,"sourceStart":35772,"tag":"node... | [] | [{"source":"False.elim","source_end":35788,"source_start":35778,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98207","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98209","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 246 | 9 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8cd21fb93db917494e21a5522aaa3f4a04d6123cab790548466fb31eff5c356 | 3c121cd15d11b45f4f136ecfcd0bc680acf218839a25b858e13ab6e34c815fa6 | 00ce241354a533e839bbb997a1c80c99214a03b3e875053b41ee8a709d1bec01 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,742 | Int.even_iff_not_odd | Mathlib/Algebra/Ring/Int.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Int.not_odd_iff</a>, <a>Int.even_iff</a>] | m n : ℤ
⊢ Even n ↔ ¬Odd n | ((:c Iff) ((:c Even) (:c Int) (:c Int.instAdd) (:fv _uniq.11465)) ((:c Not) ((:c Odd) (:c Int) (:c Int.instSemiring) (:fv _uniq.11465)))) | [{"name":"m","sexp":"(:c Int)"},{"name":"n","sexp":"(:c Int)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Even) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Add) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:fv FV1)))) (:arg :explicit 1 (:app (:c Not) (:arg :explicit 0 (:app (:c Odd) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11463","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Int)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11465","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3450,"sourceStart":3448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3452,"sourceStart":3451,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"not_odd_iff","source_end":3463,"source_start":3452,"syntax_kind":"ident"},{"source":"even_iff","source_end":3473,"source_start":3465,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11463","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11465","is_instance":false,"is_let":false,"user_name":"n"}] | 30 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd2a8d1606168425c38e5b015bba3044e46edc4c738c8ad67b63d165c3d60087 | cdc21f5d365378f47ead7c428e7e2cbaac3bbd90e66f863a8cd113e357cbc791 | 5c6234b6933a66bbb8a54a106ecef62c2bc3ffce85a2a41d87b3665e4d15eca4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,743 | vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hp with ⟨p2, ⟨hp2, ⟨v2, ⟨hv2, hv2p⟩⟩⟩⟩ | k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
s : Set P
p : P
v : V
hp : p ∈ spanPoints k s
hv : v ∈ vectorSpan k s
⊢ v +ᵥ p ∈ spanPoints k s | case intro.intro.intro.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
s : Set P
p : P
v : V
hv : v ∈ vectorSpan k s
p2 : P
hp2 : p2 ∈ s
v2 : V
hv2 : v2 ∈ vectorSpan k s
hv2p : p = v2 +ᵥ p2
⊢ v +ᵥ p ∈ spanPoints k s | ((:c Membership.mem) (:fv _uniq.22893) ((:c Set) (:fv _uniq.22893)) ((:c Set.instMembership) (:fv _uniq.22893)) ((:c HVAdd.hVAdd) (:fv _uniq.22890) (:fv _uniq.22893) (:fv _uniq.22893) ((:c instHVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c AddAction.toVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c SubNegMonoid.toAddMo... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.22887))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.22890))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.22887) (:fv _uniq.22890) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:app (:c HVAdd.hVAdd) ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":5530,"sourceStart":5524,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"hp","sourceEnd":5533,"sourceStart":5531,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"hp","source_end":5533,"source_start":5531,"syntax_kind":"ident"},{"source":"⟨p2, ⟨hp2, ⟨v2, ⟨hv2, hv2p⟩⟩⟩⟩","source_end":5585,"source_start":5539,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 32 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2175e07084368642ff635830daff05a0294085c0c3569413ed84118ca886bd5a | 95796096678b4ec5fe4d01593890adfdbaddccf0ecfdb45c3d1b3196f2293cb8 | 1b28c83c58036e5ce43aa4fe19632a3ba22dcf3bda4ba996f8e29c09de1a7edc | ca6fdccbde76746cfa1d6efafa8187b6d30e59e74f52c8b8f230cad3b475eaa0 |
cat-searcher/leandojo-benchmark-4-random | test | 2,744 | vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hv2p, <a>vadd_vadd</a>] | case intro.intro.intro.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
s : Set P
p : P
v : V
hv : v ∈ vectorSpan k s
p2 : P
hp2 : p2 ∈ s
v2 : V
hv2 : v2 ∈ vectorSpan k s
hv2p : p = v2 +ᵥ p2
⊢ v +ᵥ p ∈ spanPoints k s | case intro.intro.intro.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
s : Set P
p : P
v : V
hv : v ∈ vectorSpan k s
p2 : P
hp2 : p2 ∈ s
v2 : V
hv2 : v2 ∈ vectorSpan k s
hv2p : p = v2 +ᵥ p2
⊢ v + v2 +ᵥ p2 ∈ spanPoints k s | ((:c Membership.mem) (:fv _uniq.22893) ((:c Set) (:fv _uniq.22893)) ((:c Set.instMembership) (:fv _uniq.22893)) ((:c HVAdd.hVAdd) (:fv _uniq.22890) (:fv _uniq.22893) (:fv _uniq.22893) ((:c instHVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c AddAction.toVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c SubNegMonoid.toAddMo... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.22887))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.22890))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.22887) (:fv _uniq.22890) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:app (:c HVAdd.hVAdd) ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":5590,"sourceStart":5588,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5592,"sourceStart":5591,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":16,"semanticR... | [] | [{"source":"hv2p","source_end":5596,"source_start":5592,"syntax_kind":"ident"},{"source":"vadd_vadd","source_end":5607,"source_start":5598,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 32 | 5 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3224967fb00f0e69cda267bd0e1b58d110489bb72444fa6d4668771c28918ec8 | ca6fdccbde76746cfa1d6efafa8187b6d30e59e74f52c8b8f230cad3b475eaa0 | 6f1ad7dd433a8102237a1e11bb3410c9ef952fa8de2eafb3ad504a5fb5c0c1c5 | fabd91ba74fe663520376a16389c250bb47687a7a0a6dd085a3c691fa4088464 |
cat-searcher/leandojo-benchmark-4-random | test | 2,745 | vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan | Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨p2, hp2, v + v2, (<a>vectorSpan</a> k s).<a>Submodule.add_mem</a> hv hv2, <a>rfl</a>⟩ | case intro.intro.intro.intro
k : Type u_1
V : Type u_2
P : Type u_3
inst✝³ : Ring k
inst✝² : AddCommGroup V
inst✝¹ : Module k V
inst✝ : AffineSpace V P
s : Set P
p : P
v : V
hv : v ∈ vectorSpan k s
p2 : P
hp2 : p2 ∈ s
v2 : V
hv2 : v2 ∈ vectorSpan k s
hv2p : p = v2 +ᵥ p2
⊢ v + v2 +ᵥ p2 ∈ spanPoints k s | ((:c Membership.mem) (:fv _uniq.22893) ((:c Set) (:fv _uniq.22893)) ((:c Set.instMembership) (:fv _uniq.22893)) ((:c HVAdd.hVAdd) (:fv _uniq.22890) (:fv _uniq.22893) (:fv _uniq.22893) ((:c instHVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c AddAction.toVAdd) (:fv _uniq.22890) (:fv _uniq.22893) ((:c SubNegMonoid.toAddMo... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Ring) (:fv _uniq.22887))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.22890))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.22887) (:fv _uniq.22890) ((:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:app (:c HVAdd.hVAdd) ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":5616,"sourceStart":5611,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":5620,"sourceStart":5617,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"p2","sourceEnd":5622,"sourceStart":5620,"tag":"identifier"},{"source":",","sourceEnd":5623,"sourc... | [] | [{"source":"⟨p2, hp2, v + v2, (vectorSpan k s).add_mem hv hv2, rfl⟩","source_end":5676,"source_start":5617,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.22887","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.22890","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 32 | 9 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c5cfb1cb7eb3cd0b3ac3716752fb1bd87987b7a3ab68489d1e13b5b42128d2f | fabd91ba74fe663520376a16389c250bb47687a7a0a6dd085a3c691fa4088464 | 890507d3b5b4ab2a508eb6fbf607edeae23bb13c4afde6a195c62ba36d16312d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,746 | HasFDerivWithinAt.mul | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert hc.mul' hd | 𝕜 : Type u_1
