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 | 4,004 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rfl","sourceEnd":3361,"sourceStart":3358,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3361,"sourceStart":3358,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 22 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93746e9889d88faf37679dc8e31ffa05f9c9f3d96cbdd7e16697ec969b1e9932 | e33ea32b5599e2387ef474c8d9651cd1dac7ceb5ff2224ea70492a8cd1d309b0 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,005 | Int.existsUnique_mem_box | Mathlib/Order/Interval/Finset/Box.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use <a>Max.max</a> x.1.<a>Int.natAbs</a> x.2.<a>Int.natAbs</a> | n : ℕ
x✝ x : ℤ × ℤ
⊢ ∃! n, x ∈ box n | case h
n : ℕ
x✝ x : ℤ × ℤ
⊢ (fun n => x ∈ box n) (max x.1.natAbs x.2.natAbs) ∧ ∀ (y : ℕ), (fun n => x ∈ box n) y → y = max x.1.natAbs x.2.natAbs | ((:c ExistsUnique) (:c Nat) (:lambda n (:c Nat) ((:c Membership.mem) ((:c Prod) (:c Int) (:c Int)) ((:c Finset) ((:c Prod) (:c Int) (:c Int))) ((:c Finset.instMembership) ((:c Prod) (:c Int) (:c Int))) (:fv _uniq.70558) ((:c Finset.box) ((:c Prod) (:c Int) (:c Int)) ((:c instOrderedRingProd) (:c Int) (:c Int) (:c Int.i... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x✝","sexp":"((:c Prod) (:c Int) (:c Int))"},{"name":"x","sexp":"((:c Prod) (:c Int) (:c Int))"}] | (:app (:c ExistsUnique) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69862","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69866","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:app (:c Prod) (:arg :explicit 0 (:c Int)) (:arg... | {"children":[{"source":"use","sourceEnd":3693,"sourceStart":3690,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"name":"Max.max","semanticRole":"global","source":"max","sourceEnd":3697,"sourceStart":3694,"tag":"iden... | [] | [{"source":"max x.1.natAbs x.2.natAbs","source_end":3719,"source_start":3694,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69862","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69866","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 26 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a02f843db56eedfa1e6c717721d8c884477316f9dbef5e108af523835c36dbf3 | fa99ecd63c8bc5cbf0a2e4fdeccb476ea2f0fe58f62d6d948845f32547c1818a | f3006e78a4509bb8d982ec9badfbbda9e10cce811e9213bc5b46fb91b1f58578 | 3e93a186cf1a5c68332e737713dcc263cdb2c865a75aa47928ae94f25e9b4aa0 |
cat-searcher/leandojo-benchmark-4-random | test | 4,006 | Int.existsUnique_mem_box | Mathlib/Order/Interval/Finset/Box.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Int.mem_box</a>, <a>and_self_iff</a>, <a>forall_eq'</a>] | case h
n : ℕ
x✝ x : ℤ × ℤ
⊢ (fun n => x ∈ box n) (max x.1.natAbs x.2.natAbs) ∧ ∀ (y : ℕ), (fun n => x ∈ box n) y → y = max x.1.natAbs x.2.natAbs | ((:c And) ((:lambda n (:c Nat) ((:c Membership.mem) ((:c Prod) (:c Int) (:c Int)) ((:c Finset) ((:c Prod) (:c Int) (:c Int))) ((:c Finset.instMembership) ((:c Prod) (:c Int) (:c Int))) (:fv _uniq.70558) ((:c Finset.box) ((:c Prod) (:c Int) (:c Int)) ((:c instOrderedRingProd) (:c Int) (:c Int) (:c Int.instOrderedRing) (... | [{"name":"n","sexp":"(:c Nat)"},{"name":"x✝","sexp":"((:c Prod) (:c Int) (:c Int))"},{"name":"x","sexp":"((:c Prod) (:c Int) (:c Int))"}] | (:app (:c And) (:arg :explicit 0 (:app (:lambda n :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:c Int... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69862","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69866","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:app (:c Prod) (:arg :explicit 0 (:c Int)) (:arg... | {"children":[{"source":"simp","sourceEnd":3725,"sourceStart":3721,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":3730,"sourceStart":3726,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":3730,"s... | [] | [{"source":"mem_box","source_end":3739,"source_start":3732,"syntax_kind":"ident"},{"source":"and_self_iff","source_end":3753,"source_start":3741,"syntax_kind":"ident"},{"source":"forall_eq'","source_end":3765,"source_start":3755,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69862","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69866","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 26 | 6 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a0e8554c8bbf2a24c2021ab26470a0ec8c3d502a8652b2251690935c877f1ba8 | 3e93a186cf1a5c68332e737713dcc263cdb2c865a75aa47928ae94f25e9b4aa0 | 6af28e6a269c1301b0b3e40b9aece4cf0301a5539f58faca80b0674e43fd3292 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,007 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' s using <a>Finset.cons_induction_on</a> with a s ha ih | ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
s : Finset α
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
⊢ ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a | case h₁
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
⊢ ⨅ i, ∑ a ∈ ∅, f i a = ∑ a ∈ ∅, ⨅ i, f i a
case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α... | ((:c Eq) (:c ENNReal) ((:c iInf) (:c ENNReal) (:fv _uniq.88199) ((:c ConditionallyCompleteLattice.toInfSet) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.t... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","s... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 3 (:lambda i :explicit (:fv FV0) (:app (:c Finset.sum) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"induction'","sourceEnd":27506,"sourceStart":27496,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"semanticRole":"local","source":"s","sourceEnd":27508,"sourceStart":27507,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarge... | [] | [{"source":"s","source_end":27508,"source_start":27507,"syntax_kind":"ident"},{"source":"Finset.cons_induction_on","source_end":27539,"source_start":27515,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ecae9d98fd83fe49a1b84f7bcc5d39d199093681082e0d74767d872cfa4f991 | 9144c6be07920fe6ab50247d0c93aea17a3ee82db4d17c8acf71fe9578a53220 | 93ea677fee3ffe52f8191efca319680892c79eccd3b04b100273036311293db1 | 83e8d5bf6fec9e13f7ed5b8d66c09518037943b8200a4495bad52fa3e8a0276d |
cat-searcher/leandojo-benchmark-4-random | test | 4,008 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finset.sum_empty</a>, <a>ciInf_const</a>] | case h₁
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
⊢ ⨅ i, ∑ a ∈ ∅, f i a = ∑ a ∈ ∅, ⨅ i, f i a | ((:c Eq) (:c ENNReal) ((:c iInf) (:c ENNReal) (:fv _uniq.88199) ((:c ConditionallyCompleteLattice.toInfSet) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.t... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","s... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 3 (:lambda i :explicit (:fv FV0) (:app (:c Finset.sum) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":27564,"sourceStart":27560,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27569,"sourceStart":27565,"tag":"atom"}],"kind"... | [] | [{"source":"Finset.sum_empty","source_end":27587,"source_start":27571,"syntax_kind":"ident"},{"source":"ciInf_const","source_end":27600,"source_start":27589,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 7 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b00b282a4e557ed3658fbf2353d0579d622e7bf59018ee0ec4ef2e1c25613900 | ecd0d54b6d2bdaf7197732d8a6cc126cb864d77f0284687d724d65e82ecf5bf3 | f720db190c45f6352236fb98655dd6107fa19d2d68a42f409ed852f110711824 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,009 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finset.sum_cons</a>, ← ih] | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
⊢ ⨅ i, ∑ a ∈ Finset.cons a s ha, f i a = ∑ a ∈ Finset... | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
⊢ ⨅ i, f i a + ∑ a ∈ s, f i a = (⨅ i, f i a) + ⨅ i, ∑... | ((:c Eq) (:c ENNReal) ((:c iInf) (:c ENNReal) (:fv _uniq.88199) ((:c ConditionallyCompleteLattice.toInfSet) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.t... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a✝","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 3 (:lambda i :explicit (:fv FV0) (:app (:c Finset.sum) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"simp","sourceEnd":27611,"sourceStart":27607,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":27616,"sourceStart":27612,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":276... | [] | [{"source":"Finset.sum_cons","source_end":27633,"source_start":27618,"syntax_kind":"ident"},{"source":"ih","source_end":27641,"source_start":27639,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 14 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59d74457ada7b369b9c6c351181d4a62711022f07b175beef0544e219c374fe7 | d0b55b86c216702b7364ad294c9cb0b16930c54cd8ecb3fd4228ced3fc92af06 | 70f67c645e3f5f5da2ae53a88ad496524f1c373f8bcabc9fef1e86e1a9f89328 | a967d02ecf9c6d4b702db1f923f85c11d4c5768e0a1d1fe182975c51a8457449 |
cat-searcher/leandojo-benchmark-4-random | test | 4,010 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>ENNReal.iInf_add_iInf</a> fun i j => ?_).<a>Eq.symm</a> | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
⊢ ⨅ i, f i a + ∑ a ∈ s, f i a = (⨅ i, f i a) + ⨅ i, ∑... | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j : ι
⊢ ∃ k, f k a + ∑ a ∈ s, f k a ≤ f i a + ∑ a ∈... | ((:c Eq) (:c ENNReal) ((:c iInf) (:c ENNReal) (:fv _uniq.88199) ((:c ConditionallyCompleteLattice.toInfSet) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder) (:c ENNReal) ((:c CompleteLinearOrder.t... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a✝","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c InfSet) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 3 (:lambda i :explicit (:fv FV0) (:app (:c HAdd.hAdd) (:arg :im... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"refine","sourceEnd":27653,"sourceStart":27647,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":27655,"sourceStart":27654,"tag":"atom"},{"children":[{"name":"ENNReal.iInf_add_iInf","semanticRole":"global","source":"iInf_add_iInf","sourceEnd":27668,"sourceStart":27655,"tag":"ident... | [] | [{"source":"(iInf_add_iInf fun i j => ?_).symm","source_end":27688,"source_start":27654,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 15 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ad48cdf528318f2267c8a80eae238d2e94d7efd26bd63562f5769d37d21de70 | a967d02ecf9c6d4b702db1f923f85c11d4c5768e0a1d1fe182975c51a8457449 | 8568ca9f0f118f4a81f3a25cd5390444ea69ff4979feed536ae531cc415de953 | 0bcd71ef885b9aba61625950cf1fb1c0184f0f489a7c78ee1197d9dcf396addb |
cat-searcher/leandojo-benchmark-4-random | test | 4,011 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (h (<a>Finset.cons</a> a s ha) i j).<a>Exists.imp</a> fun k hk => ?_ | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j : ι
⊢ ∃ k, f k a + ∑ a ∈ s, f k a ≤ f i a + ∑ a ∈... | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j k : ι
hk : ∀ a_1 ∈ Finset.cons a s ha, f k a_1 ≤ ... | ((:c Exists) (:fv _uniq.88199) (:lambda k (:fv _uniq.88199) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSem... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a✝","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda k :explicit (:fv FV0) (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"refine","sourceEnd":27699,"sourceStart":27693,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":27701,"sourceStart":27700,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"h","sourceEnd":27702,"sourceStart":27701,"tag":"identifier"},{"chi... | [] | [{"source":"(h (Finset.cons a s ha) i j).imp fun k hk => ?_","source_end":27747,"source_start":27700,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 16 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 351ac26d944e019cd1120c6df66004dc88825da85ddd9e645961e24d194ec33f | 0bcd71ef885b9aba61625950cf1fb1c0184f0f489a7c78ee1197d9dcf396addb | f1029e1175a5f388d922cab86d67f30b43f4c681e53fb207fa1716fd387e919d | 8f144d5a83b2746c98671c6e1b248b4ce3b63d75cb051a7ff14ff1624527550e |
cat-searcher/leandojo-benchmark-4-random | test | 4,012 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.forall_mem_cons</a>] at hk | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j k : ι
hk : ∀ a_1 ∈ Finset.cons a s ha, f k a_1 ≤ ... | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j k : ι
hk : (f k a ≤ f i a ∧ f k a ≤ f j a) ∧ ∀ x ... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a✝","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"rw","sourceEnd":27754,"sourceStart":27752,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27756,"sourceStart":27755,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.forall_me... | [] | [{"source":"Finset.forall_mem_cons","source_end":27778,"source_start":27756,"syntax_kind":"ident"},{"source":"hk","source_end":27785,"source_start":27783,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 17 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 28194f6dcd17b9430b384b7d48d7d24a3618c389739e6cbafd30ab6263944f21 | 8f144d5a83b2746c98671c6e1b248b4ce3b63d75cb051a7ff14ff1624527550e | eb7508fbc38450441880d4521ce136565ec6cf9c7cf8b3931a3c118379fdd8db | e63a09c176a924f8176d5a7bac0fba1d5280654e6beedd70402178f53617d47e |
cat-searcher/leandojo-benchmark-4-random | test | 4,013 | ENNReal.iInf_sum | Mathlib/Data/ENNReal/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>add_le_add</a> hk.1.1 (<a>Finset.sum_le_sum</a> fun a ha => (hk.2 a ha).2) | case h₂
ι : Sort u_1
f✝ g : ι → ℝ≥0∞
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
α : Type u_2
f : ι → α → ℝ≥0∞
inst✝ : Nonempty ι
h : ∀ (t : Finset α) (i j : ι), ∃ k, ∀ a ∈ t, f k a ≤ f i a ∧ f k a ≤ f j a
a : α
s : Finset α
ha : a ∉ s
ih : ⨅ i, ∑ a ∈ s, f i a = ∑ a ∈ s, ⨅ i, f i a
i j k : ι
hk : (f k a ≤ f i a ∧ f k a ≤ f j a) ∧ ∀ x ... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OrderedSemiring.toPartialOrder) (:c ENNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toOrderedCommSemiring) (:c ENNReal) (:c ENNReal.instCanonicallyOrderedCommSe... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"f✝","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"g","sexp":"(:forall _ (:fv _uniq.88199) (:c ENNReal))"},{"name":"a✝","sexp":"(:c ENNReal)"},{"name":"b","sexp":"(:c ENNReal)"},{"name":"c","sexp":"(:c ENNReal)"},{"name":"d","sexp":"(:c ENNReal)"},{"name":"r","... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:fv FV0) (:c ENNReal))"... | {"children":[{"source":"exact","sourceEnd":27795,"sourceStart":27790,"tag":"atom"},{"children":[{"name":"add_le_add","semanticRole":"global","source":"add_le_add","sourceEnd":27806,"sourceStart":27796,"tag":"identifier"},{"children":[{"children":[{"children":[{"contextIndex":22,"semanticRole":"local","source":"hk","sou... | [] | [{"source":"add_le_add hk.1.1 (Finset.sum_le_sum fun a ha => (hk.2 a ha).2)","source_end":27859,"source_start":27796,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.88199","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.88203","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 210 | 20 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e104c431c3bbdc35992d47c7158ee9bc6924dbdfa53f3ea73550eb37b70129b | e63a09c176a924f8176d5a7bac0fba1d5280654e6beedd70402178f53617d47e | e67288b44f9429b3d5ad9ffaa20e98609fca406299cd8d9ab56812fea2f6cf6f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,014 | Mathlib.Tactic.Ring.atom_pf | Mathlib/Tactic/Ring/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | u : Lean.Level
R : Type u_1
α : Q(Type u)
sα : Q(CommSemiring «$α»)
inst✝ : CommSemiring R
a : R
⊢ a = a ^ Nat.rawCast 1 * Nat.rawCast 1 + 0 | ((:c Eq) (:fv _uniq.186484) (:fv _uniq.187975) ((:c HAdd.hAdd) (:fv _uniq.186484) (:fv _uniq.186484) (:fv _uniq.186484) ((:c instHAdd) (:fv _uniq.186484) ((:c Distrib.toAdd) (:fv _uniq.186484) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.186484) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.1864... | [{"name":"u","sexp":"(:c Lean.Level)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"((:c Qq.Quoted) ((:c Lean.Expr.sort) ((:c Lean.Level.succ) (:fv _uniq.186468))))"},{"name":"sα","sexp":"((:c Qq.Quoted) ((:c Lean.Expr.app) ((:c Lean.Expr.const) ((:c Lean.Name.mkStr1) (:lit \"CommSemiring\")) ((:c List.c... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.186468","is_instance":false,"is_let":false,"name":"u","sexp":"(:c Lean.Level)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.186484","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":36093,"sourceStart":36089,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.186468","is_instance":false,"is_let":false,"user_name":"u"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.186484","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 103 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a306c18e5aa57b14d0680709977993273c6dc2649e8ec42c69574a9782bc550 | 610e5a91e30777589d0324fc479ad06a653f792b8cb6a82afdf6ebe401851b72 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,015 | Prod.segment_subset | Mathlib/Analysis/Convex/Segment.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro z ⟨a, b, ha, hb, hab, hz⟩ | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
ι : Type u_5
π : ι → Type u_6
inst✝⁴ : OrderedSemiring 𝕜
inst✝³ : AddCommMonoid E
inst✝² : AddCommMonoid F
inst✝¹ : Module 𝕜 E
inst✝ : Module 𝕜 F
x y : E × F
⊢ [x-[𝕜]y] ⊆ [x.1-[𝕜]y.1] ×ˢ [x.2-[𝕜]y.2] | case intro.intro.intro.intro.intro
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
ι : Type u_5
π : ι → Type u_6
inst✝⁴ : OrderedSemiring 𝕜
inst✝³ : AddCommMonoid E
inst✝² : AddCommMonoid F
inst✝¹ : Module 𝕜 E
inst✝ : Module 𝕜 F
x y z : E × F
a b : 𝕜
ha : 0 ≤ a
hb : 0 ≤ b
hab : a + b = 1
hz : a • x + b • y = z... | ((:c HasSubset.Subset) ((:c Set) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222))) ((:c Set.instHasSubset) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222))) ((:c segment) (:fv _uniq.365216) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222)) (:fv _uniq.365236) ((:c Prod.instAddCommMonoid) (:fv _uniq.365219) (:fv _uniq.... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.365228) (:sort (+ u_6 1)))"},{"name":"inst✝⁴","sexp":"((:c OrderedSemiring) ... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.365216","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.365219","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rintro","sourceEnd":25248,"sourceStart":25242,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"z","sourceEnd":25250,"sourceStart":25249,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"z","sourceEnd":25250,"sourceStart":25249,"... | [{"role":"fresh_name","source":"z","source_end":25250,"source_start":25249,"syntax_kind":"ident"},{"role":"fresh_name","source":"a","source_end":25255,"source_start":25254,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":25258,"source_start":25257,"syntax_kind":"ident"},{"role":"fresh_name","source... | [{"source":"⟨a, b, ha, hb, hab, hz⟩","source_end":25278,"source_start":25251,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.365216","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.365219","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 175 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f65ff366a13f215f9ae6e492fc673c9b97e0564aa58f4448ed8a1163941b1423 | 2b2366f14c635aaa7d4caa6df928b6501c14c0ea53413aabdb9588ef5f7e1feb | 1c66be3319194decc9445ed6003a819855853be9939cd846e2847a3ad080621b | f2947105fb2596d3bb5d51a320685b4c81771db26991e227100cc7b2154a6cc2 |