inst✝¹² : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
G : Type u_4
inst✝⁷ : NormedAddCommGroup G
inst✝⁶ : NormedSpace 𝕜 G
G' : Type u_5
inst✝⁵ : NormedAddCommGroup G'
inst✝⁴ : Normed... | case h.e'_10.h.e'_6
𝕜 : Type u_1
inst✝¹² : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
G : Type u_4
inst✝⁷ : NormedAddCommGroup G
inst✝⁶ : NormedSpace 𝕜 G
G' : Type u_5
inst✝⁵ : NormedAddCommGrou... | ((:c HasFDerivWithinAt) (:fv _uniq.904745) (:fv _uniq.904748) (:fv _uniq.904751) (:fv _uniq.904754) (:fv _uniq.904862) (:fv _uniq.907450) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.907450) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.907450) ((:c NormedCommRing.toNonUnitalNormedCommRing... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.904745))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.904751))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:fv _uniq.904745) (:fv _uniq.904751) ((:c ... | (:app (:c HasFDerivWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"convert","sourceEnd":18878,"sourceStart":18871,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"hc.mul'","sourceEnd":18886,"sourceStart":18879,"tag":"identifier"},{"children":[{"contextIndex":45,"s... | [] | [{"source":"hc.mul' hd","source_end":18889,"source_start":18879,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"in... | 122 | 4 | exact | true | 1 | 45 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af4241801faa0908ccee46288654475b7c36dd995fa5d2b21698f902b493e621 | a6f5b860c4f021ee398351fe55f1638e0576310d24af9a0311de8c0728903fc5 | 73bf59fc075836b7a30e3fe6ff4c5226795369a519300f54f69ad54cc1224c41 | 6dd709c8b902b0376fcc8bd54992e2511c2f48bbe351a6f897bd6337311d66d4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,747 | HasFDerivWithinAt.mul | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext z | case h.e'_10.h.e'_6
𝕜 : Type u_1
inst✝¹² : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
G : Type u_4
inst✝⁷ : NormedAddCommGroup G
inst✝⁶ : NormedSpace 𝕜 G
G' : Type u_5
inst✝⁵ : NormedAddCommGrou... | case h.e'_10.h.e'_6.h
𝕜 : Type u_1
inst✝¹² : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
G : Type u_4
inst✝⁷ : NormedAddCommGroup G
inst✝⁶ : NormedSpace 𝕜 G
G' : Type u_5
inst✝⁵ : NormedAddCommGr... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.904745) (:fv _uniq.904745) ((:c DivisionSemiring.toSemiring) (:fv _uniq.904745) ((:c Semifield.toDivisionSemiring) (:fv _uniq.904745) ((:c Field.toSemifield) (:fv _uniq.904745) ((:c NormedField.toField) (:fv _uniq.904745) ((:c NontriviallyNormedField.toNormedField) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.904745))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.904751))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:fv _uniq.904745) (:fv _uniq.904751) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"ext","sourceEnd":18895,"sourceStart":18892,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"z","sourceEnd":18897,"sourceStart":18896,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"z","sourceEnd":18897,"sourceStart":18896,"tag... | [{"role":"fresh_name","source":"z","source_end":18897,"source_start":18896,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"in... | 122 | 5 | exact | true | 1 | 45 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11e386d99a5788bb63eeda21454118705718351bad40e62a4546c72bf59fa7db | 6dd709c8b902b0376fcc8bd54992e2511c2f48bbe351a6f897bd6337311d66d4 | bb3115d7175333ff0af45e4ad4763aa377f4c2e697b0eefe906044fd46bf177d | 6e2f65a4039694cc2d22eb9121d54ea6e1c9e51f8cefbc8516d9ff74d305b64d |
cat-searcher/leandojo-benchmark-4-random | test | 2,748 | HasFDerivWithinAt.mul | Mathlib/Analysis/Calculus/FDeriv/Mul.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mul_comm</a> | case h.e'_10.h.e'_6.h
𝕜 : Type u_1
inst✝¹² : NontriviallyNormedField 𝕜
E : Type u_2
inst✝¹¹ : NormedAddCommGroup E
inst✝¹⁰ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
G : Type u_4
inst✝⁷ : NormedAddCommGroup G
inst✝⁶ : NormedSpace 𝕜 G
G' : Type u_5
inst✝⁵ : NormedAddCommGr... | ((:c Eq) (:fv _uniq.907450) ((:c DFunLike.coe) ((:c ContinuousLinearMap) (:fv _uniq.904745) (:fv _uniq.904745) ((:c DivisionSemiring.toSemiring) (:fv _uniq.904745) ((:c Semifield.toDivisionSemiring) (:fv _uniq.904745) ((:c Field.toSemifield) (:fv _uniq.904745) ((:c NormedField.toField) (:fv _uniq.904745) ((:c Nontrivia... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.904745))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.904751))"},{"name":"inst✝¹⁰","sexp":"((:c NormedSpace) (:fv _uniq.904745) (:fv _uniq.904751) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV30)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:ins... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"name":"inst✝¹²","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"apply","sourceEnd":18905,"sourceStart":18900,"tag":"atom"},{"name":"mul_comm","semanticRole":"global","source":"mul_comm","sourceEnd":18914,"sourceStart":18906,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply mul_comm","sourceEnd":18914,"sourceStart":18900,"tag":"node"} | [] | [{"source":"mul_comm","source_end":18914,"source_start":18906,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.904745","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.904748","is_instance":true,"is_let":false,"user_name":"inst✝¹²"},{"binder_role":":implicit","context_index":2,"in... | 122 | 6 | exact | true | 1 | 46 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7dde20c6a55628030d86d33691b55d43eee8c2b92a96cdc1e6d0c4055e26ecf | 6e2f65a4039694cc2d22eb9121d54ea6e1c9e51f8cefbc8516d9ff74d305b64d | 17fed598486d1d88343a6b8baeb040a11dfb90eab79dd8b8ff2d9ea747b50713 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,749 | Polynomial.mirror_leadingCoeff | Mathlib/Algebra/Polynomial/Mirror.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← p.mirror_mirror, <a>Polynomial.mirror_trailingCoeff</a>, p.mirror_mirror] | R : Type u_1
inst✝ : Semiring R
p q : R[X]
⊢ p.mirror.leadingCoeff = p.trailingCoeff | ((:c Eq) (:fv _uniq.19646) ((:c Polynomial.leadingCoeff) (:fv _uniq.19646) (:fv _uniq.19649) ((:c Polynomial.mirror) (:fv _uniq.19646) (:fv _uniq.19649) (:fv _uniq.19663))) ((:c Polynomial.trailingCoeff) (:fv _uniq.19646) (:fv _uniq.19649) (:fv _uniq.19663))) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Semiring) (:fv _uniq.19646))"},{"name":"p","sexp":"((:c Polynomial) (:fv _uniq.19646) (:fv _uniq.19649))"},{"name":"q","sexp":"((:c Polynomial) (:fv _uniq.19646) (:fv _uniq.19649))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.leadingCoeff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Polynomial.mirror) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19646","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19649","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Semiring) (:arg :explici... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":6219,"sourceStart":6217,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6221,"sourceStart":6220,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"p.mirror_mirror","source_end":6240,"source_start":6225,"syntax_kind":"ident"},{"source":"mirror_trailingCoeff","source_end":6262,"source_start":6242,"syntax_kind":"ident"},{"source":"p.mirror_mirror","source_end":6279,"source_start":6264,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19646","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19649","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 38 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 408ca269b4c9665db33990c6ae5c5d811690dd064b73719a2ba867d90c50cf18 | 4a1cfaf7bf091bf6fe172d89e1325783cec7152179e5627fea5120a6b9e42111 | a836fcdbbc99d5240af1e3cc34c0e8c7a8985667defccbc53995934e526d1942 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,750 | AddCommGrp.asHom_injective | Mathlib/Algebra/Category/Grp/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>congr_arg</a> (fun k : <a>AddCommGrp.of</a> ℤ ⟶ G => (k : ℤ → G) (1 : ℤ)) w <;> simp | G : AddCommGrp
h k : ↑G
w : asHom h = asHom k
⊢ h = k | ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c AddCommGroup) (:fv _uniq.30639)) (:fv _uniq.30642) (:fv _uniq.30645)) | [{"name":"G","sexp":"(:c AddCommGrp)"},{"name":"h","sexp":"((:c CategoryTheory.Bundled.α) (:c AddCommGroup) (:fv _uniq.30639))"},{"name":"k","sexp":"((:c CategoryTheory.Bundled.α) (:c AddCommGroup) (:fv _uniq.30639))"},{"name":"w","sexp":"((:c Eq) ((:c Quiver.Hom) (:c AddCommGrp) ((:c CategoryTheory.CategoryStruct.toQu... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30639","is_instance":false,"is_let":false,"name":"G","sexp":"(:c AddCommGrp)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.30642","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c CategoryTheory.Bundled.α) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"convert","sourceEnd":13219,"sourceStart":13212,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"congr_arg","semanticRole":"global","source":"congr_... | [] | [{"source":"congr_arg (fun k : AddCommGrp.of ℤ ⟶ G => (k : ℤ → G) (1 : ℤ)) w","source_end":13294,"source_start":13220,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30639","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.30642","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 115 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f42bd367d44cb3f9d310f97e4da83e8615395f4b5f217e6f7407a864038db46c | 984463d434f2c10f3bb6eab10f015c00bd1ff637b3a922191dabad1e7039c7f8 | c85212fa0fc0cedec7cb03ceb041222705cc825ac9379839d99492bd36939f7b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,751 | bernoulli'_one | Mathlib/NumberTheory/Bernoulli.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>bernoulli'_def</a>] | A : Type u_1
inst✝¹ : CommRing A
inst✝ : Algebra ℚ A
⊢ bernoulli' 1 = 1 / 2 | A : Type u_1
inst✝¹ : CommRing A
inst✝ : Algebra ℚ A
⊢ 1 - ∑ k ∈ range 1, ↑(Nat.choose 1 k) / (↑1 - ↑k + 1) * bernoulli' k = 1 / 2 | ((:c Eq) (:c Rat) ((:c bernoulli') ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) ((:c HDiv.hDiv) (:c Rat) (:c Rat) (:c Rat) ((:c instHDiv) (:c Rat) (:c Rat.instDiv)) ((:c OfNat.ofNat) (:c Rat) (:lit 1) ((:c Rat.instOfNat) (:lit 1))) ((:c OfNat.ofNat) (:c Rat) (:lit 2) ((:c Rat.instOfNat) (:lit 2)))... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.11807))"},{"name":"inst✝","sexp":"((:c Algebra) (:c Rat) (:fv _uniq.11807) (:c Rat.commSemiring) ((:c CommSemiring.toSemiring) (:fv _uniq.11807) ((:c CommRing.toCommSemiring) (:fv _uniq.11807) (:fv _uniq.11810))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c bernoulli') (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 1))))))))) (:arg :explicit 2 (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.11807","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11810","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"rw","sourceEnd":4136,"sourceStart":4134,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4138,"sourceStart":4137,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"bernoulli'_def","sem... | [] | [{"source":"bernoulli'_def","source_end":4152,"source_start":4138,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.11807","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11810","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 19 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fe6f56bb1e0255ef65448e652da2b728d60087039794e9735c7a2ee12d9a8eb | 687260ecee8e9a836a63f0298ef70c10be4f875847093d18cc140b1daf1a5a59 | 4817e665aa924aeefb2c60e87e348f4d2bb167d5dcacd39114e15cef4c8f6258 | e8f4fc9387c174389a3c896560e677360a4127825a841dd72754dccc60751f9e |
cat-searcher/leandojo-benchmark-4-random | test | 2,752 | bernoulli'_one | Mathlib/NumberTheory/Bernoulli.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | A : Type u_1
inst✝¹ : CommRing A
inst✝ : Algebra ℚ A
⊢ 1 - ∑ k ∈ range 1, ↑(Nat.choose 1 k) / (↑1 - ↑k + 1) * bernoulli' k = 1 / 2 | ((:c Eq) (:c Rat) ((:c HSub.hSub) (:c Rat) (:c Rat) (:c Rat) ((:c instHSub) (:c Rat) (:c Rat.instSub)) ((:c OfNat.ofNat) (:c Rat) (:lit 1) ((:c Rat.instOfNat) (:lit 1))) ((:c Finset.sum) (:c Nat) (:c Rat) (:c Rat.addCommMonoid) ((:c Finset.range) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:lamb... | [{"name":"A","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.11807))"},{"name":"inst✝","sexp":"((:c Algebra) (:c Rat) (:fv _uniq.11807) (:c Rat.commSemiring) ((:c CommSemiring.toSemiring) (:fv _uniq.11807) ((:c CommRing.toCommSemiring) (:fv _uniq.11807) (:fv _uniq.11810))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:c Rat)) (:arg :implicit-type 2 (:c Rat)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:c Rat)) (:arg :explicit 1 (:c Rat)) (:arg :explicit 2 (:c Rat))))) ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.11807","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11810","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"source":"norm_num","sourceEnd":4164,"sourceStart":4156,"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"}],"kind":"Mathlib... | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.11807","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11810","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 19 | 7 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 814fb52d5165b69dead8386b051c269e53696af517a23434563c86ff427eec2c | e8f4fc9387c174389a3c896560e677360a4127825a841dd72754dccc60751f9e | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,753 | CategoryTheory.induct_on_objects | Mathlib/CategoryTheory/IsConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let aux (j₁ j₂ : J) (f : j₁ ⟶ j₂) := <a>congrArg</a> <a>ULift.up</a> <| (h1 f).<a>Iff.eq</a> | J : Type u₁
inst✝² : Category.{v₁, u₁} J
K : Type u₂
inst✝¹ : Category.{v₂, u₂} K
inst✝ : IsPreconnected J
p : Set J
j₀ : J
h0 : j₀ ∈ p
h1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)
j : J
⊢ j ∈ p | J : Type u₁
inst✝² : Category.{v₁, u₁} J
K : Type u₂
inst✝¹ : Category.{v₂, u₂} K
inst✝ : IsPreconnected J
p : Set J
j₀ : J
h0 : j₀ ∈ p
h1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)
j : J
aux : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → { down := j₁ ∈ p } = { down := j₂ ∈ p } :=
fun j₁ j₂ f => congrArg ULift.up (Iff.eq (h1 f))
⊢... | ((:c Membership.mem) (:fv _uniq.11717) ((:c Set) (:fv _uniq.11717)) ((:c Set.instMembership) (:fv _uniq.11717)) (:fv _uniq.11863) (:fv _uniq.11859)) | [{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11717))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11722))"},{"name":"inst✝","sexp":"((:c CategoryTheory.IsPreconnected) (:fv _uniq.11717) (:fv _uniq.... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"let","sourceEnd":8379,"sourceStart":8376,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"aux","sourceEnd":8383,"sourceStart":8380,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":8385,"sourceStart":8384,"tag":"atom"},{"children":[{"semantic... | [] | [{"source":"J","source_end":8398,"source_start":8397,"syntax_kind":"ident"},{"source":"j₁ ⟶ j₂","source_end":8418,"source_start":8405,"syntax_kind":"«term_⟶_»"},{"source":"congrArg ULift.up <| (h1 f).eq","source_end":8453,"source_start":8423,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 31 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0cde6f070387ac251b04cbc06888180205f503dbae0f4d3315a89049f6aca5d8 | ffd1117004471778bc8b4825b9f142e5b980b91fd3e2da4ab124fc25f0adb924 | 503b1ced49a6159e2b88aaca44eb38a22302574874a539194d7811f313ea7236 | b1d87826a0d04bbcac96d71a5297485d310125e8794f06d5ff69d2410d60972f |
cat-searcher/leandojo-benchmark-4-random | test | 2,754 | CategoryTheory.induct_on_objects | Mathlib/CategoryTheory/IsConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | injection <a>CategoryTheory.constant_of_preserves_morphisms</a> (fun k => <a>ULift.up</a>.{u₁} (k ∈ p)) aux j j₀ with i | J : Type u₁
inst✝² : Category.{v₁, u₁} J
K : Type u₂
inst✝¹ : Category.{v₂, u₂} K
inst✝ : IsPreconnected J
p : Set J
j₀ : J
h0 : j₀ ∈ p
h1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)
j : J
aux : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → { down := j₁ ∈ p } = { down := j₂ ∈ p } :=