cat-searcher/leandojo-benchmark-4-random | test | 4,016 | Prod.segment_subset | Mathlib/Analysis/Convex/Segment.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨⟨a, b, ha, hb, hab, <a>congr_arg</a> <a>Prod.fst</a> hz⟩, a, b, ha, hb, hab, <a>congr_arg</a> <a>Prod.snd</a> hz⟩ | case intro.intro.intro.intro.intro
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
ι : Type u_5
π : ι → Type u_6
inst✝⁴ : OrderedSemiring 𝕜
inst✝³ : AddCommMonoid E
inst✝² : AddCommMonoid F
inst✝¹ : Module 𝕜 E
inst✝ : Module 𝕜 F
x y z : E × F
a b : 𝕜
ha : 0 ≤ a
hb : 0 ≤ b
hab : a + b = 1
hz : a • x + b • y = z... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222)) ((:c Set) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.365219) (:fv _uniq.365222))) (:fv _uniq.368794) ((:c SProd.sprod) ((:c Set) (:fv _uniq.365219)) ((:c Set) (:fv _uniq.365222)) ((:c Set) ((:c ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.365228) (:sort (+ u_6 1)))"},{"name":"inst✝⁴","sexp":"((:c OrderedSemiring) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.365216","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.365219","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":25286,"sourceStart":25281,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":25290,"sourceStart":25287,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":25293,"sourceStart":25290,"tag":"atom"},{"children":[{"contextIndex":15,"semanticRole":"local","source":"a... | [] | [{"source":"⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩","source_end":25381,"source_start":25287,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.365216","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.365219","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 175 | 5 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d9709bfcaacab630efbd72b540811e8043f179f8f64499739bd3329526eaf9e | f2947105fb2596d3bb5d51a320685b4c81771db26991e227100cc7b2154a6cc2 | 1db83adcd3e6005ae25f2ebc1bdbf96afdb85fe39967cedd59de18ec69c9429d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,017 | IsSigmaCompact.image_of_continuousOn | Mathlib/Topology/Compactness/SigmaCompact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hs with ⟨K, hcompact, hcov⟩ | X : Type u_1
Y : Type u_2
ι : Type u_3
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s✝ t : Set X
f : X → Y
s : Set X
hs : IsSigmaCompact s
hf : ContinuousOn f s
⊢ IsSigmaCompact (f '' s) | case intro.intro
X : Type u_1
Y : Type u_2
ι : Type u_3
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s✝ t : Set X
f : X → Y
s : Set X
hf : ContinuousOn f s
K : ℕ → Set X
hcompact : ∀ (n : ℕ), IsCompact (K n)
hcov : ⋃ n, K n = s
⊢ IsSigmaCompact (f '' s) | ((:c IsSigmaCompact) (:fv _uniq.3717) (:fv _uniq.3726) ((:c Set.image) (:fv _uniq.3714) (:fv _uniq.3717) (:fv _uniq.3871) (:fv _uniq.3872))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.3714))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.3717))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.3714))"},{"name":"t","... | (:app (:c IsSigmaCompact) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV9))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rcases","sourceEnd":4218,"sourceStart":4212,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":10,"semanticRole":"local","source":"hs","sourceEnd":4221,"sourceStart":4219,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"hs","source_end":4221,"source_start":4219,"syntax_kind":"ident"},{"source":"⟨K, hcompact, hcov⟩","source_end":4250,"source_start":4227,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b8e733684d15d663c47dd114f8eae36a0c93a788380fc9c5b7e38e07e93c5a9 | fa91c4dd96c764103c279b5e19f726e906beaf143c6715f401da2770e8208ebd | 4171985548e70d1564e852a901f75210e399c93ebe2bd095c028e6baf0760311 | e4221a9fb0e2fe3cf194e3aafda44d683830b257b8fd41caa55633d625c1e749 |
cat-searcher/leandojo-benchmark-4-random | test | 4,018 | IsSigmaCompact.image_of_continuousOn | Mathlib/Topology/Compactness/SigmaCompact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun n ↦ f '' K n, ?_, hcov.symm ▸ image_iUnion.symm⟩ | case intro.intro
X : Type u_1
Y : Type u_2
ι : Type u_3
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s✝ t : Set X
f : X → Y
s : Set X
hf : ContinuousOn f s
K : ℕ → Set X
hcompact : ∀ (n : ℕ), IsCompact (K n)
hcov : ⋃ n, K n = s
⊢ IsSigmaCompact (f '' s) | case intro.intro
X : Type u_1
Y : Type u_2
ι : Type u_3
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s✝ t : Set X
f : X → Y
s : Set X
hf : ContinuousOn f s
K : ℕ → Set X
hcompact : ∀ (n : ℕ), IsCompact (K n)
hcov : ⋃ n, K n = s
⊢ ∀ (n : ℕ), IsCompact ((fun n => f '' K n) n) | ((:c IsSigmaCompact) (:fv _uniq.3717) (:fv _uniq.3726) ((:c Set.image) (:fv _uniq.3714) (:fv _uniq.3717) (:fv _uniq.3871) (:fv _uniq.3872))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.3714))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.3717))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.3714))"},{"name":"t","... | (:app (:c IsSigmaCompact) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV8)) (:arg :explicit 3 (:fv FV9))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"refine","sourceEnd":4259,"sourceStart":4253,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":4263,"sourceStart":4260,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":4266,"sourceStart":4263,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"n"... | [] | [{"source":"⟨fun n ↦ f '' K n, ?_, hcov.symm ▸ image_iUnion.symm⟩","source_end":4321,"source_start":4260,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b511e45c312032e0f926993bbd0fe64e9b2eb7c5b1f6a09f47f1b375743a8a8c | e4221a9fb0e2fe3cf194e3aafda44d683830b257b8fd41caa55633d625c1e749 | d73a6291fec3a5e6f5c2cd92169dd8183ce0aaa01b82c58ec72e0b714863cb28 | 0a6f11326193b307d72aae2bb44d283d86da5088e3edc963721e58102b1e7a88 |
cat-searcher/leandojo-benchmark-4-random | test | 4,019 | IsSigmaCompact.image_of_continuousOn | Mathlib/Topology/Compactness/SigmaCompact.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun n ↦ (hcompact n).<a>IsCompact.image_of_continuousOn</a> (hf.mono (hcov.symm ▸ <a>Set.subset_iUnion</a> K n)) | case intro.intro
X : Type u_1
Y : Type u_2
ι : Type u_3
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s✝ t : Set X
f : X → Y
s : Set X
hf : ContinuousOn f s
K : ℕ → Set X
hcompact : ∀ (n : ℕ), IsCompact (K n)
hcov : ⋃ n, K n = s
⊢ ∀ (n : ℕ), IsCompact ((fun n => f '' K n) n) | (:forall n (:c Nat) ((:c IsCompact) (:fv _uniq.3717) (:fv _uniq.3726) ((:lambda n (:c Nat) ((:c Set.image) (:fv _uniq.3714) (:fv _uniq.3717) (:fv _uniq.3871) ((:fv _uniq.3896) 0))) 0))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.3714))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.3717))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.3714))"},{"name":"t","... | (:forall n :explicit (:c Nat) (:app (:c IsCompact) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:lambda n :explicit (:c Nat) (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":4329,"sourceStart":4324,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":4333,"sourceStart":4330,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":4335,"sourceStart":4334,"tag":"identifier"}],"kind":"null","source":"n","sourc... | [] | [{"source":"fun n ↦ (hcompact n).image_of_continuousOn (hf.mono (hcov.symm ▸ subset_iUnion K n))","source_end":4418,"source_start":4330,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3714","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3717","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 6 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 89328e51c9d96bd962445ded01a30e7c9a614a9e6b1554a5e17f265de1c8d820 | 0a6f11326193b307d72aae2bb44d283d86da5088e3edc963721e58102b1e7a88 | aed4aa9375667c1bae9b324644471cda015d8d5e66752a2bd466b877e4272d8e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,020 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>Field.exists_primitive_element</a> F E with α hα | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
⊢ Fintype.card (E ≃ₐ[F] E) = finrank F E | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
⊢ Fintype.card (E ≃ₐ[F] E) = finrank F E | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"cases'","sourceEnd":3664,"sourceStart":3658,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Field.exists_primitive_element","semanticRole":"global","source":"Field.exists_primitive_element","sourceEnd":3695,"sourceStart":3665,"... | [] | [{"source":"Field.exists_primitive_element F E","source_end":3699,"source_start":3665,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb0b85326f66069ca030101dd855a3c96e1bb7ea489ce2bcc8df60db012932b4 | 7e297cd2d7ae16e8428c1dcc0d0c8fd086389ed9c56e730a772c2f696c69622a | a093c386a405bb054b5e85d67672be1cea9049a2480817f9f88d1dc321728254 | d1a70d657578b42a361b48b90267b86f748ceacf9b93e491c081e2c782a9b2ea |
cat-searcher/leandojo-benchmark-4-random | test | 4,021 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let iso : F⟮α⟯ ≃ₐ[F] E := { toFun := fun e => e.val invFun := fun e => ⟨e, by rw [hα]; exact <a>IntermediateField.mem_top</a>⟩ left_inv := fun _ => by ext; rfl right_inv := fun _ => <a>rfl</a> map_mul' := fun _ _ => <a>rfl</a> map_add' := fun _ _ => <a>rfl</a> commutes' := fun _ => <a>rfl</a> } | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
⊢ Fintype.card (E ≃ₐ[F] E) = finrank F E | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"let","sourceEnd":3717,"sourceStart":3714,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"iso","sourceEnd":3721,"sourceStart":3718,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":3723,"... | [] | [{"source":"F⟮α⟯ ≃ₐ[F] E","source_end":3745,"source_start":3724,"syntax_kind":"«term_≃ₐ[_]_»"},{"source":"{ toFun := fun e => e.val\n invFun := fun e => ⟨e, by rw [hα]; exact IntermediateField.mem_top⟩\n left_inv := fun _ => by ext; rfl\n right_inv := fun _ => rfl\n map_mul' := fun _ _ => rfl\n ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 5 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62d8278993ba9b2db8a83c1b599fc0cfe479a5edd9e136842a397d7a33a7a899 | d1a70d657578b42a361b48b90267b86f748ceacf9b93e491c081e2c782a9b2ea | 2e2563800183ee0d24fb8c575d6d5dc06d99d827a0a4cff936c927059054e335 | 8177d613bf4fcd96db0b81b3603f4b93b8dab749a73603d5a7030ea5d554d332 |
cat-searcher/leandojo-benchmark-4-random | test | 4,022 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have H : <a>IsIntegral</a> F α := <a>IsGalois.integral</a> F α | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":4035,"sourceStart":4031,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"H","sourceEnd":4037,"sourceStart":4036,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"H","sourceEnd":4037,"sourceStart":4036,"tag":"node"},{"ch... | [] | [{"source":"IsIntegral F α","source_end":4055,"source_start":4040,"syntax_kind":"Lean.Parser.Term.app"},{"source":"IsGalois.integral F α","source_end":4081,"source_start":4059,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 22 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2df9fc521bda82a34f21967f0cffe53b78bf7bb54aba2f3d4a1364e60d1e53e5 | 8177d613bf4fcd96db0b81b3603f4b93b8dab749a73603d5a7030ea5d554d332 | 8c193b14675e1b93cceef65c8fb4fe0a6aeb3ab7df59be1d537bc98327d01f8f | cfdf52b45958621015c438f960be137fcf26b80e0db9ca31688fbe09e8242dd3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,023 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_sep : (<a>minpoly</a> F α).<a>Polynomial.Separable</a> := <a>IsGalois.separable</a> F α | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":4088,"sourceStart":4084,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_sep","sourceEnd":4094,"sourceStart":4089,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_sep","sourceEnd":4094,"sourceStart":4089,"tag":"nod... | [] | [{"source":"(minpoly F α).Separable","source_end":4121,"source_start":4097,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"IsGalois.separable F α","source_end":4148,"source_start":4125,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 23 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50b10c4e38bb24ab5252afff70f6916eca10c0e0589bc8d959c4f4ef32b1ff23 | cfdf52b45958621015c438f960be137fcf26b80e0db9ca31688fbe09e8242dd3 | 14179650aa8a724fdae69263362f78cb220378572a496458abcb5730bb3d6ba6 | 7cad1f97fed4ae4e96d6ebccf56013f54ef281137af42436b3e5bcbc9d32b379 |
cat-searcher/leandojo-benchmark-4-random | test | 4,024 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_splits : (<a>minpoly</a> F α).<a>Polynomial.Splits</a> (<a>algebraMap</a> F E) := <a>IsGalois.splits</a> F α | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":4155,"sourceStart":4151,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_splits","sourceEnd":4164,"sourceStart":4156,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_splits","sourceEnd":4164,"sourceStart":4156,"tag... | [] | [{"source":"(minpoly F α).Splits (algebraMap F E)","source_end":4205,"source_start":4167,"syntax_kind":"Lean.Parser.Term.app"},{"source":"IsGalois.splits F α","source_end":4229,"source_start":4209,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 24 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4d1e0ef4321a35a785c258f4cb411f0552031a4d308c979c64bb5ef6b7ee0b7e | 7cad1f97fed4ae4e96d6ebccf56013f54ef281137af42436b3e5bcbc9d32b379 | f26df67903dc5e3961551ce7688ec883e02101787e23d1a1d4cc45ef2363f8f3 | f98c0cb255042ef752e48f60c1e8df6adc4c4370939cd2135597257e58df4a98 |
cat-searcher/leandojo-benchmark-4-random | test | 4,025 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h_splits : <a>Polynomial.Splits</a> (<a>algebraMap</a> F F⟮α⟯) (<a>minpoly</a> F α) := by simpa using <a>Polynomial.splits_comp_of_splits</a> (<a>algebraMap</a> F E) iso.symm.toAlgHom.toRingHom h_splits | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"replace","sourceEnd":4239,"sourceStart":4232,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_splits","sourceEnd":4248,"sourceStart":4240,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_splits","sourceEnd":4248,"sourceStart":4240,"... | [] | [{"source":"Polynomial.Splits (algebraMap F F⟮α⟯) (minpoly F α)","source_end":4308,"source_start":4251,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Polynomial.splits_comp_of_splits (algebraMap F E) iso.symm.toAlgHom.toRingHom h_splits","source_end":4423,"source_start":4337,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 25 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 76c8696cd15ae99f9655374b7d86fefe411ca56e00abfcc3bcb3327151f34934 | f98c0cb255042ef752e48f60c1e8df6adc4c4370939cd2135597257e58df4a98 | 883143023601174d6b36dce3878124b36d498cee342bf7dfb1ab296b2b95757b | 076e785899869001b22291522d2a5978c3832d7b51333a8d01fa713a591659aa |
cat-searcher/leandojo-benchmark-4-random | test | 4,026 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>LinearEquiv.finrank_eq</a> iso.toLinearEquiv] | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":4428,"sourceStart":4426,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4430,"sourceStart":4429,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4433,"sourceStart":... | [] | [{"source":"LinearEquiv.finrank_eq iso.toLinearEquiv","source_end":4474,"source_start":4434,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 28 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3fd937c2b697d9face9e79759749b4b2329a718087316de8dff5c8eea1ecf59b | 076e785899869001b22291522d2a5978c3832d7b51333a8d01fa713a591659aa | e6f5cc5b5ed2e699fd2d8073576c782465158df666962ac57ba0adbb6914971c | b0814a415e0b54bf579cdc19f0fd54a9fcdaab01a340618a0e77ea4b01f61b14 |
cat-searcher/leandojo-benchmark-4-random | test | 4,027 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank</a> F E H h_sep h_splits] | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":4480,"sourceStart":4478,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4482,"sourceStart":4481,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4485,"sourceStart":... | [] | [{"source":"IntermediateField.AdjoinSimple.card_aut_eq_finrank F E H h_sep h_splits","source_end":4557,"source_start":4486,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 31 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72ad74b88dfe3d9a3fbb6078b993b0e5963aa199ad1451500796f2d279c5a847 | b0814a415e0b54bf579cdc19f0fd54a9fcdaab01a340618a0e77ea4b01f61b14 | 6ed3ad36a1081e505849e2137de0248921fc12c2f215d4bcb783db7d53225aee | 4560bbe2399e4ed7025c7cd25ca579f05e42f732e4f31fd182c27fc232f4e162 |
cat-searcher/leandojo-benchmark-4-random | test | 4,028 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Fintype.card_congr</a> | case intro
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ ... | case intro.f
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ... | ((:c Eq) (:c Nat) ((:c Fintype.card) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Fintype.card) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":4566,"sourceStart":4561,"tag":"atom"},{"name":"Fintype.card_congr","semanticRole":"global","source":"Fintype.card_congr","sourceEnd":4585,"sourceStart":4567,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Fintype.card_congr","sourceEnd":4585,"sourceStart... | [] | [{"source":"Fintype.card_congr","source_end":4585,"source_start":4567,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 34 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8d9a269ed8c08f083177f959ff773fcebd37e189f4d1e2bd866adf754aabc57 | 4560bbe2399e4ed7025c7cd25ca579f05e42f732e4f31fd182c27fc232f4e162 | 2ec26018621b3ad0f0f4c86d2868ffbf52e15dcae4ea46c1867998cb9dedc7b8 | f312ef45c4285e6fa4ecede64de606969fe117fbd9db420dcc234008bc15e72a |
cat-searcher/leandojo-benchmark-4-random | test | 4,029 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Equiv.mk</a> (fun ϕ => iso.trans (ϕ.trans iso.symm)) fun ϕ => iso.symm.trans (ϕ.trans iso) | case intro.f