fun j₁ j₂ f => congrArg ULift.up (Iff.eq (h1 f))
⊢... | J : Type u₁
inst✝² : Category.{v₁, u₁} J
K : Type u₂
inst✝¹ : Category.{v₂, u₂} K
inst✝ : IsPreconnected J
p : Set J
j₀ : J
h0 : j₀ ∈ p
h1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)
j : J
aux : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → { down := j₁ ∈ p } = { down := j₂ ∈ p } :=
fun j₁ j₂ f => congrArg ULift.up (Iff.eq (h1 f))
i... | ((:c Membership.mem) (:fv _uniq.11717) ((:c Set) (:fv _uniq.11717)) ((:c Set.instMembership) (:fv _uniq.11717)) (:fv _uniq.11863) (:fv _uniq.11859)) | [{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11717))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11722))"},{"name":"inst✝","sexp":"((:c CategoryTheory.IsPreconnected) (:fv _uniq.11717) (:fv _uniq.... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"injection","sourceEnd":8465,"sourceStart":8456,"tag":"atom"},{"children":[{"name":"CategoryTheory.constant_of_preserves_morphisms","semanticRole":"global","source":"constant_of_preserves_morphisms","sourceEnd":8497,"sourceStart":8466,"tag":"identifier"},{"children":[{"children":[{"source":"(","s... | [] | [{"source":"constant_of_preserves_morphisms (fun k => ULift.up.{u₁} (k ∈ p)) aux j j₀","source_end":8545,"source_start":8466,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 31 | 5 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ed3bdeceae3e5962570908b5b6dc55e54205eac61b15458139f16a0d1f26a0a8 | b1d87826a0d04bbcac96d71a5297485d310125e8794f06d5ff69d2410d60972f | bf61d2d857b6592b65dd369d2734e7eef74ba6a75599051dc04498b78257b17b | a4ba22edac2ccb86a0b5072c6e20331c13241d2732c9fb25658a57de24674af1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,755 | CategoryTheory.induct_on_objects | Mathlib/CategoryTheory/IsConnected.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [i] | J : Type u₁
inst✝² : Category.{v₁, u₁} J
K : Type u₂
inst✝¹ : Category.{v₂, u₂} K
inst✝ : IsPreconnected J
p : Set J
j₀ : J
h0 : j₀ ∈ p
h1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)
j : J
aux : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → { down := j₁ ∈ p } = { down := j₂ ∈ p } :=
fun j₁ j₂ f => congrArg ULift.up (Iff.eq (h1 f))
i... | ((:c Membership.mem) (:fv _uniq.11717) ((:c Set) (:fv _uniq.11717)) ((:c Set.instMembership) (:fv _uniq.11717)) (:fv _uniq.11863) (:fv _uniq.11859)) | [{"name":"J","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11717))"},{"name":"K","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.11722))"},{"name":"inst✝","sexp":"((:c CategoryTheory.IsPreconnected) (:fv _uniq.11717) (:fv _uniq.... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"source":"rwa","sourceEnd":8558,"sourceStart":8555,"tag":"atom"},{"children":[{"source":"[","sourceEnd":8560,"sourceStart":8559,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":12,"semanticRole":"local","source":"i","sourceEnd":8561,"sourceStar... | [] | [{"source":"i","source_end":8561,"source_start":8560,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11717","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11720","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"intern... | 31 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ef9435680abf722af954f9727c0e4b375cdf0051ea6ab928e5ab669c5c0945e | a4ba22edac2ccb86a0b5072c6e20331c13241d2732c9fb25658a57de24674af1 | 416e1aedf9434fadb758bfa4b2d7dc55bff50b44374f6239649d799d4305a867 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,756 | CategoryTheory.MonoidalCategory.leftUnitor_inv_tensor_id | Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | coherence | C : Type u_1
inst✝¹ : Category.{u_2, u_1} C
inst✝ : MonoidalCategory C
X Y : C
⊢ (λ_ X).inv ⊗ 𝟙 Y = (λ_ (X ⊗ Y)).inv ≫ (α_ (𝟙_ C) X Y).inv | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.18015) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.18015) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.18015) (:fv _uniq.18019))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.18015) (:fv _uniq.18019) ((:c CategoryTheory.MonoidalCategory.t... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18015))"},{"name":"inst✝","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.18015) (:fv _uniq.18019))"},{"name":"X","sexp":"(:fv _uniq.18015)"},{"name":"Y","sexp":"(:fv _uniq.18015)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18015","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18019","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CategoryTheory.Category... | {"children":[{"children":[{"children":[{"children":[{"source":"coherence","sourceEnd":2074,"sourceStart":2065,"tag":"atom"}],"kind":"Mathlib.Tactic.Coherence.coherence","source":"coherence","sourceEnd":2074,"sourceStart":2065,"tag":"node"}],"kind":"null","source":"coherence","sourceEnd":2074,"sourceStart":2065,"tag":"n... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18015","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18019","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 13 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fea57da59aff50d83421d9f53f3fbc3beeaa3a20329c567ad3c2c1ebd8e2892c | a0cf7a3f0aa1d96a0722cb0eb06e4ae94335cdd1111095b7b4aacf0c798fede0 | b2f7f26289c74cdfb8835f2144a4eb532f0170ed70184762aee6e8dea9fff001 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,757 | DFinsupp.neLocus_zero_right | Mathlib/Data/DFinsupp/NeLocus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | α : Type u_1
N : α → Type u_2
inst✝² : DecidableEq α
inst✝¹ : (a : α) → DecidableEq (N a)
inst✝ : (a : α) → Zero (N a)
f g : Π₀ (a : α), N a
⊢ f.neLocus 0 = f.support | case a
α : Type u_1
N : α → Type u_2
inst✝² : DecidableEq α
inst✝¹ : (a : α) → DecidableEq (N a)
inst✝ : (a : α) → Zero (N a)
f g : Π₀ (a : α), N a
a✝ : α
⊢ a✝ ∈ f.neLocus 0 ↔ a✝ ∈ f.support | ((:c Eq) ((:c Finset) (:fv _uniq.6486)) ((:c DFinsupp.neLocus) (:fv _uniq.6486) (:fv _uniq.6491) (:fv _uniq.6498) (:fv _uniq.6513) (:fv _uniq.6524) (:fv _uniq.6561) ((:c OfNat.ofNat) ((:c DFinsupp) (:fv _uniq.6486) (:lambda a (:fv _uniq.6486) ((:fv _uniq.6491) 0)) (:fv _uniq.6524)) (:lit 0) ((:c Zero.toOfNat0) ((:c DFi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:forall _ (:fv _uniq.6486) (:sort (+ u_2 1)))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.6486))"},{"name":"inst✝¹","sexp":"(:forall a (:fv _uniq.6486) ((:c DecidableEq) ((:fv _uniq.6491) 0)))"},{"name":"inst✝","sexp":"(:forall a (:fv _uniq.6486)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c DFinsupp.neLocus) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:forall a :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6486","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6491","is_instance":false,"is_let":false,"name":"N","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"},{... | {"children":[{"source":"ext","sourceEnd":2746,"sourceStart":2743,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":2746,"sourceStart":2743,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6486","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6491","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 21 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40fde3f312e448f21001ba8b43ebfd960b666b49100908d5e0ba0c177f4294bb | 058a6bb78eaad93480434ff6da393e4770f4b4ca778483cfd09d307d6390cd38 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 6c6884034cee9701d5820b4cf548f1e8f871a6763aff3ff6cde3934645f9d93d |
cat-searcher/leandojo-benchmark-4-random | test | 2,758 | DFinsupp.neLocus_zero_right | Mathlib/Data/DFinsupp/NeLocus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>DFinsupp.mem_neLocus</a>, <a>DFinsupp.mem_support_iff</a>, <a>DFinsupp.coe_zero</a>, <a>Pi.zero_apply</a>] | case a
α : Type u_1
N : α → Type u_2
inst✝² : DecidableEq α
inst✝¹ : (a : α) → DecidableEq (N a)
inst✝ : (a : α) → Zero (N a)
f g : Π₀ (a : α), N a
a✝ : α
⊢ a✝ ∈ f.neLocus 0 ↔ a✝ ∈ f.support | ((:c Iff) ((:c Membership.mem) (:fv _uniq.6486) ((:c Finset) (:fv _uniq.6486)) ((:c Finset.instMembership) (:fv _uniq.6486)) (:fv _uniq.6885) ((:c DFinsupp.neLocus) (:fv _uniq.6486) (:fv _uniq.6491) (:fv _uniq.6498) (:fv _uniq.6513) (:fv _uniq.6524) (:fv _uniq.6561) ((:c OfNat.ofNat) ((:c DFinsupp) (:fv _uniq.6486) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:forall _ (:fv _uniq.6486) (:sort (+ u_2 1)))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.6486))"},{"name":"inst✝¹","sexp":"(:forall a (:fv _uniq.6486) ((:c DecidableEq) ((:fv _uniq.6491) 0)))"},{"name":"inst✝","sexp":"(:forall a (:fv _uniq.6486)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6486","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6491","is_instance":false,"is_let":false,"name":"N","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))"},{... | {"children":[{"source":"rw","sourceEnd":2751,"sourceStart":2749,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2753,"sourceStart":2752,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"DFinsupp.mem_neLocus... | [] | [{"source":"mem_neLocus","source_end":2764,"source_start":2753,"syntax_kind":"ident"},{"source":"mem_support_iff","source_end":2781,"source_start":2766,"syntax_kind":"ident"},{"source":"coe_zero","source_end":2791,"source_start":2783,"syntax_kind":"ident"},{"source":"Pi.zero_apply","source_end":2806,"source_start":2793... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.6486","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.6491","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 21 | 5 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc0545931db147979d6154b6409e205b0836f365a14f9e221b47990cdae6503a | 6c6884034cee9701d5820b4cf548f1e8f871a6763aff3ff6cde3934645f9d93d | 5ceb0e8605d64ffeb24040873d2ed3487dd9dc6b2bed1ff30b30036fd1675159 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,759 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro r hr | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
⊢ I ≤ (homogeneousHull 𝒜 I).toIdeal | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ r ∈ (homogeneousHull 𝒜 I).toIdeal | ((:c LE.le) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c Preorder.toLE) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c PartialOrder.toPreorder) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c Co... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":21384,"sourceStart":21379,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"r","sourceEnd":21386,"sourceStart":21385,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hr","sourceEnd":21389,"sourceStart":21387,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"r","source_end":21386,"source_start":21385,"syntax_kind":"ident"},{"role":"fresh_name","source":"hr","source_end":21389,"source_start":21387,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c35e8cf0ac36faf3f59bdcf07f63742b3c85edfa79be9af972157ae65ce0dbc | 88acdb6f54720f55a538e1a1bfff7c61ad7ff52b843c89fe558bfa69a17a2bd6 | 66179dd87ef1e39e2330f992a6046ffe024ca9ccc69a369037160ab619ae3660 | 8ab2f4bc2f7f814e5c5c6cde675d055caf8e7e9ed827e5b0e001646fc51ad2bf |
cat-searcher/leandojo-benchmark-4-random | test | 2,760 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical rw [← <a>DirectSum.sum_support_decompose</a> 𝒜 r] refine <a>Ideal.sum_mem</a> _ ?_ intro j _ apply <a>Ideal.subset_span</a> use j use ⟨r, hr⟩ | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ r ∈ (homogeneousHull 𝒜 I).toIdeal | ((:c Membership.mem) (:fv _uniq.136965) ((:c Submodule) (:fv _uniq.136965) (:fv _uniq.136965) (:fv _uniq.136968) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.136965) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.136965) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.136965) (:fv _uniq.136968... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"classical","sourceEnd":21401,"sourceStart":21392,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":21406,"sourceStart":21404,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21408,"sourceStart":... | [] | [{"source":"DirectSum.sum_support_decompose 𝒜 r","source_end":21450,"source_start":21412,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Ideal.sum_mem _ ?_","source_end":21479,"source_start":21461,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Ideal.subset_span","source_end":21517,"source_start":21500,"syntax_kind"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 5 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8180439c51af14b4ff3f594829a6133e02b54ec5f5f65f6063d234e9ed80ffd2 | 8ab2f4bc2f7f814e5c5c6cde675d055caf8e7e9ed827e5b0e001646fc51ad2bf | d7b8529f7417b1db6069953c16b2a149380d13c5e54965bdf9e599f71f310c41 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,761 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>DirectSum.sum_support_decompose</a> 𝒜 r] | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ r ∈ (homogeneousHull 𝒜 I).toIdeal | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ ∑ i ∈ DFinsupp.support ((decompose 𝒜) r), ↑(((decompose 𝒜) r) i) ∈ (homogeneousHull 𝒜... | ((:c Membership.mem) (:fv _uniq.136965) ((:c Submodule) (:fv _uniq.136965) (:fv _uniq.136965) (:fv _uniq.136968) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.136965) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.136965) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.136965) (:fv _uniq.136968... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":21406,"sourceStart":21404,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21408,"sourceStart":21407,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":21411,"sourceSt... | [] | [{"source":"DirectSum.sum_support_decompose 𝒜 r","source_end":21450,"source_start":21412,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 8 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b7d77dabeb6dc06e0c1a11954bb37442ee5a5077945e6d81ef409349591b379 | 8ab2f4bc2f7f814e5c5c6cde675d055caf8e7e9ed827e5b0e001646fc51ad2bf | db3e0993772bfa2b42f5c3fa6a33366fca7c73cf461902688cddfdd1958a91af | 0417b973dd8133787db0b3ada8d38722789f429b608f033b8fab27f43b63f42a |
cat-searcher/leandojo-benchmark-4-random | test | 2,762 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Ideal.sum_mem</a> _ ?_ | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ ∑ i ∈ DFinsupp.support ((decompose 𝒜) r), ↑(((decompose 𝒜) r) i) ∈ (homogeneousHull 𝒜... | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ ∀ c ∈ DFinsupp.support ((decompose 𝒜) r), ↑(((decompose 𝒜) r) c) ∈ (homogeneousHull 𝒜... | ((:c Membership.mem) (:fv _uniq.136965) ((:c Submodule) (:fv _uniq.136965) (:fv _uniq.136965) (:fv _uniq.136968) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.136965) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.136965) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.136965) (:fv _uniq.136968... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":21460,"sourceStart":21454,"tag":"atom"},{"children":[{"name":"Ideal.sum_mem","semanticRole":"global","source":"Ideal.sum_mem","sourceEnd":21474,"sourceStart":21461,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":21476,"sourceStart":21475,"tag":"atom"}]... | [] | [{"source":"Ideal.sum_mem _ ?_","source_end":21479,"source_start":21461,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 11 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1205e36c25b3719d16e344a3b081d814ed04a60f7dfd758fd9e89cbc3a7c7275 | 0417b973dd8133787db0b3ada8d38722789f429b608f033b8fab27f43b63f42a | 42771ad6ffbec27addad6a3c052a39a9aa9525d8579fa614e146ca93e6ffb013 | f7cbc96202c32319be9b06b5ba899893b1d65dd84fd4b661a66b78f19541853f |
cat-searcher/leandojo-benchmark-4-random | test | 2,763 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro j _ | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