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ... | case intro.f.left_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
comm... | ((:c Equiv) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142) ((:c Field.toSemifield)... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Equiv) (:arg :explicit 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":4593,"sourceStart":4588,"tag":"atom"},{"children":[{"name":"Equiv.mk","semanticRole":"constructor","source":"Equiv.mk","sourceEnd":4602,"sourceStart":4594,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":4604,"sourceStart":4603,"tag":"atom"},{"children":... | [] | [{"source":"Equiv.mk (fun ϕ => iso.trans (ϕ.trans iso.symm)) fun ϕ => iso.symm.trans (ϕ.trans iso)","source_end":4684,"source_start":4594,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 35 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cd5154219a4216a758d3c17e79dd1b03eb877ce245f5d72ca51cca64efd41615 | f312ef45c4285e6fa4ecede64de606969fe117fbd9db420dcc234008bc15e72a | a9ee22b4f174081f2ab6c0e9f51e9fce7a72ccde90098badc8cafe397d6b8fb8 | 9be0f3d0b7e61c4168a3e0f3eeac1f968543b70f65bfa427606be7655fee38e1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,030 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hα] | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
e : E
⊢ e ∈ F⟮α⟯ | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
e : E
⊢ e ∈ ⊤ | ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) (:fv _uniq.16142) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":3815,"sourceStart":3813,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3817,"sourceStart":3816,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRo... | [] | [{"source":"hα","source_end":3820,"source_start":3817,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 10 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b303e4c4fd92b0a2dfa5ad1a9caa5b53f827eff26ec628278db0e369b680d958 | 14e0cafaf96254dfb0887352d8ef7516e8b99feae397612071cef88f5c36cc38 | 4fc329f4bfd39faeb37a1faa048797e0aa6d3c37e6bb81c08c6cce31f01d14e9 | 1f587e6fde6a4f78cf27df5d226a3e166ed4a85a7607b69898cf06fd0ba3696d |
cat-searcher/leandojo-benchmark-4-random | test | 4,031 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IntermediateField.mem_top</a> | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
e : E
⊢ e ∈ ⊤ | ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) (:fv _uniq.16142) ((:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":3828,"sourceStart":3823,"tag":"atom"},{"name":"IntermediateField.mem_top","semanticRole":"global","source":"IntermediateField.mem_top","sourceEnd":3854,"sourceStart":3829,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact IntermediateField.mem_top","sourceE... | [] | [{"source":"IntermediateField.mem_top","source_end":3854,"source_start":3829,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 14 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 179ef2dabe606ec1ff99abe6e4ae9f7e2cca7d412860d5d2892179b002bf008f | 1f587e6fde6a4f78cf27df5d226a3e166ed4a85a7607b69898cf06fd0ba3696d | ea7f3c8df69a4217472f8ee4660e5f027406fa4b1c36177777a2abd4460cbedc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,032 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
x✝ : ↥F⟮α⟯
⊢ (fun e => ⟨e, ⋯⟩) ((fun e => ↑e) x✝) = x✝ | case a
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
x✝ : ↥F⟮α⟯
⊢ ↑((fun e => ⟨e, ⋯⟩) ((fun e => ↑e) x✝)) = ↑x✝ | ((:c Eq) ((:c Subtype) (:fv _uniq.16142) (:lambda x (:fv _uniq.16142) ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :inst... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"ext","sourceEnd":3891,"sourceStart":3888,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":3891,"sourceStart":3888,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 19 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9cf2dfa0819b77c74ca44330bf981af9633b2eb0b122d1366780059590ee22bc | 828dc8429bb92899b34ee68126acb73d78dfadc166cd8d560b57434c46e3156f | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 6d164c6c07a8d31db4b41cba2685605b264d38df46811aded63a97c3c5908748 |
cat-searcher/leandojo-benchmark-4-random | test | 4,033 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case a
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
x✝ : ↥F⟮α⟯
⊢ ↑((fun e => ⟨e, ⋯⟩) ((fun e => ↑e) x✝)) = ↑x✝ | ((:c Eq) (:fv _uniq.16142) ((:c Subtype.val) (:fv _uniq.16142) (:lambda x (:fv _uniq.16142) ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.16136) (:f... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit 1) (:arg :explicit 2 (:app (:lambda e :explicit (:fv FV2) (:app (:c Subtype.mk) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit 1) (:arg :explicit 2 0) (:arg :proof 3 (:proof-of (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"rfl","sourceEnd":3896,"sourceStart":3893,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3896,"sourceStart":3893,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 21 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5aa64abcc5c3886ce9d3f498a32c8f272f85557b5a5dd0aa1613ceebfef02970 | 6d164c6c07a8d31db4b41cba2685605b264d38df46811aded63a97c3c5908748 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,034 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>Polynomial.splits_comp_of_splits</a> (<a>algebraMap</a> F E) iso.symm.toAlgHom.toRingHom h_splits | F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
commutes' := ⋯ }
H : IsInt... | ((:c Polynomial.Splits) (:fv _uniq.16136) ((:c Subtype) (:fv _uniq.16142) (:lambda x (:fv _uniq.16142) ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Polynomial.Splits) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"simpa","sourceEnd":4324,"sourceStart":4319,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"Polynomial.splits_comp_of_splits (algebraMap F E) iso.symm.toAlgHom.toRingHom h_splits","source_end":4423,"source_start":4337,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 27 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db41170e4aae5af5787e132f0d77642611784e6344080ab3c745c01b28285d08 | 8c88b6d2dacc02f87907d0073ec288a553d0879de59c288d920922f60d52e8c4 | 9bfd95b0cdb27f54495fd0b98c4719f9f4d04a9655180c62ad8b1093d361d495 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,035 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ϕ | case intro.f.left_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
comm... | case intro.f.left_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
comm... | ((:c Function.LeftInverse) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142) ((:c Fie... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Function.LeftInverse) (:arg :implicit-type 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0 ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"intro","sourceEnd":4695,"sourceStart":4690,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ϕ","sourceEnd":4698,"sourceStart":4696,"tag":"identifier"}],"kind":"null","source":"ϕ","sourceEnd":4698,"sourceStart":4696,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"ϕ","source_end":4698,"source_start":4696,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 40 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c693ab8cd248809511b4f3f344ad2bab6e454e05caa27589c668db1ec09c8f51 | 2ce0b4bc95c5f1d4bd4a70d48ccaad13aa862ddc3fa2c9bfaeb8cb6be9cd1638 | 14d24dbceca91a0088ed7f79b0d01c8d19e1165968faaf015c67114d4be79bf0 | 16aeb8cb38b67159709f4cd141441ba7994bc98cd929e4ceb1031ae2656d4796 |
cat-searcher/leandojo-benchmark-4-random | test | 4,036 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 | case intro.f.left_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
comm... | case intro.f.left_inv.h
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
co... | ((:c Eq) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142) ((:c Field.toSemifield) (:... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:ar... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"ext1","sourceEnd":4704,"sourceStart":4700,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1","sourceEnd":4704,"sourceStart":4700,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 42 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ff69ed486b32eab8757ec23bac771d6a206f51dc16084f27df7197af1bf57b2 | 16aeb8cb38b67159709f4cd141441ba7994bc98cd929e4ceb1031ae2656d4796 | e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b | 877541eabd2064229c0e77b04373cfd51e70c618488bad9afc0ef2f3ffedfb4d |
cat-searcher/leandojo-benchmark-4-random | test | 4,037 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>AlgEquiv.trans_apply</a>, <a>AlgEquiv.apply_symm_apply</a>] | case intro.f.left_inv.h
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
co... | ((:c Eq) (:fv _uniq.16142) ((:c DFunLike.coe) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :insta... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"simp","sourceEnd":4710,"sourceStart":4706,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4715,"sourceStart":4711,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4715,"s... | [] | [{"source":"trans_apply","source_end":4728,"source_start":4717,"syntax_kind":"ident"},{"source":"apply_symm_apply","source_end":4746,"source_start":4730,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 44 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1d80cfd130e150065c76b6b33862d2f2bca4105d8f732bf2a1073fc1a3864033 | 877541eabd2064229c0e77b04373cfd51e70c618488bad9afc0ef2f3ffedfb4d | c2cae41bac151b972f8afd320f2b5c589c0ca9ec3ef65ca27328d2cdb9e710cb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,038 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro ϕ | case intro.f.right_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
com... | case intro.f.right_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
com... | ((:c Function.RightInverse) ((:c AlgEquiv) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136) ((:c Field.toSemifield) (:fv _uniq.16136) (:fv _uniq.16139))) ((:c DivisionSemiring.toSemiring) (:fv _uniq.16142) ((:c Semifield.toDivisionSemiring) (:fv _uniq.16142) ((:c Fi... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Function.RightInverse) (:arg :implicit-type 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c Semiring) (:arg :explicit 0... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"intro","sourceEnd":4758,"sourceStart":4753,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ϕ","sourceEnd":4761,"sourceStart":4759,"tag":"identifier"}],"kind":"null","source":"ϕ","sourceEnd":4761,"sourceStart":4759,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"ϕ","source_end":4761,"source_start":4759,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 49 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | daf17e10b037bd97123629ca31db417b88bd4c593ab2c2e8358f4c3da37fcbfd | 549a5bf63b15346002fcb07a9825b6f90719818077cb28a99c536caf36757144 | 14d24dbceca91a0088ed7f79b0d01c8d19e1165968faaf015c67114d4be79bf0 | d43f765c26ef074f5b33f321128d8ea2322eaf977b25dc4a976ab5c9e1be0801 |
cat-searcher/leandojo-benchmark-4-random | test | 4,039 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 | case intro.f.right_inv
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
com... | case intro.f.right_inv.h
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
c... | ((:c Eq) ((:c AlgEquiv) (:fv _uniq.16136) ((:c Subtype) (:fv _uniq.16142) (:lambda x (:fv _uniq.16142) ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AlgEquiv) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"ext1","sourceEnd":4767,"sourceStart":4763,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1","sourceEnd":4767,"sourceStart":4763,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 51 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3fc9579c02d89cbc8440eb0ac181cccbe1186316271ed479d9f983852328d84 | d43f765c26ef074f5b33f321128d8ea2322eaf977b25dc4a976ab5c9e1be0801 | e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b | 6ec7ae6a164da5db2b45e71a132687968d7b2f12849f507083b118eb5fac548e |
cat-searcher/leandojo-benchmark-4-random | test | 4,040 | IsGalois.card_aut_eq_finrank | Mathlib/FieldTheory/Galois.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>AlgEquiv.trans_apply</a>, <a>AlgEquiv.symm_apply_apply</a>] | case intro.f.right_inv.h
F : Type u_1
inst✝⁴ : Field F
E : Type u_2
inst✝³ : Field E
inst✝² : Algebra F E
inst✝¹ : FiniteDimensional F E
inst✝ : IsGalois F E
α : E
hα : F⟮α⟯ = ⊤
iso : ↥F⟮α⟯ ≃ₐ[F] E :=
{ toFun := fun e => ↑e, invFun := fun e => ⟨e, ⋯⟩, left_inv := ⋯, right_inv := ⋯, map_mul' := ⋯, map_add' := ⋯,
c... | ((:c Eq) ((:c Subtype) (:fv _uniq.16142) (:lambda x (:fv _uniq.16142) ((:c Membership.mem) (:fv _uniq.16142) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _uniq.16139) (:fv _uniq.16145) (:fv _uniq.16387)) ((:c SetLike.instMembership) ((:c IntermediateField) (:fv _uniq.16136) (:fv _uniq.16142) (:fv _u... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Field) (:fv _uniq.16136))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.16142))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.16136) (:fv _uniq.16142) ((:c Semifield.toCommSemiring) (:fv _uniq.16136)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c IntermediateField) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :inst... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Field) (:arg :explicit ... | {"children":[{"source":"simp","sourceEnd":4773,"sourceStart":4769,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":4778,"sourceStart":4774,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":4778,"s... | [] | [{"source":"trans_apply","source_end":4791,"source_start":4780,"syntax_kind":"ident"},{"source":"symm_apply_apply","source_end":4809,"source_start":4793,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.16136","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16139","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 28 | 53 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 14f7ce766955c734e6647cb9d5c98c0b0a74293f190c0034db11ac9d677eac52 | 6ec7ae6a164da5db2b45e71a132687968d7b2f12849f507083b118eb5fac548e | eb446b3346e61e4b8d481443b5a26ebb69f2b91ddee7e97c978a74fa8fe902ee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,041 | NNReal.hasSum_coe | Mathlib/Topology/Instances/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>HasSum</a>, ← <a>NNReal.coe_sum</a>, <a>NNReal.tendsto_coe</a>] | α : Type u_1
f : α → ℝ≥0
r : ℝ≥0
⊢ HasSum (fun a => ↑(f a)) ↑r ↔ HasSum f r | ((:c Iff) ((:c HasSum) (:c Real) (:fv _uniq.18973) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:lambda a (:fv _uniq.18973) ((:c NNReal.toReal) ((:fv _uniq.19195) 0))) ((:c NNReal.toReal) (:fv _uniq.19196))) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.18973) (:c NNReal))"},{"name":"r","sexp":"(:c NNReal)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c HasSum) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18973","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.19195","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:c NNReal))"},... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7042,"sourceStart":7038,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7047,"sourceStart":7043,"tag":"atom"}],"kind":"nu... | [] | [{"source":"HasSum","source_end":7055,"source_start":7049,"syntax_kind":"ident"},{"source":"coe_sum","source_end":7068,"source_start":7061,"syntax_kind":"ident"},{"source":"tendsto_coe","source_end":7081,"source_start":7070,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18973","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.19195","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5796c735201cd4d837de8a92ff94fa7ae1101a81cb0cf82999a4e92ff8a1fbb | 86e986612367facea68a4e06e6902837886dc33340ffa8a18fa24880b5c81aff | 03bf92f16188a57f661d9c93c8da90bfef1456be8195127a537d75c21e0c8404 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,042 | Finsupp.erase_add | Mathlib/Data/Finsupp/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext s | 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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
⊢ erase a (f + f') = erase a f + erase a f' | case h
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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
s : α
⊢ (erase a (f + f')) s = (erase a f + erase a f') s | ((:c Eq) ((:c Finsupp) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZero) (:fv _uniq.120517) (:fv _uniq.120541))) ((:c Finsupp.erase) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZero) (:fv _uniq.120517) (:fv _uniq.120541)) (:fv _uniq.120877) ((:c HAdd.hAdd) ((:c Finsupp) (:fv _uniq.120505) (:... | [{"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 Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV4))))))) (:arg :explicit 1 (:app (:c Finsupp.erase) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV4)) (:arg :instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"ext","sourceEnd":44408,"sourceStart":44405,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":44410,"sourceStart":44409,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"s","sourceEnd":44410,"sourceStart":44409,"tag... | [{"role":"fresh_name","source":"s","source_end":44410,"source_start":44409,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 325 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2e1c2387e9adbe16b5c7709f018e6034748d8388ed896c1a5d7f80e3f1c5fa2e | 00ea0e99090d8e7f0981603c94face4ac15e044565697e0d6ea16c80f1ea96da | f0930d4bc5f383728a98d736a6db287d5b1a71b12af2320f3f1fe190348aeb4d | 05a3974c50cd61ddffcc72b409b16321dcd971595a9ebc78b705062f2e0353bd |
cat-searcher/leandojo-benchmark-4-random | test | 4,043 | Finsupp.erase_add | Mathlib/Data/Finsupp/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hs : s = a | case h
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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
s : α
⊢ (erase a (f + f')) s = (erase a f + erase a f') s | case pos
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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
s : α
hs : s = a
⊢ (erase a (f + f')) s = (erase a f + erase a f') s
case neg
α : Type u_1
β : Type u_2