⊢ ∀ c ∈ DFinsupp.support ((decompose 𝒜) r), ↑(((decompose 𝒜) r) c) ∈ (homogeneousHull 𝒜... | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ↑(((decompose 𝒜) r) j) ∈ (homogeneou... | (:forall c (:fv _uniq.136956) (:forall _ ((:c Membership.mem) (:fv _uniq.136956) ((:c Finset) (:fv _uniq.136956)) ((:c Finset.instMembership) (:fv _uniq.136956)) 0 ((:c DFinsupp.support) (:fv _uniq.136956) (:lambda i (:fv _uniq.136956) ((:c Subtype) (:fv _uniq.136965) (:lambda x (:fv _uniq.136965) ((:c Membership.mem) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:forall c :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"intro","sourceEnd":21487,"sourceStart":21482,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":21489,"sourceStart":21488,"tag":"identifier"},{"children":[{"source":"_","sourceEnd":21491,"sourceStart":21490,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_... | [{"role":"fresh_name","source":"j","source_end":21489,"source_start":21488,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 12 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8076857bc49a64d69772c66d509897ba794390874e05bd6840cfa96f1fe22640 | f7cbc96202c32319be9b06b5ba899893b1d65dd84fd4b661a66b78f19541853f | 373f309915399c6cab2361c338e558adc12876c91d833551bd8f8acb8b0ccc6a | adb5e88e9fe6d42ab5316d6729db0dd49112a5420ed2aa915df4d6060a3b69da |
cat-searcher/leandojo-benchmark-4-random | test | 2,764 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Ideal.subset_span</a> | ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ↑(((decompose 𝒜) r) j) ∈ (homogeneou... | case a
ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ↑(((decompose 𝒜) r) j) ∈ {r |... | ((:c Membership.mem) (:fv _uniq.136965) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) (:fv _uniq.136965) ((:c Submodule.setLike) (:fv _uniq.136965) (:fv _uniq.136965) (:fv _uniq.136968) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"apply","sourceEnd":21499,"sourceStart":21494,"tag":"atom"},{"name":"Ideal.subset_span","semanticRole":"global","source":"Ideal.subset_span","sourceEnd":21517,"sourceStart":21500,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Ideal.subset_span","sourceEnd":21517,"sourceSta... | [] | [{"source":"Ideal.subset_span","source_end":21517,"source_start":21500,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 13 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a9f09c37606c0de821788ad53471275e2e6bf1f50d2dac57a7cb49b888ca1b5 | adb5e88e9fe6d42ab5316d6729db0dd49112a5420ed2aa915df4d6060a3b69da | 84f99f1545be4dc41533e19cb606294d391e776ae8cc5afc3aa5ca00c4f24887 | 9980ad02fbc71355544dda97876514b173223aeb61eb1c1851e38e38865c33db |
cat-searcher/leandojo-benchmark-4-random | test | 2,765 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use j | case a
ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ↑(((decompose 𝒜) r) j) ∈ {r |... | case h
ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ∃ x, ↑(((decompose 𝒜) ↑x) j) ... | ((:c Membership.mem) (:fv _uniq.136965) ((:c Set) (:fv _uniq.136965)) ((:c Set.instMembership) (:fv _uniq.136965)) ((:c Subtype.val) (:fv _uniq.136965) (:lambda x (:fv _uniq.136965) ((:c Membership.mem) (:fv _uniq.136965) ((:c Set) (:fv _uniq.136965)) ((:c Set.instMembership) (:fv _uniq.136965)) 0 ((:c SetLike.coe) (:f... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 3 (:app (:c Subtype.val) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"use","sourceEnd":21523,"sourceStart":21520,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"j","sourceEnd":21525,"sourceStart":21524,"tag":"identifier"}],"... | [] | [{"source":"j","source_end":21525,"source_start":21524,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 14 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bcbc597abfe3d28b06492c4c44570c445bc6507a13209104edd729b083be3b05 | 9980ad02fbc71355544dda97876514b173223aeb61eb1c1851e38e38865c33db | fc3b530afdedaa6b904f307db2a56b946dd3f48c3ee7e952c204bd1b276abec9 | 9512e27eac35403c5f47f6c069a07556685d51e5633886d4fd1e6492c80f7d7a |
cat-searcher/leandojo-benchmark-4-random | test | 2,766 | Ideal.le_toIdeal_homogeneousHull | Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use ⟨r, hr⟩ | case h
ι : Type u_1
σ : Type u_2
R : Type u_3
A : Type u_4
inst✝⁵ : Semiring A
inst✝⁴ : DecidableEq ι
inst✝³ : AddMonoid ι
inst✝² : SetLike σ A
inst✝¹ : AddSubmonoidClass σ A
𝒜 : ι → σ
inst✝ : GradedRing 𝒜
I : Ideal A
r : A
hr : r ∈ I
j : ι
a✝ : j ∈ DFinsupp.support ((decompose 𝒜) r)
⊢ ∃ x, ↑(((decompose 𝒜) ↑x) j) ... | ((:c Exists) ((:c Subtype) (:fv _uniq.136965) (:lambda x (:fv _uniq.136965) ((:c Membership.mem) (:fv _uniq.136965) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) ((:c SetLike.instMembership) ((:c Ideal) (:fv _uniq.136965) (:fv _uniq.136968)) (:fv _uniq.136965) ((:c Submodule.setLike) (:fv _uniq.136965) (:fv _uniq.... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"σ","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"A","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁵","sexp":"((:c Semiring) (:fv _uniq.136965))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.136956))"},{"name":"inst✝³","sexp":"((:c Ad... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda x :explicit (:fv FV3) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Ideal) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"name":"σ","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"use","sourceEnd":21531,"sourceStart":21528,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"source":"⟨","sourceEnd":21535,"sourceStart":21532,"tag":"atom"},{"children":[{"contextIndex":13,"sem... | [] | [{"source":"⟨r, hr⟩","source_end":21543,"source_start":21532,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.136956","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.136959","is_instance":false,"is_let":false,"user_name":"σ"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 184 | 15 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 15e46082e10a187f3b0c27092c386cf009a01b88c70bc452c824ab174013e79e | 9512e27eac35403c5f47f6c069a07556685d51e5633886d4fd1e6492c80f7d7a | ff5c8704be20158cdff00c57d7bc9b7ab9e0e30f19c7be48513cf8c8ad49549f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,767 | Fintype.prod_boole | Mathlib/Algebra/BigOperators/GroupWithZero/Finset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Finset.prod_boole</a>] | ι : Type u_1
κ : Type u_2
G₀ : Type u_3
M₀ : Type u_4
inst✝² : Fintype ι
inst✝¹ : CommMonoidWithZero M₀
p : ι → Prop
inst✝ : DecidablePred p
⊢ (∏ i : ι, if p i then 1 else 0) = if ∀ (i : ι), p i then 1 else 0 | ((:c Eq) (:fv _uniq.12523) ((:c Finset.prod) (:fv _uniq.12514) (:fv _uniq.12523) ((:c CommMonoidWithZero.toCommMonoid) (:fv _uniq.12523) (:fv _uniq.12529)) ((:c Finset.univ) (:fv _uniq.12514) (:fv _uniq.12526)) (:lambda i (:fv _uniq.12514) ((:c ite) (:fv _uniq.12523) ((:fv _uniq.12533) 0) ((:fv _uniq.12542) 0) ((:c OfN... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"κ","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.12514))"},{"name":"inst✝¹","sexp":"((:c CommMonoidWithZero) (:fv _uniq.12523))"},{"name":"p","sexp":"(:fora... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 3 (:app (:c Finset.univ) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12514","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12517","is_instance":false,"is_let":false,"name":"κ","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2418,"sourceStart":2414,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"Finset.prod_boole","source_end":2437,"source_start":2420,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.12514","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12517","is_instance":false,"is_let":false,"user_name":"κ"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 22 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e1a34d5a44de145aa18b9a448c28c8db796a00e48b66f296e7939c7d4025ee98 | 6778b2279b7ef7989999ccbfd1275189f7c9728c79b32a50e66ff993c2c10f20 | c9adf37a931f80ae47abeaf7d756055ebf834b1083cd49b54734f629ff259e83 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,768 | LinearMap.range_rangeRestrict | Mathlib/Algebra/Module/Submodule/Range.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [f.range_codRestrict _] | R : Type u_1
R₂ : Type u_2
R₃ : Type u_3
K : Type u_4
K₂ : Type u_5
M : Type u_6
M₂ : Type u_7
M₃ : Type u_8
V : Type u_9
V₂ : Type u_10
inst✝¹⁰ : Semiring R
inst✝⁹ : Semiring R₂
inst✝⁸ : Semiring R₃
inst✝⁷ : AddCommMonoid M
inst✝⁶ : AddCommMonoid M₂
inst✝⁵ : AddCommMonoid M₃
inst✝⁴ : Module R M
inst✝³ : Module R₂ M₂
i... | ((:c Eq) ((:c Submodule) (:fv _uniq.171635) ((:c Subtype) (:fv _uniq.171650) (:lambda x (:fv _uniq.171650) ((:c Membership.mem) (:fv _uniq.171650) ((:c Submodule) (:fv _uniq.171635) (:fv _uniq.171650) (:fv _uniq.171665) (:fv _uniq.171674) (:fv _uniq.171725)) ((:c SetLike.instMembership) ((:c Submodule) (:fv _uniq.17163... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"K","sexp":"(:sort (+ u_4 1))"},{"name":"K₂","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:lambda x :explicit (:fv FV6) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171632","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.171635","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":18764,"sourceStart":18760,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"f.range_codRestrict _","source_end":18787,"source_start":18766,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171632","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.171635","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 159 | 2 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9672e79ee47dbfac24ed2af6f6de84482d9b100e3c6a032ccbfdb416ef6e985 | 6848314634f1840feed80c4ff953c173f2c6599aa1d211062ff88924ff149915 | 57c5bcd5c23b09d13636f38578d58ff6ea39913e31b4901734af9fec9edd078d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,769 | Orientation.oangle_zero_right | Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Orientation.oangle</a>] | V : Type u_1
V' : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : NormedAddCommGroup V'
inst✝³ : InnerProductSpace ℝ V
inst✝² : InnerProductSpace ℝ V'
inst✝¹ : Fact (finrank ℝ V = 2)
inst✝ : Fact (finrank ℝ V' = 2)
o : Orientation ℝ V (Fin 2)
x : V
⊢ o.oangle x 0 = 0 | ((:c Eq) (:c Real.Angle) ((:c Orientation.oangle) (:fv _uniq.18225) (:fv _uniq.18231) (:fv _uniq.18247) (:fv _uniq.18542) (:fv _uniq.19455) (:fv _uniq.20701) ((:c OfNat.ofNat) (:fv _uniq.18225) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.18225) ((:c NegZeroClass.toZero) (:fv _uniq.18225) ((:c SubNegZeroMonoid.toNegZeroClas... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"V'","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.18225))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.18228))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.18225) (:c Real.RCLike) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c Orientation.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductSpace) (:arg :explicit 0 (:c Real)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18225","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18228","is_instance":false,"is_let":false,"name":"V'","sexp":"(:sort Type)"},{"binder_role":":instance-impl... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2695,"sourceStart":2691,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"oangle","source_end":2703,"source_start":2697,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18225","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18228","is_instance":false,"is_let":false,"user_name":"V'"},{"binder_role":":instance-implicit","context_index":2,"internal_... | 18 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de8fe3ea1c44671c1f691748cb4762d33f5483c577743969923d8bd896540805 | bad5efd09e74ca1f15eeaa3c4c15dc9cc71bf05bffb34e5f00f479459e5b9555 | cc5982895895acafa8f38a0357a9cc12f03ac728056fa2340fe5e95684a03f2e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,770 | List.get_eq_iff | .lake/packages/batteries/Batteries/Data/List/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α✝ : Type u_1
l : List α✝
n : Fin l.length
x : α✝
⊢ l.get n = x ↔ l.get? ↑n = some x | ((:c Iff) ((:c Eq) (:fv _uniq.33015) ((:c List.get) (:fv _uniq.33015) (:fv _uniq.33016) (:fv _uniq.33017)) (:fv _uniq.33018)) ((:c Eq) ((:c Option) (:fv _uniq.33015)) ((:c List.get?) (:fv _uniq.33015) (:fv _uniq.33016) ((:c Fin.val) ((:c List.length) (:fv _uniq.33015) (:fv _uniq.33016)) (:fv _uniq.33017))) ((:c Option.... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.33015))"},{"name":"n","sexp":"((:c Fin) ((:c List.length) (:fv _uniq.33015) (:fv _uniq.33016)))"},{"name":"x","sexp":"(:fv _uniq.33015)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c List.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 2 (:fv FV4)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Option) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33015","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33016","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c List) (:arg :explicit 0 (:fv FV1)))... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9948,"sourceStart":9944,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.33015","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.33016","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 67 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f59af891e233a8c8d714f9f7dc51151af5b3c3e5657874dc6a647733135740f4 | 4911f435a8de85c014c95c82d81dbab295de1a16e9eee31c6b5b0eecc3e542fb | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,771 | Matrix.mulVec_one | Mathlib/Data/Matrix/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | l : Type u_1
m : Type u_2
n : Type u_3
o : Type u_4
m' : o → Type u_5
n' : o → Type u_6
R : Type u_7
S : Type u_8
α : Type v
β : Type w
γ : Type u_9
inst✝¹ : NonAssocSemiring α
inst✝ : Fintype n
A : Matrix m n α
⊢ A *ᵥ 1 = fun i => ∑ j : n, A i j | case h
l : Type u_1
m : Type u_2
n : Type u_3
o : Type u_4
m' : o → Type u_5
n' : o → Type u_6
R : Type u_7
S : Type u_8
α : Type v
β : Type w
γ : Type u_9
inst✝¹ : NonAssocSemiring α
inst✝ : Fintype n
A : Matrix m n α
x✝ : m
⊢ (A *ᵥ 1) x✝ = ∑ j : n, A x✝ j | ((:c Eq) (:forall _ (:fv _uniq.512385) (:fv _uniq.512409)) ((:c Matrix.mulVec) (:fv _uniq.512385) (:fv _uniq.512388) (:fv _uniq.512409) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.512409) (:fv _uniq.512417)) (:fv _uniq.513147) (:fv _uniq.513148) ((:c OfNat.ofNat) (:forall _ (:fv _uniq.512388) (:fv _un... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"o","sexp":"(:sort (+ u_4 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.512391) (:sort (+ u_5 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.512391) (:sort (+ u_6 1)))"},{"name":"R","se... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV1) (:fv FV8))) (:arg :explicit 1 (:app (:c Matrix.mulVec) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV8)) (:arg :instance 3 (:instance-of (:app (:c NonUnitalNonAssocSemiring) (:arg :explicit 0 (:fv FV8... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.512382","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.512385","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":66460,"sourceStart":66457,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":66460,"sourceStart":66457,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.512382","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.512385","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 636 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | beda3e4506ab713d6355abeffba856110a6491825cced6bae0d2b7f725667222 | b9a2eb5952df286308437e3483215ec62693f93cda4b0ea1c2185170c6e36b37 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | e222d3242958f86cafee38b31691ef6d3108e58d8b41c790c6605c61de4e799a |
cat-searcher/leandojo-benchmark-4-random | test | 2,772 | Matrix.mulVec_one | Mathlib/Data/Matrix/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Matrix.mulVec</a>, <a>Matrix.dotProduct</a>] | case h
l : Type u_1
m : Type u_2
n : Type u_3
o : Type u_4
m' : o → Type u_5
n' : o → Type u_6
R : Type u_7
S : Type u_8
α : Type v
β : Type w
γ : Type u_9
inst✝¹ : NonAssocSemiring α
inst✝ : Fintype n
A : Matrix m n α
x✝ : m