γ : ... | ((:c Eq) (:fv _uniq.120517) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZero) (:fv _uniq.120517) (:fv _uniq.120541))) (:fv _uniq.120505) (:lambda _ (:fv _uniq.120505) (:fv _uniq.120517)) ((:c Finsupp.instFunLike) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZe... | [{"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 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV4))))))) (:arg :implicit-type 1 (:fv FV0)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":44420,"sourceStart":44412,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hs","sourceEnd":44423,"sourceStart":44421,"tag":"identifier"},{"source":":","sourceEnd":44425,"sourceStart":44424,"tag":"atom"}],"kind":"null","source":"hs :","sourceEnd":44425,"so... | [] | [{"source":"s = a","source_end":44431,"source_start":44426,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 325 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | acbff7fa432291a37941334b97daaf4e47ea696e3cdd1b448e5525ceafa245c1 | 05a3974c50cd61ddffcc72b409b16321dcd971595a9ebc78b705062f2e0353bd | cb56bfd641de5fcf0079834bdbec3faf491da1b715dfb424ee9c7af856a90654 | 7966af55c831f4efdaa3e712e8e82b6000b3233879ab936985b946c8d1a8646e |
cat-searcher/leandojo-benchmark-4-random | test | 4,044 | Finsupp.erase_add | Mathlib/Data/Finsupp/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finsupp.add_apply</a>, <a>Finsupp.erase_ne</a> hs, <a>Finsupp.erase_ne</a> hs, <a>Finsupp.erase_ne</a> hs, <a>Finsupp.add_apply</a>] | case neg
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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
s : α
hs : ¬s = a
⊢ (erase a (f + f')) s = (erase a f + erase a f') s | ((:c Eq) (:fv _uniq.120517) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZero) (:fv _uniq.120517) (:fv _uniq.120541))) (:fv _uniq.120505) (:lambda _ (:fv _uniq.120505) (:fv _uniq.120517)) ((:c Finsupp.instFunLike) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZe... | [{"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 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV4))))))) (:arg :implicit-type 1 (:fv FV0)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":44506,"sourceStart":44504,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44508,"sourceStart":44507,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finsupp.add_appl... | [] | [{"source":"add_apply","source_end":44517,"source_start":44508,"syntax_kind":"ident"},{"source":"erase_ne hs","source_end":44530,"source_start":44519,"syntax_kind":"Lean.Parser.Term.app"},{"source":"erase_ne hs","source_end":44543,"source_start":44532,"syntax_kind":"Lean.Parser.Term.app"},{"source":"erase_ne hs","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 325 | 19 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0f68ca4e9b3d1fcb3654e1322da056e97637052495aeb05a302f61c4edde121 | 8e1a62466a38703a400b3401ae8c9c2e6476374241c809b2ab80414e44948af9 | 52268f3b27d33e0a2d88ff8baca148e18ceb9385c04b072ab09ab82950a9aa98 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,045 | Finsupp.erase_add | Mathlib/Data/Finsupp/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hs, <a>Finsupp.add_apply</a>, <a>Finsupp.erase_same</a>, <a>Finsupp.erase_same</a>, <a>Finsupp.erase_same</a>, <a>add_zero</a>] | case pos
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
inst✝ : AddZeroClass M
a : α
f f' : α →₀ M
s : α
hs : s = a
⊢ (erase a (f + f')) s = (erase a f + erase a f') s | ((:c Eq) (:fv _uniq.120517) ((:c DFunLike.coe) ((:c Finsupp) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZero) (:fv _uniq.120517) (:fv _uniq.120541))) (:fv _uniq.120505) (:lambda _ (:fv _uniq.120505) (:fv _uniq.120517)) ((:c Finsupp.instFunLike) (:fv _uniq.120505) (:fv _uniq.120517) ((:c AddZeroClass.toZe... | [{"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 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Finsupp) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :instance 2 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV4))))))) (:arg :implicit-type 1 (:fv FV0)) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":44439,"sourceStart":44437,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44441,"sourceStart":44440,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"hs","source_end":44443,"source_start":44441,"syntax_kind":"ident"},{"source":"add_apply","source_end":44454,"source_start":44445,"syntax_kind":"ident"},{"source":"erase_same","source_end":44466,"source_start":44456,"syntax_kind":"ident"},{"source":"erase_same","source_end":44478,"source_start":44468,"syntax... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120505","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120508","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 325 | 9 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 663e33ab87c20e6c6493e300f01a85f766a2d06affe6a251ced8d572029176f6 | 116778ed38fd220480bd368888ed70d314959cb43b0a9616d8c2653f97f1147c | b54d4eda1e266cc4957583bce2510673f3f8b46cb986989019db09921aa3328d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,046 | Rat.neg_mkRat | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | if z : d = 0 then simp [z]; rfl else simp [← <a>Rat.normalize_eq_mkRat</a> z, <a>Rat.neg_normalize</a>] | n : Int
d : Nat
⊢ -mkRat n d = mkRat (-n) d | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c mkRat) (:fv _uniq.23272) (:fv _uniq.23273))) ((:c mkRat) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) (:fv _uniq.23272)) (:fv _uniq.23273))) | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c mkRat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 2 (:app (:c ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"if","sourceEnd":11417,"sourceStart":11415,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"z","sourceEnd":11419,"sourceStart":11418,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"z","sourceEnd":11419,"sourceStart":11418,"tag":"n... | [] | [{"source":"d = 0","source_end":11427,"source_start":11422,"syntax_kind":"«term_=_»"},{"source":"z","source_end":11440,"source_start":11439,"syntax_kind":"ident"},{"source":"normalize_eq_mkRat z","source_end":11482,"source_start":11462,"syntax_kind":"Lean.Parser.Term.app"},{"source":"neg_normalize","source_end":11497,"... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"user_name":"d"}] | 57 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eee3bbddccad5adc2058e41ada090a75ade1eba2d138062a0b47ec3148f304a5 | 8df473edd5fe919e4b524f06599b9e161d4df641da3061892f735696ea6b0fed | e2509784c4450b75d3e8460c2a42adb751ba5227e68e41029bec30ed67e9ec7c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,047 | Rat.neg_mkRat | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [z] | n : Int
d : Nat
z : d = 0
⊢ -mkRat n d = mkRat (-n) d | n : Int
d : Nat
z : d = 0
⊢ -0 = 0 | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c mkRat) (:fv _uniq.23272) (:fv _uniq.23273))) ((:c mkRat) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) (:fv _uniq.23272)) (:fv _uniq.23273))) | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"},{"name":"z","sexp":"((:c Eq) (:c Nat) (:fv _uniq.23273) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c mkRat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 2 (:app (:c ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"source":"simp","sourceEnd":11437,"sourceStart":11433,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11439,"sourceStart":11438,"tag":"a... | [] | [{"source":"z","source_end":11440,"source_start":11439,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 57 | 8 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9880133784bf2cf002f881ed45651a1c6402bc8f8929f02f5e92e5e0ae691c58 | 511738b089f56a9863bebcd0ee125a6d9a601664039a0b159f39c82e07046423 | 0b369a71875dd066d055bceb7c917c198c985d75e450232ad383d6f9ad9f27b4 | d467ee9bb9915d3c4f5ce2c0cd9597c92acfc8a309cbc23c7c3def081af37965 |
cat-searcher/leandojo-benchmark-4-random | test | 4,048 | Rat.neg_mkRat | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | n : Int
d : Nat
z : d = 0
⊢ -0 = 0 | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0)))) | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"},{"name":"z","sexp":"((:c Eq) (:c Nat) (:fv _uniq.23273) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:ins... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"source":"rfl","sourceEnd":11446,"sourceStart":11443,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":11446,"sourceStart":11443,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 57 | 10 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1832829c52e76bcd39c5732fe8bfdc4fff8b3c6feca620887d82f21b25d5b621 | d467ee9bb9915d3c4f5ce2c0cd9597c92acfc8a309cbc23c7c3def081af37965 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,049 | Rat.neg_mkRat | .lake/packages/batteries/Batteries/Data/Rat/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← <a>Rat.normalize_eq_mkRat</a> z, <a>Rat.neg_normalize</a>] | n : Int
d : Nat
z : ¬d = 0
⊢ -mkRat n d = mkRat (-n) d | ((:c Eq) (:c Rat) ((:c Neg.neg) (:c Rat) (:c Rat.instNeg) ((:c mkRat) (:fv _uniq.23272) (:fv _uniq.23273))) ((:c mkRat) ((:c Neg.neg) (:c Int) (:c Int.instNegInt) (:fv _uniq.23272)) (:fv _uniq.23273))) | [{"name":"n","sexp":"(:c Int)"},{"name":"d","sexp":"(:c Nat)"},{"name":"z","sexp":"((:c Not) ((:c Eq) (:c Nat) (:fv _uniq.23273) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c mkRat) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))))) (:arg :explicit 2 (:app (:c ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Int)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"name":"d","sexp":"(:c Nat)"},{"binder_role":":explicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11456,"sourceStart":11452,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"normalize_eq_mkRat z","source_end":11482,"source_start":11462,"syntax_kind":"Lean.Parser.Term.app"},{"source":"neg_normalize","source_end":11497,"source_start":11484,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.23272","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.23273","is_instance":false,"is_let":false,"user_name":"d"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 57 | 12 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a7422d04d32792ce57f7f1b4d0c1996e6b9160d6709721714899ecc7eb08cb9 | dc1b40ee49839020a297b87f3b1dbd99c9fa8b32d016aacf26ccd0a29292933a | 4fd1806323a0d6d2106be33ee1cfd109148869f33c58f0022d12a9bbb94b0f39 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,050 | PFunctor.M.ichildren_mk | Mathlib/Data/PFunctor/Univariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>PFunctor.M.ichildren</a>, <a>PFunctor.Obj.iget</a>] | F : PFunctor.{u}
X : Type u_1
f : X → ↑F X
inst✝¹ : DecidableEq F.A
inst✝ : Inhabited F.M
x : ↑F F.M
i : F.Idx
⊢ ichildren i (M.mk x) = x.iget i | F : PFunctor.{u}
X : Type u_1
f : X → ↑F X
inst✝¹ : DecidableEq F.A
inst✝ : Inhabited F.M
x : ↑F F.M
i : F.Idx
⊢ (if H' : i.fst = (M.mk x).head then (M.mk x).children (cast ⋯ i.snd) else default) =
if h : i.fst = x.fst then x.snd (cast ⋯ i.snd) else default | ((:c Eq) ((:c PFunctor.M) (:fv _uniq.21836)) ((:c PFunctor.M.ichildren) (:fv _uniq.21836) (:fv _uniq.21988) (:fv _uniq.21987) (:fv _uniq.21990) ((:c PFunctor.M.mk) (:fv _uniq.21836) (:fv _uniq.21989))) ((:c PFunctor.Obj.iget) (:fv _uniq.21836) (:fv _uniq.21987) ((:c PFunctor.M) (:fv _uniq.21836)) (:fv _uniq.21988) (:fv... | [{"name":"F","sexp":"(:c PFunctor)"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.21839) ((:c PFunctor.Obj) (:fv _uniq.21836) (:fv _uniq.21839)))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) ((:c PFunctor.A) (:fv _uniq.21836)))"},{"name":"inst✝","sexp":"((:c Inhabited) ((:c PFunctor... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PFunctor.M) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c PFunctor.M.ichildren) (:arg :implicit 0) (:arg :instance 1 (:instance-of (:app (:c Inhabited) (:arg :explicit 0 (:app (:c PFunctor.M) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21836","is_instance":false,"is_let":false,"name":"F","sexp":"(:c PFunctor)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21839","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":explicit","co... | {"children":[{"source":"dsimp","sourceEnd":18927,"sourceStart":18922,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":18932,"sourceStart":18928,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":18... | [] | [{"source":"ichildren","source_end":18943,"source_start":18934,"syntax_kind":"ident"},{"source":"PFunctor.Obj.iget","source_end":18962,"source_start":18945,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21836","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21839","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 134 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 92d8e48dfaf84bf467c0e90daef21fd57db8a9d17bc357a945b6d78e45751762 | 1a3f44653166d3385f2da39b09ef7da85992f1f39cc82022a9b8006e7188e9df | 4459f8e91beb32c5aefb756801b35f98dc2e418c8ba3cf69dc5a0f44ad45c51b | c20bea7e28ba652240853a926f2728af582a20241c0e3d3c49783639bd5ae18e |
cat-searcher/leandojo-benchmark-4-random | test | 4,051 | PFunctor.M.ichildren_mk | Mathlib/Data/PFunctor/Univariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr with h | F : PFunctor.{u}
X : Type u_1
f : X → ↑F X
inst✝¹ : DecidableEq F.A
inst✝ : Inhabited F.M
x : ↑F F.M
i : F.Idx
⊢ (if H' : i.fst = (M.mk x).head then (M.mk x).children (cast ⋯ i.snd) else default) =
if h : i.fst = x.fst then x.snd (cast ⋯ i.snd) else default | ((:c Eq) ((:c PFunctor.M) (:fv _uniq.21836)) ((:c dite) ((:c PFunctor.M) (:fv _uniq.21836)) ((:c Eq) ((:c PFunctor.A) (:fv _uniq.21836)) ((:c Sigma.fst) ((:c PFunctor.A) (:fv _uniq.21836)) (:lambda x ((:c PFunctor.A) (:fv _uniq.21836)) ((:c PFunctor.B) (:fv _uniq.21836) 0)) (:fv _uniq.21990)) ((:c PFunctor.M.head) (:fv... | [{"name":"F","sexp":"(:c PFunctor)"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.21839) ((:c PFunctor.Obj) (:fv _uniq.21836) (:fv _uniq.21839)))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) ((:c PFunctor.A) (:fv _uniq.21836)))"},{"name":"inst✝","sexp":"((:c Inhabited) ((:c PFunctor... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PFunctor.M) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c dite) (:arg :implicit-type 0 (:app (:c PFunctor.M) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PFunctor.A) (:arg :explicit 0 (:fv FV0)))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21836","is_instance":false,"is_let":false,"name":"F","sexp":"(:c PFunctor)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21839","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":explicit","co... | {"children":[{"source":"congr","sourceEnd":18971,"sourceStart":18966,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"with","sourceEnd":18976,"sourceStart":18972,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"h","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21836","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21839","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":explicit","context_index":2,"internal_name":"_un... | 134 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0812dc9fa8e97c410a318cd1c21e37ca581599a2fa26e61b39d7644b595cd9a8 | c20bea7e28ba652240853a926f2728af582a20241c0e3d3c49783639bd5ae18e | 044fc71ead8b853838b243365458546cfdecba6a3d9d4db603f9e2435bddd338 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,052 | Ordinal.log_mono_right | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hx, <a>Ordinal.log_zero_right</a>, <a>Ordinal.zero_le</a>] | b x y : Ordinal.{u_1}
xy : x ≤ y
hx : x = 0
⊢ log b x ≤ log b y | ((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c Ordinal.log) (:fv _uniq.30049) (:fv _uniq.30050)) ((:c Ordinal.log) (:fv _uniq.30049) (:fv _uniq.30051))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"x","sexp":"(:c Ordinal)"},{"name":"y","sexp":"(:c Ordinal)"},{"name":"xy","sexp":"((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.30050) (:fv _uniq.30051))"},{"name":"hx","sexp":"((:c... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 3 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explici... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30049","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.30050","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Ordinal)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14687,"sourceStart":14683,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":14692,"sourceStart":14688,"tag":"atom"}],"kind"... | [] | [{"source":"hx","source_end":14696,"source_start":14694,"syntax_kind":"ident"},{"source":"log_zero_right","source_end":14712,"source_start":14698,"syntax_kind":"ident"},{"source":"Ordinal.zero_le","source_end":14729,"source_start":14714,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30049","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.30050","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 96 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e8fd65468e99481b51105a84755c1bbefd242913621edd29970256a3046dced3 | d1860591c952b782324e1cdace6e7919def2e53b7bddde6a058545bc6a5a8b8b | 0fbdd4ae62ad2726aacc235b26a6111950f2ba5798cc5f13922db2b0c10fbbc4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,053 | Ordinal.log_mono_right | Mathlib/SetTheory/Ordinal/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Ordinal.log_of_not_one_lt_left</a> hb, <a>Ordinal.zero_le</a>] | b x y : Ordinal.{u_1}
xy : x ≤ y
hx : ¬x = 0
hb : ¬1 < b
⊢ log b x ≤ log b y | ((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c Ordinal.log) (:fv _uniq.30049) (:fv _uniq.30050)) ((:c Ordinal.log) (:fv _uniq.30049) (:fv _uniq.30051))) | [{"name":"b","sexp":"(:c Ordinal)"},{"name":"x","sexp":"(:c Ordinal)"},{"name":"y","sexp":"(:c Ordinal)"},{"name":"xy","sexp":"((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.30050) (:fv _uniq.30051))"},{"name":"hx","sexp":"((:c... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 3 (:app (:c Ordinal.log) (:arg :explicit 0 (:fv FV1)) (:arg :explici... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30049","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.30050","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Ordinal)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14908,"sourceStart":14904,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":14913,"sourceStart":14909,"tag":"atom"}],"kind"... | [] | [{"source":"log_of_not_one_lt_left hb","source_end":14940,"source_start":14915,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Ordinal.zero_le","source_end":14957,"source_start":14942,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.30049","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.30050","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 96 | 7 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f52b0aed5344bdfd08d18939926882476a098c3679dfaac4d2838f9efa1a661 | 6fb32bd5b52e3f7e77891590c34cd9e22856aba1af27270521487a6dbdb6c8bd | 9e35ec693ed5a242fe56a7afc910d0f76cc839dd7e88d00bfe775308b3bd277c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,054 | RCLike.add_conj | Mathlib/Analysis/RCLike/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RCLike.re_add_im</a>, <a>RCLike.conj_eq_re_sub_im</a>] | K : Type u_1