⊢ (A *ᵥ 1) x✝ = ∑ j : n, A x✝ j | ((:c Eq) (:fv _uniq.512409) ((:c Matrix.mulVec) (:fv _uniq.512385) (:fv _uniq.512388) (:fv _uniq.512409) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.512409) (:fv _uniq.512417)) (:fv _uniq.513147) (:fv _uniq.513148) ((:c OfNat.ofNat) (:forall _ (:fv _uniq.512388) (:fv _uniq.512409)) (:lit 1) ((:c One.t... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"o","sexp":"(:sort (+ u_4 1))"},{"name":"m'","sexp":"(:forall _ (:fv _uniq.512391) (:sort (+ u_5 1)))"},{"name":"n'","sexp":"(:forall _ (:fv _uniq.512391) (:sort (+ u_6 1)))"},{"name":"R","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:app (:c Matrix.mulVec) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV8)) (:arg :instance 3 (:instance-of (:app (:c NonUnitalNonAssocSemiring) (:arg :explicit 0 (:fv FV8))))) (:arg :instance 4 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.512382","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.512385","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":66466,"sourceStart":66462,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":66468,"sourceStart":66467,"tag":"a... | [] | [{"source":"mulVec","source_end":66474,"source_start":66468,"syntax_kind":"ident"},{"source":"dotProduct","source_end":66486,"source_start":66476,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.512382","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.512385","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 636 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 634a07f3e0046f35f66a1f72550d65f2e176c20d00a21395c9bac113029d3d03 | e222d3242958f86cafee38b31691ef6d3108e58d8b41c790c6605c61de4e799a | 5692b3411f0ba54d70847319cf46deabfe46fd903de33b5abb1a4af6ad19fa9c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,773 | Set.le_edist_of_le_infsep | Mathlib/Topology/MetricSpace/Infsep.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hs : s.Nontrivial | α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
⊢ d ≤ dist x y | case pos
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
hs : s.Nontrivial
⊢ d ≤ dist x y
case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy... | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.48395) ((:c Dist.dist) (:fv _uniq.48225) ((:c PseudoMetricSpace.toDist) (:fv _uniq.48225) (:fv _uniq.48231)) (:fv _uniq.48396) (:fv _uniq.48398))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48225))"},{"name":"x✝","sexp":"(:fv _uniq.48225)"},{"name":"y✝","sexp":"(:fv _uniq.48225)"},{"name":"z","sexp":"(:fv _uniq.48225)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.48225))... | (: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 (:fv FV9)) (:arg :explicit 3 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"by_cases","sourceEnd":16556,"sourceStart":16548,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hs","sourceEnd":16559,"sourceStart":16557,"tag":"identifier"},{"source":":","sourceEnd":16561,"sourceStart":16560,"tag":"atom"}],"kind":"null","source":"hs :","sourceEnd":16561,"so... | [] | [{"source":"s.Nontrivial","source_end":16574,"source_start":16562,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 149 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e46ceb8eca168a0cf53f659789723e77fd4f44a25bdfd6f41da82712e7e1311 | 7be5b9bc4745b0829b9201246e2a2ae016c5da51122f7f198d8dc6c6036439cc | 6b05c4eadd6c9a4d0477cfef9ea5d12f2cf37169c3c8e72c13b8dc9a4d7a576b | 36f773afc8452124e47a09bc587ac349568c919af934b5b2d49411d06eabd956 |
cat-searcher/leandojo-benchmark-4-random | test | 2,774 | Set.le_edist_of_le_infsep | Mathlib/Topology/MetricSpace/Infsep.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hs.le_infsep_iff.1 hd x hx y hy hxy | case pos
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
hs : s.Nontrivial
⊢ d ≤ dist x y | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.48395) ((:c Dist.dist) (:fv _uniq.48225) ((:c PseudoMetricSpace.toDist) (:fv _uniq.48225) (:fv _uniq.48231)) (:fv _uniq.48396) (:fv _uniq.48398))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48225))"},{"name":"x✝","sexp":"(:fv _uniq.48225)"},{"name":"y✝","sexp":"(:fv _uniq.48225)"},{"name":"z","sexp":"(:fv _uniq.48225)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.48225))... | (: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 (:fv FV9)) (:arg :explicit 3 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":16585,"sourceStart":16580,"tag":"atom"},{"children":[{"children":[{"source":"hs.le_infsep_iff","sourceEnd":16602,"sourceStart":16586,"tag":"identifier"},{"source":".","sourceEnd":16603,"sourceStart":16602,"tag":"atom"},{"children":[{"sour... | [] | [{"source":"hs.le_infsep_iff.1 hd x hx y hy hxy","source_end":16621,"source_start":16586,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 149 | 7 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a74bd5496e3509a044869caf9ed39913b7c5d9fb38c9870939fbb02c60bed26 | b1f9c652981fda1fd2ab784975695f0d365fc80feaafcfc2dc4d947a634d5040 | a22bff45e39884e7f1ea868bdc888ece7a26e3ca37c5f9aecec81853fa0c6231 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,775 | Set.le_edist_of_le_infsep | Mathlib/Topology/MetricSpace/Infsep.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.not_nontrivial_iff</a>] at hs | case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
hs : ¬s.Nontrivial
⊢ d ≤ dist x y | case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
hs : s.Subsingleton
⊢ d ≤ dist x y | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.48395) ((:c Dist.dist) (:fv _uniq.48225) ((:c PseudoMetricSpace.toDist) (:fv _uniq.48225) (:fv _uniq.48231)) (:fv _uniq.48396) (:fv _uniq.48398))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48225))"},{"name":"x✝","sexp":"(:fv _uniq.48225)"},{"name":"y✝","sexp":"(:fv _uniq.48225)"},{"name":"z","sexp":"(:fv _uniq.48225)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.48225))... | (: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 (:fv FV9)) (:arg :explicit 3 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":16629,"sourceStart":16627,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16631,"sourceStart":16630,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.not_nontrivi... | [] | [{"source":"not_nontrivial_iff","source_end":16649,"source_start":16631,"syntax_kind":"ident"},{"source":"hs","source_end":16656,"source_start":16654,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 149 | 14 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e3866d900f0afb710a7840423fb443e8ffb8ef91045a15408d81a9cb2b9b051 | 26d5f51407f693c0cf6c417f3e03c198f0c25fbde5583c8daa26312606b7c6e8 | 933a0a5856ec590be4177c179b5af0ce4bc5eaecfe0fc6157b57da868d99db04 | d63565ca7232b4d1ef6b6abdfd9b703086eee3dc6ea38068d551de7266d5f349 |
cat-searcher/leandojo-benchmark-4-random | test | 2,776 | Set.le_edist_of_le_infsep | Mathlib/Topology/MetricSpace/Infsep.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hs.infsep_zero] at hd | case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ s.infsep
hs : s.Subsingleton
⊢ d ≤ dist x y | case neg
α : Type u_1
β : Type u_2
inst✝ : PseudoMetricSpace α
x✝ y✝ z : α
s t : Set α
d : ℝ
x : α
hx : x ∈ s
y : α
hy : y ∈ s
hxy : x ≠ y
hd : d ≤ 0
hs : s.Subsingleton
⊢ d ≤ dist x y | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.48395) ((:c Dist.dist) (:fv _uniq.48225) ((:c PseudoMetricSpace.toDist) (:fv _uniq.48225) (:fv _uniq.48231)) (:fv _uniq.48396) (:fv _uniq.48398))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.48225))"},{"name":"x✝","sexp":"(:fv _uniq.48225)"},{"name":"y✝","sexp":"(:fv _uniq.48225)"},{"name":"z","sexp":"(:fv _uniq.48225)"},{"name":"s","sexp":"((:c Set) (:fv _uniq.48225))... | (: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 (:fv FV9)) (:arg :explicit 3 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":16663,"sourceStart":16661,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16665,"sourceStart":16664,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.Subsingleton... | [] | [{"source":"hs.infsep_zero","source_end":16679,"source_start":16665,"syntax_kind":"ident"},{"source":"hd","source_end":16686,"source_start":16684,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48225","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48228","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 149 | 17 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a00e66c34a2ff4de0d41648e07c7bed0d25c22d4f196c38cc19467e47e3d6ee6 | d63565ca7232b4d1ef6b6abdfd9b703086eee3dc6ea38068d551de7266d5f349 | c7b0b30ee436881d6d1b3b565587906eec12cbdeb87aa47d835826f3eba4b346 | 55793150d984d7c1a9385b0a1b73013bcbbbcf48b39fd5f10df18ad18582909b |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.