E : Type u_2
inst✝ : RCLike K
z : K
⊢ z + (starRingEnd K) z = ↑(re z) + ↑(im z) * I + (↑(re z) - ↑(im z) * I) | ((:c Eq) (:fv _uniq.77616) ((:c HAdd.hAdd) (:fv _uniq.77616) (:fv _uniq.77616) (:fv _uniq.77616) ((:c instHAdd) (:fv _uniq.77616) ((:c Distrib.toAdd) (:fv _uniq.77616) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.77616) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.77616) ((:c NonUn... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c RCLike) (:fv _uniq.77616))"},{"name":"z","sexp":"(:fv _uniq.77616)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77616","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77619","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14019,"sourceStart":14017,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14021,"sourceStart":14020,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"re_add_im","source_end":14030,"source_start":14021,"syntax_kind":"ident"},{"source":"conj_eq_re_sub_im","source_end":14049,"source_start":14032,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77616","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77619","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 127 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 512c64b2c9fe980113d72db202160a8cd1fc18cad08765a763f6309af4eec679 | 37abee27d4f9ba217d2466956b255a96db00d6b88ad9f9d25f07b0a9f9318cd7 | 6ee8e40010d4e8f844ad7eea486b26b8e1d4be12d4fa41e7853b9b63951d8a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,055 | RCLike.add_conj | Mathlib/Analysis/RCLike/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_add_sub_cancel</a>, <a>two_mul</a>] | K : Type u_1
E : Type u_2
inst✝ : RCLike K
z : K
⊢ ↑(re z) + ↑(im z) * I + (↑(re z) - ↑(im z) * I) = 2 * ↑(re z) | ((:c Eq) (:fv _uniq.77616) ((:c HAdd.hAdd) (:fv _uniq.77616) (:fv _uniq.77616) (:fv _uniq.77616) ((:c instHAdd) (:fv _uniq.77616) ((:c Distrib.toAdd) (:fv _uniq.77616) ((:c NonUnitalNonAssocSemiring.toDistrib) (:fv _uniq.77616) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.77616) ((:c NonUn... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c RCLike) (:fv _uniq.77616))"},{"name":"z","sexp":"(:fv _uniq.77616)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77616","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77619","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14076,"sourceStart":14074,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14078,"sourceStart":14077,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"add_add_sub_cancel","source_end":14096,"source_start":14078,"syntax_kind":"ident"},{"source":"two_mul","source_end":14105,"source_start":14098,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.77616","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.77619","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 127 | 10 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 776537cb1f2629a9fa4759c31aca1616dec32e8c2ed3b8d02926234c18575351 | 2cac09ac34fbeb00078494bf3b299f6fb9684e560b09147ca917f62c1692726a | 17d6219d3ffda0571bed9784d9d22af804cf6831e3b9ea06a46a9d6f8edfc83e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,056 | compact_open_separated_mul_left | Mathlib/Topology/Algebra/Group/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>compact_open_separated_mul_right</a> (hK.image <a>MulOpposite.continuous_op</a>) (opHomeomorph.isOpenMap U hU) (<a>Set.image_subset</a> <a>MulOpposite.op</a> hKU) with ⟨V, hV : V ∈ 𝓝 (<a>MulOpposite.op</a> (1 : G)), hV' : <a>MulOpposite.op</a> '' K * V ⊆ <a>MulOpposite.op</a> '' U⟩ | G : Type w
H : Type x
α : Type u
β : Type v
inst✝² : TopologicalSpace G
inst✝¹ : MulOneClass G
inst✝ : ContinuousMul G
K U : Set G
hK : IsCompact K
hU : IsOpen U
hKU : K ⊆ U
⊢ ∃ V ∈ 𝓝 1, V * K ⊆ U | case intro.intro
G : Type w
H : Type x
α : Type u
β : Type v
inst✝² : TopologicalSpace G
inst✝¹ : MulOneClass G
inst✝ : ContinuousMul G
K U : Set G
hK : IsCompact K
hU : IsOpen U
hKU : K ⊆ U
V : Set Gᵐᵒᵖ
hV : V ∈ 𝓝 (op 1)
hV' : op '' K * V ⊆ op '' U
⊢ ∃ V ∈ 𝓝 1, V * K ⊆ U | ((:c Exists) ((:c Set) (:fv _uniq.363734)) (:lambda V ((:c Set) (:fv _uniq.363734)) ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.363734)) ((:c Filter) (:fv _uniq.363734)) ((:c instMembershipSetFilter) (:fv _uniq.363734)) 0 ((:c nhds) (:fv _uniq.363734) (:fv _uniq.363743) ((:c OfNat.ofNat) (:fv _uniq.363734) (:li... | [{"name":"G","sexp":"(:sort (+ w 1))"},{"name":"H","sexp":"(:sort (+ x 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.363734))"},{"name":"inst✝¹","sexp":"((:c MulOneClass) (:fv _uniq.363734))"},{"name":"inst✝","sexp":"((:c Con... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda V :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rcases","sourceEnd":80041,"sourceStart":80035,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"compact_open_separated_mul_right","semanticRole":"global","source":"compact_open_separated_mul_right","sourceEnd":80074,"sourceStart"... | [] | [{"source":"compact_open_separated_mul_right (hK.image continuous_op) (opHomeomorph.isOpenMap U hU)\n (image_subset op hKU)","source_end":80157,"source_start":80042,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨V, hV : V ∈ 𝓝 (op (1 : G)), hV' : op '' K * V ⊆ op '' U⟩","source_end":80235,"source_start":80167,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 604 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 076114c101e2950ca473306770840983b76a80117686a4cdaba2844552717084 | 30448ebb33890782eb907555062019e4a8db0698db41a4014c4709b8a8b66bf4 | 9d241f359865b71ddd2bb5ff3cc5c2620142889cc9df75a857c5cbd084c06611 | e748bad90ce79676a56f681538c2486779870e779603c8bd1d44367d6abd155f |
cat-searcher/leandojo-benchmark-4-random | test | 4,057 | compact_open_separated_mul_left | Mathlib/Topology/Algebra/Group/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>MulOpposite.op</a> ⁻¹' V, continuous_op.continuousAt hV, ?_⟩ | case intro.intro
G : Type w
H : Type x
α : Type u
β : Type v
inst✝² : TopologicalSpace G
inst✝¹ : MulOneClass G
inst✝ : ContinuousMul G
K U : Set G
hK : IsCompact K
hU : IsOpen U
hKU : K ⊆ U
V : Set Gᵐᵒᵖ
hV : V ∈ 𝓝 (op 1)
hV' : op '' K * V ⊆ op '' U
⊢ ∃ V ∈ 𝓝 1, V * K ⊆ U | case intro.intro
G : Type w
H : Type x
α : Type u
β : Type v
inst✝² : TopologicalSpace G
inst✝¹ : MulOneClass G
inst✝ : ContinuousMul G
K U : Set G
hK : IsCompact K
hU : IsOpen U
hKU : K ⊆ U
V : Set Gᵐᵒᵖ
hV : V ∈ 𝓝 (op 1)
hV' : op '' K * V ⊆ op '' U
⊢ op ⁻¹' V * K ⊆ U | ((:c Exists) ((:c Set) (:fv _uniq.363734)) (:lambda V ((:c Set) (:fv _uniq.363734)) ((:c And) ((:c Membership.mem) ((:c Set) (:fv _uniq.363734)) ((:c Filter) (:fv _uniq.363734)) ((:c instMembershipSetFilter) (:fv _uniq.363734)) 0 ((:c nhds) (:fv _uniq.363734) (:fv _uniq.363743) ((:c OfNat.ofNat) (:fv _uniq.363734) (:li... | [{"name":"G","sexp":"(:sort (+ w 1))"},{"name":"H","sexp":"(:sort (+ x 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.363734))"},{"name":"inst✝¹","sexp":"((:c MulOneClass) (:fv _uniq.363734))"},{"name":"inst✝","sexp":"((:c Con... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda V :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":80244,"sourceStart":80238,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":80248,"sourceStart":80245,"tag":"atom"},{"children":[{"children":[{"name":"MulOpposite.op","semanticRole":"global","source":"op","sourceEnd":80250,"sourceStart":80248,"tag":"identifier"},{"source":... | [] | [{"source":"⟨op ⁻¹' V, continuous_op.continuousAt hV, ?_⟩","source_end":80297,"source_start":80245,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 604 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 746e3763b9dc219b31e9b613a81a7239ba769ea773f8edb09a145de7ef0aa539 | e748bad90ce79676a56f681538c2486779870e779603c8bd1d44367d6abd155f | 99101fd9c18b05e74d2478937c67cf3996b36a1a8157f6ee848a4f2639379d2e | 9798dc37463a82525ad09837bbbf00fcd3684ddb3d1b6ffedc2f8bc24cc72840 |
cat-searcher/leandojo-benchmark-4-random | test | 4,058 | compact_open_separated_mul_left | Mathlib/Topology/Algebra/Group/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>Set.image_preimage_eq</a> V <a>MulOpposite.op_surjective</a>, ← <a>Set.image_op_mul</a>, <a>Set.image_subset_iff</a>, <a>Set.preimage_image_eq</a> _ <a>MulOpposite.op_injective</a>] at hV' | case intro.intro
G : Type w
H : Type x
α : Type u
β : Type v
inst✝² : TopologicalSpace G
inst✝¹ : MulOneClass G
inst✝ : ContinuousMul G
K U : Set G
hK : IsCompact K
hU : IsOpen U
hKU : K ⊆ U
V : Set Gᵐᵒᵖ
hV : V ∈ 𝓝 (op 1)
hV' : op '' K * V ⊆ op '' U
⊢ op ⁻¹' V * K ⊆ U | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.363734)) ((:c Set.instHasSubset) (:fv _uniq.363734)) ((:c HMul.hMul) ((:c Set) (:fv _uniq.363734)) ((:c Set) (:fv _uniq.363734)) ((:c Set) (:fv _uniq.363734)) ((:c instHMul) ((:c Set) (:fv _uniq.363734)) ((:c Set.mul) (:fv _uniq.363734) ((:c MulOneClass.toMul) (:fv _uniq.3637... | [{"name":"G","sexp":"(:sort (+ w 1))"},{"name":"H","sexp":"(:sort (+ x 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.363734))"},{"name":"inst✝¹","sexp":"((:c MulOneClass) (:fv _uniq.363734))"},{"name":"inst✝","sexp":"((:c Con... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rwa","sourceEnd":80303,"sourceStart":80300,"tag":"atom"},{"children":[{"source":"[","sourceEnd":80305,"sourceStart":80304,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":80308,"sourceStart":80305,"tag":"atom"}],"kind":"token.«← »","source"... | [] | [{"source":"hV'","source_end":80424,"source_start":80421,"syntax_kind":"ident"},{"source":"image_preimage_eq V op_surjective","source_end":80342,"source_start":80309,"syntax_kind":"Lean.Parser.Term.app"},{"source":"image_op_mul","source_end":80360,"source_start":80348,"syntax_kind":"ident"},{"source":"image_subset_iff"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.363734","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.363736","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 604 | 6 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2f51a0288e7988fe74416106b937903a6098b6a989332edd5f895e0efdb5c58 | 9798dc37463a82525ad09837bbbf00fcd3684ddb3d1b6ffedc2f8bc24cc72840 | 979f1112d68cdcd8d2880532f3e9d794c0eebde9051bd20d99e4481314583018 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,059 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nontriviality E | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"nontriviality","sourceEnd":97727,"sourceStart":97714,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"E","sourceEnd":97729,"sourceStart":97728,"tag":"identifier"}],"kind":"null","source":"E\n -- first, we use the lemma `to_ring_inverse` to rewrite in terms of `Ring.... | [] | [{"source":"E\n -- first, we use the lemma `to_ring_inverse` to rewrite in terms of `Ring.inverse` in the ring\n -- `E →L[𝕜] E`","source_end":97729,"source_start":97728,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 4 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e7e8b4ad1869314f370d6d9a1d23543b35821dcabeba0462e71f1b3d4e4a0fb4 | 3658021a4ea7ec2799bd8ae8ddda57f9e00df1389ee89a47445b7f32216f48a2 | e4cd31fef42f816e4e4c7b83b1cf0074b3637c75f3d3a670bbcf6e265e41d712 | bbc0bb33e94de26a7e4bab62290522d4b77e1c96a6c436253809373452a6e4a8 |
cat-searcher/leandojo-benchmark-4-random | test | 4,060 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let O₁ : (E →L[𝕜] E) → F →L[𝕜] E := fun f => f.comp (e.symm : F →L[𝕜] E) | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"let","sourceEnd":97854,"sourceStart":97851,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"O₁","sourceEnd":97859,"sourceStart":97855,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":978... | [] | [{"source":"(E →L[𝕜] E) → F →L[𝕜] E","source_end":97897,"source_start":97862,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"fun f => f.comp (e.symm : F →L[𝕜] E)","source_end":97942,"source_start":97901,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 5 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1ea5d9a49b0dd076fa229a0ac7b0e68c5ccf958d259c13ef550635960b06907 | bbc0bb33e94de26a7e4bab62290522d4b77e1c96a6c436253809373452a6e4a8 | df98c77d753a9f4327a22f976b3326aa2707310ae524a4ad4541be909295c425 | 95c75b81846b28dfa5fec9eb770b301e610440acb8a41158982bb3aa753a0157 |
cat-searcher/leandojo-benchmark-4-random | test | 4,061 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let O₂ : (E →L[𝕜] F) → E →L[𝕜] E := fun f => (e.symm : F →L[𝕜] E).<a>ContinuousLinearMap.comp</a> f | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"let","sourceEnd":97948,"sourceStart":97945,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"O₂","sourceEnd":97953,"sourceStart":97949,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":979... | [] | [{"source":"(E →L[𝕜] F) → E →L[𝕜] E","source_end":97991,"source_start":97956,"syntax_kind":"Lean.Parser.Term.arrow"},{"source":"fun f => (e.symm : F →L[𝕜] E).comp f","source_end":98036,"source_start":97995,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 6 | exact | true | 1 | 35 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4b3d0f399e27546369b5ed34bc01f6d00ae2bb1b521c1e9ead993204610e8370 | 95c75b81846b28dfa5fec9eb770b301e610440acb8a41158982bb3aa753a0157 | 598d714db4576f7005a86035c1d455c4b89a57b7dfb6214fcb3783f105f6adf1 | 619b951c8ad865c64da4faea044f9223e8225106bf9b33dcef275a871c887644 |
cat-searcher/leandojo-benchmark-4-random | test | 4,062 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>ContinuousLinearMap.inverse</a> = O₁ ∘ <a>Ring.inverse</a> ∘ O₂ := <a>funext</a> (<a>ContinuousLinearMap.to_ring_inverse</a> e) | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"have","sourceEnd":98043,"sourceStart":98039,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":98044,"sourceStart":98044,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":98044,"sourceStart":98044,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"ContinuousLinearMap.inverse = O₁ ∘ Ring.inverse ∘ O₂","source_end":98106,"source_start":98046,"syntax_kind":"«term_=_»"},{"source":"funext (to_ring_inverse e)","source_end":98136,"source_start":98110,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 7 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f47f50c1d813a80b491a0cfef4991ab36cc7008b639a70948d64d0b8e3d45c57 | 619b951c8ad865c64da4faea044f9223e8225106bf9b33dcef275a871c887644 | d3518a0bd6a08a124ca4b763a6f02691840c8aefab4e655d94b2af9759816281 | 4f06e4a07d7af30f128bb2296924cdd717a385f49657acdc28210ed02a83c3a0 |
cat-searcher/leandojo-benchmark-4-random | test | 4,063 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"rw","sourceEnd":98141,"sourceStart":98139,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":98143,"sourceStart":98142,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":37,"seman... | [] | [{"source":"this","source_end":98147,"source_start":98143,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 8 | exact | true | 1 | 37 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b740d366f964dd14f50e55a93a179aa625eb53fda469b406e0cb7628984e50cb | 4f06e4a07d7af30f128bb2296924cdd717a385f49657acdc28210ed02a83c3a0 | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | da58f872e36fd0326f4f84fbe561f3c3141bf0b54c5db73c2ec785f2c58b8d11 |
cat-searcher/leandojo-benchmark-4-random | test | 4,064 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₁ : <a>ContDiff</a> 𝕜 n O₁ := contDiff_id.clm_comp <a>contDiff_const</a> | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"have","sourceEnd":98257,"sourceStart":98253,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":98262,"sourceStart":98258,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₁","sourceEnd":98262,"sourceStart":98258,"tag":"nod... | [] | [{"source":"ContDiff 𝕜 n O₁","source_end":98285,"source_start":98265,"syntax_kind":"Lean.Parser.Term.app"},{"source":"contDiff_id.clm_comp contDiff_const","source_end":98324,"source_start":98289,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 11 | exact | true | 1 | 37 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b353b61fe1d74739af418ee0769fe0ba451f31cce7c02a6dbf5cbf7f53bd85f | da58f872e36fd0326f4f84fbe561f3c3141bf0b54c5db73c2ec785f2c58b8d11 | 2de33247876c358c5460d717ec06bbbebe4168263294f050469e305269a15702 | b6e5ccc661f7246ba5705c93843e31e8f356d8d4c41b2a74bf4f18eef8959baa |
cat-searcher/leandojo-benchmark-4-random | test | 4,065 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₂ : <a>ContDiff</a> 𝕜 n O₂ := contDiff_const.clm_comp <a>contDiff_id</a> | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"have","sourceEnd":98331,"sourceStart":98327,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":98336,"sourceStart":98332,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₂","sourceEnd":98336,"sourceStart":98332,"tag":"nod... | [] | [{"source":"ContDiff 𝕜 n O₂","source_end":98359,"source_start":98339,"syntax_kind":"Lean.Parser.Term.app"},{"source":"contDiff_const.clm_comp contDiff_id","source_end":98398,"source_start":98363,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 12 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc169f4c1cc46fc512a7dadf6663969c567820425f4dee145269c93e3ee78431 | b6e5ccc661f7246ba5705c93843e31e8f356d8d4c41b2a74bf4f18eef8959baa | a2e67eb0fe11d869a2b8a3c8f175dcd54cfeb6378c1e350e495422da603b2e9a | 7e2056cea87db87d692bcfe4dc22d8e7b956ef2f501078864c2f19a671017aa6 |
cat-searcher/leandojo-benchmark-4-random | test | 4,066 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine h₁.contDiffAt.comp _ (<a>ContDiffAt.comp</a> _ ?_ h₂.contDiffAt) | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"refine","sourceEnd":98407,"sourceStart":98401,"tag":"atom"},{"children":[{"source":"h₁.contDiffAt.comp","sourceEnd":98428,"sourceStart":98408,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":98430,"sourceStart":98429,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"... | [] | [{"source":"h₁.contDiffAt.comp _ (ContDiffAt.comp _ ?_ h₂.contDiffAt)","source_end":98469,"source_start":98408,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 13 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6df13cd699026ee047fcff9cd6f453a69ea0b4ee64f6e39a21f6ffef5b03bdd6 | 7e2056cea87db87d692bcfe4dc22d8e7b956ef2f501078864c2f19a671017aa6 | 9f9d98d1045ba9766ce25c1ef97c729c7b25129e23faca514549e6503d751708 | 1bd7ea48a77dca5a9256d4d754682250aa257b1a2f925b89167e408b73b09fc8 |
cat-searcher/leandojo-benchmark-4-random | test | 4,067 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>contDiffAt_ring_inverse</a> 𝕜 (1 : (E →L[𝕜] E)ˣ) | 𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : NormedSpace �... | case h.e'_11
𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : ... | ((:c ContDiffAt) (:fv _uniq.1912313) (:fv _uniq.1912316) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (:app (:c ContDiffAt) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiri... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"convert","sourceEnd":98479,"sourceStart":98472,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"contDiffAt_ring_inverse","semanticRole":"global","source":"contDiffAt_ring_inverse","sourceEnd":98503,"... | [] | [{"source":"contDiffAt_ring_inverse 𝕜 (1 : (E →L[𝕜] E)ˣ)","source_end":98533,"source_start":98480,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 14 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb44c48c29d0145cc9a4971dd1fe991ac204fd629c3446b36933f55abe481aba | 1bd7ea48a77dca5a9256d4d754682250aa257b1a2f925b89167e408b73b09fc8 | 8ce59be6c97357f170fbc24e199cdf49d9b5a53aa6f4a0f903f2928aca3c0b0e | 1d716dce928b2b02801d619fadd84e2b27519cc350496b1f15db7d1376367a13 |
cat-searcher/leandojo-benchmark-4-random | test | 4,068 | contDiffAt_map_inverse | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [O₂, <a>ContinuousLinearMap.one_def</a>] | case h.e'_11
𝕜 : Type u_1
inst✝¹¹ : NontriviallyNormedField 𝕜
D : Type uD
inst✝¹⁰ : NormedAddCommGroup D
inst✝⁹ : NormedSpace 𝕜 D
E : Type uE
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedSpace 𝕜 E
F : Type uF
inst✝⁶ : NormedAddCommGroup F
inst✝⁵ : NormedSpace 𝕜 F
G : Type uG
inst✝⁴ : NormedAddCommGroup G
inst✝³ : ... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.1912313) (:fv _uniq.1912313) ((:c DivisionSemiring.toSemiring) (:fv _uniq.1912313) ((:c Semifield.toDivisionSemiring) (:fv _uniq.1912313) ((:c Field.toSemifield) (:fv _uniq.1912313) ((:c NormedField.toField) (:fv _uniq.1912313) ((:c NontriviallyNormedField.toNormedField) (:... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.1912313))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝¹⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.1912318))"},{"name":"inst✝⁹","sexp":"((:c NormedSpace) (:fv _uniq.1912313) (:fv _uniq.1912318) ((:... | (: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.1912313","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"name":"inst✝¹¹","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"simp","sourceEnd":98540,"sourceStart":98536,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":98542,"sourceStart":98541,"tag":"a... | [] | [{"source":"O₂","source_end":98546,"source_start":98542,"syntax_kind":"ident"},{"source":"one_def","source_end":98555,"source_start":98548,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1912313","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1912316","is_instance":true,"is_let":false,"user_name":"inst✝¹¹"},{"binder_role":":implicit","context_index":2,"... | 476 | 15 | exact | true | 1 | 39 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 218762f699ac92a4999a2a4fa54ed928f76ef854b0c8e03e6d823fa78d471475 | 1d716dce928b2b02801d619fadd84e2b27519cc350496b1f15db7d1376367a13 | 1c4e454bd93ac35177b4b31dcf2c5fefe3af919c8123f64fb40dde148b6e0f9d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,069 | Finset.max'_mem | Mathlib/Data/Finset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Finset.max'</a>, <a>Finset.max</a>, <a>id_eq</a>, <a>Finset.coe_sup'</a>] | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
s : Finset α
H : s.Nonempty
x : α
⊢ s.max = ↑(s.max' H) | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
s : Finset α
H : s.Nonempty
x : α
⊢ s.sup WithBot.some = s.sup (WithBot.some ∘ fun x => x) | ((:c Eq) ((:c WithBot) (:fv _uniq.362193)) ((:c Finset.max) (:fv _uniq.362193) (:fv _uniq.362208) (:fv _uniq.362211)) ((:c WithBot.some) (:fv _uniq.362193) ((:c Finset.max') (:fv _uniq.362193) (:fv _uniq.362208) (:fv _uniq.362211) (:fv _uniq.362218)))) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.362193))"},{"name":"s","se... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Finset.max) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV7)))) (:arg :explicit 2 (:app (:c WithBot.some)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.362190","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.362193","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":65289,"sourceStart":65285,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":65294,"sourceStart":65290,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":652... | [] | [{"source":"max'","source_end":65300,"source_start":65296,"syntax_kind":"ident"},{"source":"Finset.max","source_end":65312,"source_start":65302,"syntax_kind":"ident"},{"source":"id_eq","source_end":65319,"source_start":65314,"syntax_kind":"ident"},{"source":"coe_sup'","source_end":65329,"source_start":65321,"syntax_kin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.362190","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.362193","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 555 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d41fe25e29597ab674b302f6a22b4546dd3c9095e140b0dde6a5523a9cd987e | 96c04ade0757f52e87c85ad90ba5e79d833e70b8e9ebd39be51e4263d4365d5e | b8f1e9deb78734606e302eaa319f63e8d357e5b7edd9acafde70bd9143d772e1 | 5fb58b5e237c92e4c753ef5db019af7c1372e08a0d352d578cdb3fd29ce45ba6 |
cat-searcher/leandojo-benchmark-4-random | test | 4,070 | Finset.max'_mem | Mathlib/Data/Finset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | F : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
ι : Type u_5
κ : Type u_6
inst✝ : LinearOrder α
s : Finset α
H : s.Nonempty
x : α
⊢ s.sup WithBot.some = s.sup (WithBot.some ∘ fun x => x) | ((:c Eq) ((:c WithBot) (:fv _uniq.362193)) ((:c Finset.sup) ((:c WithBot) (:fv _uniq.362193)) (:fv _uniq.362193) ((:c WithBot.semilatticeSup) (:fv _uniq.362193) ((:c Lattice.toSemilatticeSup) (:fv _uniq.362193) ((:c DistribLattice.toLattice) (:fv _uniq.362193) ((:c instDistribLatticeOfLinearOrder) (:fv _uniq.362193) (:... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.362193))"},{"name":"s","se... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Finset.sup) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c SemilatticeSup) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.362190","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.362193","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rfl","sourceEnd":65335,"sourceStart":65332,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":65335,"sourceStart":65332,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.362190","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.362193","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 555 | 6 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f4c74919095413debe584809ec580e2cdf91a85c9beae135e7f14dadcaa842f | 5fb58b5e237c92e4c753ef5db019af7c1372e08a0d352d578cdb3fd29ce45ba6 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,071 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases H | α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
n : ℕ
m : Fin n → β
H : Agrees arr f m
k : ℕ
hk : k = n + 1
x : α
m' : Fin k → β
hm₁ : ∀ (i : Fin k) (h : ↑i < n), m' i = m ⟨↑i, h⟩
hm₂ : ∀ (h : n < k), f x = m' ⟨n, h⟩
⊢ Agrees (arr.push x) f m' | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
⊢ Agrees (arr.push x) f m' | ((:c UFModel.Agrees) (:fv _uniq.12045) (:fv _uniq.12046) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054)) (:fv _uniq.12047) (:fv _uniq.12052) (:fv _uniq.12055)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:forall _ ((:c Fin) (:fv _uniq.12049)) (:fv _uniq.12046))"},{"name":... | (:app (:c UFModel.Agrees) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Array.push) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 3 (:fv FV3)) (:arg :implicit 4) (:arg :explicit 5 (:fv FV11))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"cases","sourceEnd":3237,"sourceStart":3232,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"H","sourceEnd":3239,"sourceStart":3238,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","source... | [] | [{"source":"H","source_end":3239,"source_start":3238,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3510a6b87ffcca30311198d94577781f79b607eb0dfc553ecda6a69f146d10f | 656140ca2370e381e0b1fc3bc496a859743b34086342ffdea5350bb6d6fc858d | 491d4f98a8c092bee881935584bbb6d1677696fc9dcb5a47e2cc56caaf4edaa6 | 44eaa68197b65a8326160a411efb8376f84596f0bfba75fae4eecefdc777380e |
cat-searcher/leandojo-benchmark-4-random | test | 4,072 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : k = (arr.push x).<a>Array.size</a> := by simp [hk] | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
⊢ Agrees (arr.push x) f m' | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
⊢ Agrees (arr.push x) f m' | ((:c UFModel.Agrees) (:fv _uniq.12045) (:fv _uniq.12046) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054)) (:fv _uniq.12047) (:fv _uniq.12052) (:fv _uniq.12055)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c UFModel.Agrees) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Array.push) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)))) (:arg :explicit 3 (:fv FV3)) (:arg :implicit 4) (:arg :explicit 5 (:fv FV7))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":3246,"sourceStart":3242,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":3247,"sourceStart":3247,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":3247,"sourceStart":3247,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"k = (arr.push x).size","source_end":3270,"source_start":3249,"syntax_kind":"«term_=_»"},{"source":"hk","source_end":3285,"source_start":3283,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 5 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20813674268b0c066c0e099d8f907f6a5977278ca1f671ae672396454b8a9a7b | 44eaa68197b65a8326160a411efb8376f84596f0bfba75fae4eecefdc777380e | 55bd5a1a1011b4e177c8227ebf80c447bf68db0f36d2c7fae09b345e40e0d62f | d4b7c50074b88532f4d1d906b8a96b23dc7c702cba6a8df1ac32f2bab6955401 |
cat-searcher/leandojo-benchmark-4-random | test | 4,073 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>UFModel.Agrees.mk'</a> this fun i h₁ h₂ ↦ ?_ | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
⊢ Agrees (arr.push x) f m' | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
⊢ f ((ar... | ((:c UFModel.Agrees) (:fv _uniq.12045) (:fv _uniq.12046) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054)) (:fv _uniq.12047) (:fv _uniq.12052) (:fv _uniq.12055)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c UFModel.Agrees) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :explicit 2 (:app (:c Array.push) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)))) (:arg :explicit 3 (:fv FV3)) (:arg :implicit 4) (:arg :explicit 5 (:fv FV7))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":3295,"sourceStart":3289,"tag":"atom"},{"children":[{"name":"UFModel.Agrees.mk'","semanticRole":"global","source":"mk'","sourceEnd":3299,"sourceStart":3296,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"this","sourceEnd":3304,"sourceStart"... | [] | [{"source":"mk' this fun i h₁ h₂ ↦ ?_","source_end":3327,"source_start":3296,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c2e9d05e190808d4456b850530c5722ef5296a3de419920351a6994908abe0c | d4b7c50074b88532f4d1d906b8a96b23dc7c702cba6a8df1ac32f2bab6955401 | 4a0148e135aea4b1d6f3a9701e213fc896a6b0c11e16ceb3b638e971a4c4d777 | 6c6930cb87577086b40403896aea3c9d397209d63982820aa0c77751da376b7a |
cat-searcher/leandojo-benchmark-4-random | test | 4,074 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Array.get_push</a>] | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
⊢ f ((ar... | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
⊢ f (if ... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) ((:c Array.get) (:fv _uniq.12045) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054)) ((:c Fin.mk) ((:c Array.size) (:fv _uniq.12045) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054))) (:fv _uniq.12301) (:fv _uniq.12304)))) ((:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:app (:c Array.get) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Array.push) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6)))) (:arg :explicit 2 (:app (:c Fin... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":3334,"sourceStart":3330,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3336,"sourceStart":3335,"tag":"atom"... | [] | [{"source":"Array.get_push","source_end":3350,"source_start":3336,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 9 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bd47e7d1854c85333b442a01341f8c5d05980f361a520b1f700a5760891f287d | 6c6930cb87577086b40403896aea3c9d397209d63982820aa0c77751da376b7a | 74fd808e7c2c483b918061faa95fd58245cb41c9e2ee905c010b5cdad7b4b22d | dbcaa126faee6f1728b649376e8e67cbc159bb708ecaa7a96ed9c9a27dbf6b79 |
cat-searcher/leandojo-benchmark-4-random | test | 4,075 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split <;> (rename_i h; simp at hm₁ ⊢) | case mk
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
⊢ f (if ... | case mk.isTrue
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : i < arr.size
⊢ f arr... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) ((:c dite) (:fv _uniq.12045) ((:c LT.lt) (:c Nat) (:c instLTNat) (:fv _uniq.12301) ((:c Array.size) (:fv _uniq.12045) (:fv _uniq.12048))) ((:c Nat.decLt) (:fv _uniq.12301) ((:c Array.size) (:fv _uniq.12045) (:fv _uniq.12048))) (:lambda h ((:c LT.lt) (:c Nat) (:c instLTNat) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:app (:c dite) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (: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 (:fv FV... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"source":"split","sourceEnd":3358,"sourceStart":3353,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":3358,"sourceStart":3353,"tag":"node"},{"source":"<;>... | [] | [{"source":"hm₁","source_end":3389,"source_start":3384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 11 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5732306a1e764670c9025e3eef2a8470643f9d83858b444a1a103ccb29275ece | dbcaa126faee6f1728b649376e8e67cbc159bb708ecaa7a96ed9c9a27dbf6b79 | d41eb1b30ae2eb7e61678deceee893c11a1af19fc88832b21134ea322ff3a511 | 61da230c7e1795496b6e6c94d0e3e6602bbe1977ca06b872594245e1d1d6d131 |
cat-searcher/leandojo-benchmark-4-random | test | 4,076 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hk] | α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
⊢ k = (arr.push x).size | ((:c Eq) (:c Nat) (:fv _uniq.12052) ((:c Array.size) (:fv _uniq.12045) ((:c Array.push) (:fv _uniq.12045) (:fv _uniq.12048) (:fv _uniq.12054)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV5)) (:arg :explicit 2 (:app (:c Array.size) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Array.push) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV6))))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":3281,"sourceStart":3277,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3283,"sourceStart":3282,"tag":"atom"... | [] | [{"source":"hk","source_end":3285,"source_start":3283,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d1088cd6324ff11bdeb535092a2d04c298ad0534050bd7bd6ef42bfd4abfb222 | 243f962767009a41cdc92de9f5607e994f1c6d65c9fb7b587bcf904687e43c9b | a55b331c40c5dcc55c6e556abd63391162b89e4b11baf7f6baf0d353958bbb70 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,077 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rename_i h | case mk.isFalse
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
... | case mk.isFalse
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) (:fv _uniq.12054)) ((:fv _uniq.12055) ((:c Fin.mk) (:fv _uniq.12052) (:fv _uniq.12301) (:fv _uniq.12307)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 2 (:app (:fv FV7) (:arg :explicit 0 (:app (:c Fin.mk) (:arg :implicit 0) (:arg :explicit 1 (:fv FV12)) (:arg :proof 2 (:proof-of (:metavar)))))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rename_i","sourceEnd":3372,"sourceStart":3364,"tag":"atom"},{"children":[{"children":[{"contextIndex":15,"semanticRole":"local","source":"h","sourceEnd":3374,"sourceStart":3373,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"h","sourceEnd":3374,"sourceStart":3373,"tag":"node"}],"kind":"... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 23 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4127843411dbbbee0447bf2938d7d0c421a2aeadf36c261c8441fd76f9289a22 | 4dc173f38f8810e0664ac78683ecafa5447bbe5f269b4f8af2c2757a3ce98bb6 | 8c3f348f8b972d3b3c8df7823438c9a74cdf78774d2323311fdc358bdc7f80fd | ad81b70074886d6fc6856baec018c651cc257be00660946c47cb34e4c0cb897f |
cat-searcher/leandojo-benchmark-4-random | test | 4,078 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp at hm₁ ⊢ | case mk.isFalse
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = (fun i => f (arr.get i)) ⟨↑i, h⟩
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
... | case mk.isFalse
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : ¬i < arr.size
⊢ f x... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) (:fv _uniq.12054)) ((:fv _uniq.12055) ((:c Fin.mk) (:fv _uniq.12052) (:fv _uniq.12301) (:fv _uniq.12307)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 2 (:app (:fv FV7) (:arg :explicit 0 (:app (:c Fin.mk) (:arg :implicit 0) (:arg :explicit 1 (:fv FV12)) (:arg :proof 2 (:proof-of (:metavar)))))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":3380,"sourceStart":3376,"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":[{"child... | [] | [{"source":"hm₁","source_end":3389,"source_start":3384,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 25 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43b517661b61838fab9bba2c47422a21c6e020dba9793980fecb8e1ca09a3040 | ad81b70074886d6fc6856baec018c651cc257be00660946c47cb34e4c0cb897f | e08a1565564eaee2337d588e3126ecc5a32046ef54f16c91cb8e2ac1f2f74b8d | 74b7db165e597af993ce64cb6c37e638d5d7c6d9fa1f03401be890f809e5e114 |
cat-searcher/leandojo-benchmark-4-random | test | 4,079 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hm₁ ⟨i, h₂⟩] | case mk.isTrue
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : i < arr.size
⊢ f arr... | case mk.isTrue
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : i < arr.size
⊢ ↑⟨i, ... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) ((:c GetElem.getElem) ((:c Array) (:fv _uniq.12045)) (:c Nat) (:fv _uniq.12045) (:lambda xs ((:c Array) (:fv _uniq.12045)) (:lambda i (:c Nat) ((:c LT.lt) (:c Nat) (:c instLTNat) 0 ((:c Array.size) (:fv _uniq.12045) 1)))) ((:c Array.instGetElemNatLtSize) (:fv _uniq.12045)) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:app (:c GetElem.getElem) (:arg :implicit-type 0 (:app (:c Array) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV1)) (:arg :implicit 3) (:arg :instance 4 (:instance-of (:ap... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":3402,"sourceStart":3400,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3404,"sourceStart":3403,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":3407,"sourceStart":... | [] | [{"source":"hm₁ ⟨i, h₂⟩","source_end":3427,"source_start":3408,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 30 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e0f00a60b784313026388f58f1d175fb589935d1daab96fd21db9e784086df1 | 07654121ae1e5b4df2cbd727b44df35348d006c15fc366e65f2d6d25a1b612d6 | fe9aef19178be6c50b7dbba0259e30448d724b7c385ac308a1142f9dbb1d83c2 | f02e3b65d7a7c4652725012aa55a20a02928a7bf124cf23b3e0d0577bc9d4c91 |
cat-searcher/leandojo-benchmark-4-random | test | 4,080 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | case mk.isTrue
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : i < arr.size
⊢ ↑⟨i, ... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Fin.val) (:fv _uniq.12052) ((:c Fin.mk) (:fv _uniq.12052) (:fv _uniq.12301) (:fv _uniq.12307))) ((:c Array.size) (:fv _uniq.12045) (:fv _uniq.12048))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (: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 Fin.val) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Fin.mk) (:arg :implicit 0) (:arg :explicit 1 (:fv FV12)) (:arg :proof 2 (:proof-of (:metavar))))))) (:arg :ex... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"assumption","sourceEnd":3440,"sourceStart":3430,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":3440,"sourceStart":3430,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 34 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a36234d62d9eea27b1060d6c59dd50df6705371bdd411adc7d2272e97016b23c | f02e3b65d7a7c4652725012aa55a20a02928a7bf124cf23b3e0d0577bc9d4c91 | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,081 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases show i = arr.size by apply <a>Nat.le_antisymm</a> <;> simp_all [<a>Nat.lt_succ</a>] | case mk.isFalse
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : ¬i < arr.size
⊢ f x... | case mk.isFalse.refl
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
h₁ : arr.size < (arr.push x).size
h₂ : arr.size < k
h : ¬arr.s... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) (:fv _uniq.12054)) ((:fv _uniq.12055) ((:c Fin.mk) (:fv _uniq.12052) (:fv _uniq.12301) (:fv _uniq.12307)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 2 (:app (:fv FV7) (:arg :explicit 0 (:app (:c Fin.mk) (:arg :implicit 0) (:arg :explicit 1 (:fv FV12)) (:arg :proof 2 (:proof-of (:metavar)))))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"cases","sourceEnd":3451,"sourceStart":3446,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"show","sourceEnd":3456,"sourceStart":3452,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"i","sourceEnd... | [] | [{"source":"show i = arr.size by apply Nat.le_antisymm <;> simp_all [Nat.lt_succ]","source_end":3521,"source_start":3452,"syntax_kind":"Lean.Parser.Term.show"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 39 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 16c40658b5a7be846b75db1e95f6f1158ffdeb2edae7d6e268579dd7b3457b67 | 74b7db165e597af993ce64cb6c37e638d5d7c6d9fa1f03401be890f809e5e114 | ee5b084f3516677a84c0b0f467147d9508dca2e14625504ba8f4739cecc7f74a | f2395582fe28d2bf7f056f8a7848c27fd6ad17640536e9a176a1e57290e406c1 |
cat-searcher/leandojo-benchmark-4-random | test | 4,082 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hm₂] | case mk.isFalse.refl
α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
h₁ : arr.size < (arr.push x).size
h₂ : arr.size < k
h : ¬arr.s... | ((:c Eq) (:fv _uniq.12046) ((:fv _uniq.12047) (:fv _uniq.12054)) ((:fv _uniq.12055) ((:c Fin.mk) (:fv _uniq.12052) ((:c Array.size) (:fv _uniq.12045) (:fv _uniq.12048)) (:fv _uniq.16073)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV3) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 2 (:app (:fv FV7) (:arg :explicit 0 (:app (:c Fin.mk) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Array.size) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4)))) (:arg :proof ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":3528,"sourceStart":3526,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3530,"sourceStart":3529,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":9,"semanticRo... | [] | [{"source":"hm₂","source_end":3535,"source_start":3530,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 47 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ac8bb4acb3e265c9e9700dea4f6b5673477bf7b68544742bbebdbe4e5b762c0 | f2395582fe28d2bf7f056f8a7848c27fd6ad17640536e9a176a1e57290e406c1 | e7bef7eaa41b79a7032f2b03cb4517e27fc8c067ab0e23fd32908e58ab78d8d8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,083 | UFModel.Agrees.push | Mathlib/Data/UnionFind.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Nat.le_antisymm</a> <;> simp_all [<a>Nat.lt_succ</a>] | α : Type u_1
β : Sort u_2
f : α → β
arr : Array α
k : ℕ
x : α
m' : Fin k → β
hk : k = arr.size + 1
hm₂ : ∀ (h : arr.size < k), f x = m' ⟨arr.size, h⟩
hm₁ : ∀ (i : Fin k) (h : ↑i < arr.size), m' i = f arr[↑i]
this : k = (arr.push x).size
i : ℕ
h₁ : i < (arr.push x).size
h₂ : i < k
h : ¬i < arr.size
⊢ i = arr.size | ((:c Eq) (:c Nat) (:fv _uniq.12301) ((:c Array.size) (:fv _uniq.12045) (:fv _uniq.12048))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort u_2)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.12045) (:fv _uniq.12046))"},{"name":"arr","sexp":"((:c Array) (:fv _uniq.12045))"},{"name":"k","sexp":"(:c Nat)"},{"name":"x","sexp":"(:fv _uniq.12045)"},{"name":"m'","sexp":"(:forall _ ((:c Fin) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV12)) (:arg :explicit 2 (:app (:c Array.size) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV4))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":3478,"sourceStart":3473,"tag":"atom"},{"name":"Nat.le_antisymm","semanticRole":"global","source":"Nat.le_antisymm","sourceEnd":3494,"sourceStart":3479,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Nat... | [] | [{"source":"Nat.le_antisymm","source_end":3494,"source_start":3479,"syntax_kind":"ident"},{"source":"Nat.lt_succ","source_end":3520,"source_start":3509,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.12045","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.12046","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 16 | 40 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ea7d59c903015b2c68facdb4a0ce08036c5e9afc0c03cf2dbb1d4a840a1e76d | aa9cc6521861541077150d4ef05110deee686a9a2612f230eb9c12d747fa76dc | 142aaa11261f372df657300babfdcb828227df89866b731598f66525b3eac891 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,084 | inv_mul_cancel_left₀ | Mathlib/Algebra/GroupWithZero/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | α : Type u_1
M₀ : Type u_2
G₀ : Type u_3
M₀' : Type u_4
G₀' : Type u_5
F : Type u_6
F' : Type u_7
inst✝ : GroupWithZero G₀
a b✝ c g h✝ x : G₀
h : a ≠ 0
b : G₀
⊢ a⁻¹ * a * b = b | ((:c Eq) (:fv _uniq.21938) ((:c HMul.hMul) (:fv _uniq.21938) (:fv _uniq.21938) (:fv _uniq.21938) ((:c instHMul) (:fv _uniq.21938) ((:c MulZeroClass.toMul) (:fv _uniq.21938) ((:c MulZeroOneClass.toMulZeroClass) (:fv _uniq.21938) ((:c MonoidWithZero.toMulZeroOneClass) (:fv _uniq.21938) ((:c GroupWithZero.toMonoidWithZero... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M₀","sexp":"(:sort (+ u_2 1))"},{"name":"G₀","sexp":"(:sort (+ u_3 1))"},{"name":"M₀'","sexp":"(:sort (+ u_4 1))"},{"name":"G₀'","sexp":"(:sort (+ u_5 1))"},{"name":"F","sexp":"(:sort (+ u_6 1))"},{"name":"F'","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝","sexp":"((:c Gro... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21932","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21935","is_instance":false,"is_let":false,"name":"M₀","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10858,"sourceStart":10854,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"h","source_end":10861,"source_start":10860,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21932","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.21935","is_instance":false,"is_let":false,"user_name":"M₀"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 117 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5ea9c651d95ebd79fcbe4378f856ccad48f19f65e543b4de8471520c2174813 | b65d4bcb9c5ccd4ae231a362630e7d9f80b73fe1f55f8f8675ddb0067af0260f | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,085 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>Classical.decEq</a> ι | R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
⊢ (norm R) ((algebraMap R S) x) = x ^ Fin... | R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢ (norm R) ((algebra... | ((:c Eq) (:fv _uniq.18680) ((:c DFunLike.coe) ((:c MonoidHom) (:fv _uniq.18683) (:fv _uniq.18680) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.18683) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.18683) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.18683) ((:c Ring.toSemiring) (:fv _uniq.18683) (:fv _uniq.18692)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"haveI","sourceEnd":3230,"sourceStart":3225,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":3231,"sourceStart":3231,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":3231,"sourceStart":3231,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"Classical.decEq ι","source_end":3252,"source_start":3234,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 4 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32b7d06edcec37ca899d76b0da08e2669eceaf2ea6eec68ae18572c61084db0d | 8ffa37403b01624d496315f157d117c239ecb93369f51350a35073fcf0d6b962 | cdfb05de47591e6513f67e8d3a9c041a6068ec8ace5483e8ee4ba8fc1feb0fa5 | 4395a34fdba50d8fc915f7359caf9b9e14c80e62df39dbbbca7de22a9df7c789 |
cat-searcher/leandojo-benchmark-4-random | test | 4,086 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Algebra.norm_apply</a>, ← <a>LinearMap.det_toMatrix</a> b, <a>Algebra.lmul_algebraMap</a>] | R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢ (norm R) ((algebra... | R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢ ((toMatrix b b) ((... | ((:c Eq) (:fv _uniq.18680) ((:c DFunLike.coe) ((:c MonoidHom) (:fv _uniq.18683) (:fv _uniq.18680) ((:c MulZeroOneClass.toMulOneClass) (:fv _uniq.18683) ((:c NonAssocSemiring.toMulZeroOneClass) (:fv _uniq.18683) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.18683) ((:c Ring.toSemiring) (:fv _uniq.18683) (:fv _uniq.18692)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidHom) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c MulOneClass) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":3257,"sourceStart":3255,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3259,"sourceStart":3258,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Algebra.norm_apply",... | [] | [{"source":"norm_apply","source_end":3269,"source_start":3259,"syntax_kind":"ident"},{"source":"det_toMatrix b","source_end":3289,"source_start":3275,"syntax_kind":"Lean.Parser.Term.app"},{"source":"lmul_algebraMap","source_end":3306,"source_start":3291,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 5 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 28a4531cf4bcece84966db98823ae697047a120ffb802c01fe8631b9f88200b2 | 4395a34fdba50d8fc915f7359caf9b9e14c80e62df39dbbbca7de22a9df7c789 | e5b53bcb7f99209bb1539016fd6204fe8476496c39e8d9b2c2f85efeeb079985 | 88ea0b662fd082633c93782707911d42be416e065a47bddf6be56beb966f06d3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,087 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert @<a>Matrix.det_diagonal</a> _ _ _ _ _ fun _ : ι => x | R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢ ((toMatrix b b) ((... | case h.e'_2.h.e'_6
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢... | ((:c Eq) (:fv _uniq.18680) ((:c Matrix.det) (:fv _uniq.19187) (:fv _uniq.20525) (:fv _uniq.20516) (:fv _uniq.18680) (:fv _uniq.18689) ((:c DFunLike.coe) ((:c LinearEquiv) (:fv _uniq.18680) (:fv _uniq.18680) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c CommRing.toCommSemiring) (:fv _uniq.18680) (:fv _uniq.18689)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV14)) (:arg :instance 1 (:instance-of (:metavar))) (:arg :instance 2 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV14))))) (:arg :implicit-type 3 (:fv FV0)) (:arg :instance 4 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":3317,"sourceStart":3310,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"@","sourceEnd":3319,"sourceStart":3318,"tag":"atom"},{"name":"Matrix.det_diagonal","semant... | [] | [{"source":"@det_diagonal _ _ _ _ _ fun _ : ι => x","source_end":3357,"source_start":3318,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 10 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b1e49a7cf44bb4080aa947c055db7e22753a0ba3dc3fd0ebed6c4867ee65ab78 | 88ea0b662fd082633c93782707911d42be416e065a47bddf6be56beb966f06d3 | d9d8dda6092adc55d1c2a8dc422e41d2886c01f06d858823bde3d3999e922f8e | 6ab77eb2c135214510d04dd16485107f6a05c4142700dcabd7760a0106f45206 |
cat-searcher/leandojo-benchmark-4-random | test | 4,088 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext (i j) | case h.e'_2.h.e'_6
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢... | case h.e'_2.h.e'_6.a
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι... | ((:c Eq) ((:c Matrix) (:fv _uniq.19187) (:fv _uniq.19187) (:fv _uniq.18680)) ((:c DFunLike.coe) ((:c LinearEquiv) (:fv _uniq.18680) (:fv _uniq.18680) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c CommRing.toCommSemiring) (:fv _uniq.18680) (:fv _uniq.18689))) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c C... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV14)) (:arg :explicit 1 (:fv FV14)) (:arg :explicit 2 (:fv FV0)))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearEquiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext","sourceEnd":3366,"sourceStart":3363,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":3368,"sourceStart":3367,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":3369,"sourceStart":3368,"tag":"identifier"}],"kind":"Lea... | [{"role":"fresh_name","source":"i","source_end":3369,"source_start":3368,"syntax_kind":"ident"},{"role":"fresh_name","source":"j","source_end":3371,"source_start":3370,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 15 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aae80be51238b7bc6ff0166cdd76c15d9199e40a1616ca673cd3f0b84725ed7c | 1ca7f9ca8b661c4e1ecc7a5368782586e3ffa1565ab42ac15b620fd8f4315629 | 3158be0446f5765019369c481023a71dc350ff551491f04a5f676dbc19f70643 | 5813097f372a4ddb229f9c0494573e11c5f44c374e555968ef8d891cacd518e5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,089 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Algebra.toMatrix_lsmul</a>] | case h.e'_2.h.e'_6.a
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι... | ((:c Eq) (:fv _uniq.18680) ((:c DFunLike.coe) ((:c LinearEquiv) (:fv _uniq.18680) (:fv _uniq.18680) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c CommRing.toCommSemiring) (:fv _uniq.18680) (:fv _uniq.18689))) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c CommRing.toCommSemiring) (:fv _uniq.18680) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearEquiv) (: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 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":3376,"sourceStart":3374,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3378,"sourceStart":3377,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Algebra.toMatrix_lsm... | [] | [{"source":"toMatrix_lsmul","source_end":3392,"source_start":3378,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 17 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f7e417ad0f4616136aa6831032082910395ea1b93deb0e412c8abb7c1d1a575b | 5813097f372a4ddb229f9c0494573e11c5f44c374e555968ef8d891cacd518e5 | 288d60656bba1e0ce74d15b5be90a5a82b640f57d4f6b158a121a03d001dabf7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,090 | Algebra.norm_algebraMap_of_basis | Mathlib/RingTheory/Norm.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.prod_const</a>, <a>Finset.card_univ</a>] | case h.e'_3
R : Type u_1
S : Type u_2
T : Type u_3
inst✝⁸ : CommRing R
inst✝⁷ : Ring S
inst✝⁶ : Algebra R S
K : Type u_4
L : Type u_5
F : Type u_6
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : Field F
inst✝² : Algebra K L
inst✝¹ : Algebra K F
ι : Type w
inst✝ : Fintype ι
b : Basis ι R S
x : R
this : DecidableEq ι
⊢ x ^ Fi... | ((:c Eq) (:fv _uniq.18680) ((:c HPow.hPow) (:fv _uniq.18680) (:c Nat) (:fv _uniq.18680) ((:c instHPow) (:fv _uniq.18680) (:c Nat) ((:c Monoid.toNatPow) (:fv _uniq.18680) ((:c MonoidWithZero.toMonoid) (:fv _uniq.18680) ((:c Semiring.toMonoidWithZero) (:fv _uniq.18680) ((:c CommSemiring.toSemiring) (:fv _uniq.18680) ((:c... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"S","sexp":"(:sort (+ u_2 1))"},{"name":"T","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁸","sexp":"((:c CommRing) (:fv _uniq.18680))"},{"name":"inst✝⁷","sexp":"((:c Ring) (:fv _uniq.18683))"},{"name":"inst✝⁶","sexp":"((:c Algebra) (:fv _uniq.18680) (:fv _uniq.18683) ((:c C... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:fv FV0)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3401,"sourceStart":3399,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3403,"sourceStart":3402,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Finset.prod_const","source_end":3420,"source_start":3403,"syntax_kind":"ident"},{"source":"Finset.card_univ","source_end":3438,"source_start":3422,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18680","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18683","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 25 | 22 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2d771ff01dba68b5a7edbb5408b45284b29fb62dda6498e171d2714071867d8 | 79922e0b4e177ef7db64c5fe0eac55b68ddfd60bc5e66aaeba03bce03826d395 | 8dc18dd3f79df9feec618639c06a3a189b80d3916a26f1bed547ec5d76237e81 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,091 | ModularForm.mul_slash_SL2 | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>ModularForm.mul_slash</a> | Γ : Subgroup SL(2, ℤ)
k : ℤ
f✝ : ℍ → ℂ
k1 k2 : ℤ
A : SL(2, ℤ)
f g : ℍ → ℂ
⊢ (f * g) ∣[k1 + k2] ↑A = (↑↑↑A).det • f ∣[k1] A * g ∣[k2] A | ((:c Eq) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c SlashAction.map) (:c Int) ((:c Subtype) ((:c Matrix.GeneralLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) (:c Real) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.f... | [{"name":"Γ","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :explicit 1 (:app (:c SlashAction.map) (:arg :implicit-type 0 (:c Int)) (:arg :implicit-type 1 (:app (:c Subtype) (:arg :implicit-type 0 (:app (:c Matrix.GeneralLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":10374,"sourceStart":10369,"tag":"atom"},{"name":"ModularForm.mul_slash","semanticRole":"global","source":"mul_slash","sourceEnd":10384,"sourceStart":10375,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply mul_slash","... | [] | [{"source":"mul_slash","source_end":10384,"source_start":10375,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.184575","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 53 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a3dd6fe4f857278884611db6b4dcfced257b8dfacb8c923f9689357fd593a1f4 | f51e44cb85fa5f7c290c9c1e9b63858f19a183eca88dc9a47cf6cff5524bfc15 | 7da79c3db2835c3b10c142a068d8dee101442af7581ea82f573020177f16554f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,092 | ModularForm.mul_slash_SL2 | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>UpperHalfPlane.ModularGroup.det_coe'</a>] | Γ : Subgroup SL(2, ℤ)
k : ℤ
f✝ : ℍ → ℂ
k1 k2 : ℤ
A : SL(2, ℤ)
f g : ℍ → ℂ
⊢ (↑↑↑A).det • f ∣[k1] A * g ∣[k2] A = 1 • f ∣[k1] A * g ∣[k2] A | ((:c Eq) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c HMul.hMul) (:forall _ (:c UpperHalfPlane) (:c Complex)) (:forall _ (:c UpperHalfPlane) (:c Complex)) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c instHMul) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c Pi.instMul) (:c UpperHalfPlane) (:lambda _ (:c Upp... | [{"name":"Γ","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :implicit-type 1 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :implicit-type 2 (:foral... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10441,"sourceStart":10439,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10443,"sourceStart":10442,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"det_coe'","source_end":10451,"source_start":10443,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.184575","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 53 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b24855524d68bec6b0bc522342d9d67cadb31fadd2ed716eade9b5462059897f | fe84e90c5e4a8dc18e3d70b6935790ad64c2c02423c77e45ce26745ff9238e20 | 4f132935fd82dbd76cedfbe784c684c99bd3a57ec6135488356961d082732c6c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,093 | ModularForm.mul_slash_SL2 | Mathlib/NumberTheory/ModularForms/SlashActions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>one_smul</a>] | Γ : Subgroup SL(2, ℤ)
k : ℤ
f✝ : ℍ → ℂ
k1 k2 : ℤ
A : SL(2, ℤ)
f g : ℍ → ℂ
⊢ 1 • f ∣[k1] A * g ∣[k2] A = f ∣[k1] A * g ∣[k2] A | ((:c Eq) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c HMul.hMul) (:forall _ (:c UpperHalfPlane) (:c Complex)) (:forall _ (:c UpperHalfPlane) (:c Complex)) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c instHMul) (:forall _ (:c UpperHalfPlane) (:c Complex)) ((:c Pi.instMul) (:c UpperHalfPlane) (:lambda _ (:c Upp... | [{"name":"Γ","sexp":"((:c Subgroup) ((:c Matrix.SpecialLinearGroup) ((:c Fin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c instDecidableEqFin) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c Fin.fintype) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :implicit-type 1 (:forall _ :explicit (:c UpperHalfPlane) (:c Complex))) (:arg :implicit-type 2 (:foral... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"name":"Γ","sexp":"(:app (:c Subgroup) (:arg :explicit 0 (:app (:c Matrix.SpecialLinearGroup) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10495,"sourceStart":10493,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10497,"sourceStart":10496,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"one_smul","source_end":10505,"source_start":10497,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184573","is_instance":false,"is_let":false,"user_name":"Γ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.184575","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 53 | 14 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a653ede3dc542d6a1322784822682ba80cc1fe81dde019a76dab2526c10169a | fad6892d376789ca78f2f6b97e3a7928423c4d3d75bfbd1e02a75e8302d42260 | a43cf5dacf08014f9aa83c7d3ebb171d3e3fde3fe01ad31f66e4877ced627343 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,094 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | set e := <a>FiberBundle.trivializationAt</a> F Z p.proj | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"set","sourceEnd":6885,"sourceStart":6882,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":6887,"sourceStart":6886,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":":=","so... | [] | [{"source":"trivializationAt F Z p.proj","source_end":6918,"source_start":6891,"syntax_kind":"Lean.Parser.Term.app"},{"source":"e","source_end":6887,"source_start":6886,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 4 | exact | true | 1 | 37 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48d3204106394632e70c23931a4019b9341377ebc1cc4e48bdc2063196f0d00a | 95afc2f5d451d8d3a28c7283e7ef3f2e3b43ee98aa71f1062dd8d1c0daed89a1 | a49d4c0b98ed6d43643faedc969b983ad972c673b887e169a1f86fe580ed4d88 | 050b5eb31b11252b518ca06ebdb5060bdb1e3594679eefb1eb93449a4fe1063b |
cat-searcher/leandojo-benchmark-4-random | test | 4,095 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hp : p ∈ e.source := <a>FiberBundle.mem_trivializationAt_proj_source</a> | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"have","sourceEnd":6925,"sourceStart":6921,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hp","sourceEnd":6928,"sourceStart":6926,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hp","sourceEnd":6928,"sourceStart":6926,"tag":"node"},{"... | [] | [{"source":"p ∈ e.source","source_end":6945,"source_start":6931,"syntax_kind":"«term_∈_»"},{"source":"FiberBundle.mem_trivializationAt_proj_source","source_end":6993,"source_start":6949,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 5 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f551724869525a78014cde5a2999814a6eddcc7799022709c20fa407a90c8b7e | 050b5eb31b11252b518ca06ebdb5060bdb1e3594679eefb1eb93449a4fe1063b | 1fbdaa39908cf8d6228d974fa873a519b2d2c329615159a00bd2367c763ad568 | 2fc844308ccc9b08a3e44c5ed60b08ed8b3169a40804e24354c184cc7977de54 |
cat-searcher/leandojo-benchmark-4-random | test | 4,096 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>UniqueMDiffWithinAt</a> (I.prod 𝓘(𝕜, F)) (s ×ˢ <a>Set.univ</a>) (e p) := by rw [← <a>Prod.mk.eta</a> (p := e p), <a>FiberBundle.trivializationAt_proj_fst</a>] exact hs.prod (<a>uniqueMDiffWithinAt_univ</a> _) | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"have","sourceEnd":7000,"sourceStart":6996,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7001,"sourceStart":7001,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7001,"sourceStart":7001,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"UniqueMDiffWithinAt (I.prod 𝓘(𝕜, F)) (s ×ˢ univ) (e p)","source_end":7065,"source_start":7003,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Prod.mk.eta (p := e p)","source_end":7106,"source_start":7084,"syntax_kind":"Lean.Parser.Term.app"},{"source":"FiberBundle.trivializationAt_proj_fst","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 6 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af795a3e91911ff984209e3cdf26ea936e3d235f0fd20f0f05d537d107b69942 | 2fc844308ccc9b08a3e44c5ed60b08ed8b3169a40804e24354c184cc7977de54 | 6ca30d43b9cbca4478e76b04509ddad60f8ccdf1b8d1b71fad78353a972a07c8 | 7a4c44617dc6d7d64252920f0248c1ef2afcb29c7fd209543fd003140178cf51 |
cat-searcher/leandojo-benchmark-4-random | test | 4,097 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← e.left_inv hp] | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"rw","sourceEnd":7198,"sourceStart":7196,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7200,"sourceStart":7199,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7203,"sourceStart":... | [] | [{"source":"e.left_inv hp","source_end":7217,"source_start":7204,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 13 | exact | true | 1 | 40 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 524d55bfd3a9f19515b9a2a8803a808137fe92c40346128200724fa699c19427 | 7a4c44617dc6d7d64252920f0248c1ef2afcb29c7fd209543fd003140178cf51 | fba67b0aa1db61cd4cfb14fceede8e8c4726dc8902038d974cfea2f489fb12f0 | 99cdb36063a1153164fb3599f0051ddc0897477d68395eb14acc8d1027083e9d |
cat-searcher/leandojo-benchmark-4-random | test | 4,098 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (this.preimage_partialHomeomorph e.mdifferentiable.symm (e.map_source hp)).<a>UniqueMDiffWithinAt.mono</a> ?_ | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"refine","sourceEnd":7227,"sourceStart":7221,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":7229,"sourceStart":7228,"tag":"atom"},{"children":[{"source":"this.preimage_partialHomeomorph","sourceEnd":7260,"sourceStart":7229,"tag":"identifier"},{"children":[{"name":"... | [] | [{"source":"(this.preimage_partialHomeomorph e.mdifferentiable.symm (e.map_source hp)).mono ?_","source_end":7310,"source_start":7228,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 16 | exact | true | 1 | 40 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6ec3b77539d613f13e73d52dfdafd3caa5927364068cf228801bae0f7129dd14 | 99cdb36063a1153164fb3599f0051ddc0897477d68395eb14acc8d1027083e9d | b378d5a88453aa854e7f27dced18acef0e1d77e541a07ff88fc839b33f71a0d3 | 658fbc8fd922daacca83a32b692630681879e4c34a4774f8f617efe1498c888a |
cat-searcher/leandojo-benchmark-4-random | test | 4,099 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro y ⟨hy, hys, -⟩ | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | case intro.intro
𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E'... | ((:c HasSubset.Subset) ((:c Set) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.33168))) ((:c Set.instHasSubset) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.33168))) ((:c Inter.inter) ((:c Set) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.3316... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Bundle.TotalSpace) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:fv FV24)) (:arg :explicit 2 (:fv FV27)))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"rintro","sourceEnd":7319,"sourceStart":7313,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEnd":7321,"sourceStart":7320,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"y","sourceEnd":7321,"sourceStart":7320,"tag":"... | [{"role":"fresh_name","source":"y","source_end":7321,"source_start":7320,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":7327,"source_start":7325,"syntax_kind":"ident"},{"role":"fresh_name","source":"hys","source_end":7332,"source_start":7329,"syntax_kind":"ident"}] | [{"source":"⟨hy, hys, -⟩","source_end":7338,"source_start":7322,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 17 | exact | true | 1 | 40 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87b8e9ef744dc8bd1c12298e8dcea7aeb848d55633af5cd320e1a7bd3498857b | 658fbc8fd922daacca83a32b692630681879e4c34a4774f8f617efe1498c888a | c33f76b9b151cdf6511f8b4a71ed14893b9efa451f373eb3311cbf424434a236 | 042d40f960dc90ffddd96414225c67676414cb7caa889e1186acd890be599a83 |
cat-searcher/leandojo-benchmark-4-random | test | 4,100 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>PartialHomeomorph.symm_symm</a>, e.coe_coe, e.coe_fst hy] at hys | case intro.intro
𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E'... | ((:c Membership.mem) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.33168)) ((:c Set) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.33168))) ((:c Set.instMembership) ((:c Bundle.TotalSpace) (:fv _uniq.32405) (:fv _uniq.33052) (:fv _uniq.33168))) (:fv _uniq.39935) ((:c Se... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Bundle.TotalSpace) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:fv FV24)) (:arg :explicit 2 (:fv FV27)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Bundle.TotalSpace) (:arg :implicit-type 0 (:fv FV8)) (:arg :explicit 1 (:fv FV24... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"rwa","sourceEnd":7344,"sourceStart":7341,"tag":"atom"},{"children":[{"source":"[","sourceEnd":7346,"sourceStart":7345,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"PartialHomeomorph.symm_symm","semanticRole":"global","source":"PartialHome... | [] | [{"source":"PartialHomeomorph.symm_symm","source_end":7373,"source_start":7346,"syntax_kind":"ident"},{"source":"hys","source_end":7406,"source_start":7403,"syntax_kind":"ident"},{"source":"e.coe_coe","source_end":7384,"source_start":7375,"syntax_kind":"ident"},{"source":"e.coe_fst hy","source_end":7398,"source_start":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 18 | exact | true | 1 | 43 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f9cfe0f87908356b94f57c863b0f4245f6a8100b8c5311b39187e3f6db8f0ab | 042d40f960dc90ffddd96414225c67676414cb7caa889e1186acd890be599a83 | 22daa5b3c09e01997660a71df8158defdae7942be7db8c1cc61d705c947e881d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,101 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Prod.mk.eta</a> (p := e p), <a>FiberBundle.trivializationAt_proj_fst</a>] | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"rw","sourceEnd":7078,"sourceStart":7076,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7080,"sourceStart":7079,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":7083,"sourceStart":... | [] | [{"source":"Prod.mk.eta (p := e p)","source_end":7106,"source_start":7084,"syntax_kind":"Lean.Parser.Term.app"},{"source":"FiberBundle.trivializationAt_proj_fst","source_end":7145,"source_start":7108,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 8 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33ee562f9581694dada9889b0f1c538556627871c68780dfc02096e96f0c06b9 | 93f5fae11121529228a4ae9e0265406072f29310f51e053535419d1e4914714c | 35a45188c894a03432f835be5c62d55c68e1e7ff6c0b8478ad42bcbd39eae3c0 | 2f01d1d667df26d973d400bfa5bc1a6c3d49db19dc857fc5e0d4eb7cc6637253 |
cat-searcher/leandojo-benchmark-4-random | test | 4,102 | UniqueMDiffWithinAt.smooth_bundle_preimage | Mathlib/Geometry/Manifold/MFDeriv/UniqueDifferential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hs.prod (<a>uniqueMDiffWithinAt_univ</a> _) | 𝕜 : Type u_1
inst✝²¹ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace 𝕜 E
H : Type u_3
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners 𝕜 E H
M : Type u_4
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
E' : Type u_5
inst✝... | ((:c UniqueMDiffWithinAt) (:fv _uniq.32242) (:fv _uniq.32245) ((:c Prod) (:fv _uniq.32248) (:fv _uniq.33052)) ((:c Prod.normedAddCommGroup) (:fv _uniq.32248) (:fv _uniq.33052) (:fv _uniq.32251) (:fv _uniq.33055)) ((:c Prod.normedSpace) (:fv _uniq.32242) (:fv _uniq.32248) (:fv _uniq.33052) ((:c NontriviallyNormedField.t... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²¹","sexp":"((:c NontriviallyNormedField) (:fv _uniq.32242))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²⁰","sexp":"((:c NormedAddCommGroup) (:fv _uniq.32248))"},{"name":"inst✝¹⁹","sexp":"((:c NormedSpace) (:fv _uniq.32242) (:fv _uniq.32248) ((:c Nont... | (:app (:c UniqueMDiffWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV24)))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommG... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"name":"inst✝²¹","sexp":"(:app (:c NontriviallyNormedFie... | {"children":[{"source":"exact","sourceEnd":7156,"sourceStart":7151,"tag":"atom"},{"children":[{"source":"hs.prod","sourceEnd":7164,"sourceStart":7157,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":7166,"sourceStart":7165,"tag":"atom"},{"children":[{"name":"uniqueMDiffWithinAt_univ","semanticRol... | [] | [{"source":"hs.prod (uniqueMDiffWithinAt_univ _)","source_end":7193,"source_start":7157,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.32242","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.32245","is_instance":true,"is_let":false,"user_name":"inst✝²¹"},{"binder_role":":implicit","context_index":2,"inte... | 20 | 12 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 507e739d032d2e1c99d26e06cef09837b544a9a1c3ca6bd9eb1d1132fc735b2e | 2f01d1d667df26d973d400bfa5bc1a6c3d49db19dc857fc5e0d4eb7cc6637253 | 75a680532586504f4c32b79d6dc6675fd34fca44d772d5b4c65331618c241e71 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,103 | List.takeD_eq_takeDTR | .lake/packages/batteries/Batteries/Data/List/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | funext α f n l | ⊢ @takeD = @takeDTR | case h.h.h.h
α : Type u_1
f : Nat
n : List α
l : α
⊢ takeD f n l = takeDTR f n l | ((:c Eq) (:forall α (:sort (+ u_1 1)) (:forall _ (:c Nat) (:forall _ ((:c List) 1) (:forall _ 2 ((:c List) 3)))) :implicit) (:c List.takeD) (:c List.takeDTR)) | [] | (:app (:c Eq) (:arg :implicit-type 0 (:forall α :implicit (:sort Type) (:forall _ :explicit (:c Nat) (:forall _ :explicit (:app (:c List) (:arg :explicit 0 1)) (:forall _ :explicit 2 (:app (:c List) (:arg :explicit 0 3))))))) (:arg :explicit 1 (:c List.takeD)) (:arg :explicit 2 (:c List.takeDTR))) | [] | {"children":[{"source":"funext","sourceEnd":13787,"sourceStart":13781,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"α","sourceEnd":13790,"sourceStart":13788,"tag":"identifier"},{"semanticRole":"scoped_local","source":"f","sourceEnd":13792,"sourceStart":13791,"tag":"identifier"},{"semanticRole":"sc... | [] | [] | [] | 56 | 4 | exact | true | 1 | 0 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0cf43dc2ea18923ae6706627f688e0784c3d9d590138f79f1bdd9a2f68302a7d | 721e142531530570193bdc430b68aea820977fe48b93919a9bcb1fa7923e75d1 | c8eb805fd8bd8e23030fb1527d29ee47d1613af2e2c12797453d6ce46f9b3461 | 226761daaff29b0170cd63c7f389ae98ec3c8ba45b41bf7e6093b8a01b08e181 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.