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value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 3,391 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | next h => exact fun e => zoom_zoomed₂ e ⟨h, hp⟩ | case h_1
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.lt
⊢ zoom cut l✝ (left c✝ path v✝ r✝)... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.zoom) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26623) ((:c Batteries.RBNode.Path.left) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26205) (:fv _uniq.26624) (:fv _uniq.2... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.zoom) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"children":[{"children":[{"children":[{"source":"next","sourceEnd":6407,"sourceStart":6403,"tag":"atom"},{"children":[{"children":[{"contextIndex":16,"semanticRole":"local","source":"h","sourceEnd":6409,"sourceStart":6408,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"h","sourceEnd":6409,"source... | [] | [{"source":"fun e => zoom_zoomed₂ e ⟨h, hp⟩","source_end":6456,"source_start":6419,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 11 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 83a0701c9d77683cac9b56c4f4c51130378e60a6ac096061df75f7bc4290c68f | 436e09dc57c7a0e8c20d4c820efabfd3183a6d64ea122c11683468e19388c5a5 | db7bdcdcb96b50c5fffe6b3cdabdc94eb3ac0e2aeaede186d0281df55db7015c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,392 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun e => zoom_zoomed₂ e ⟨h, hp⟩ | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
h : cut v✝ = Ordering.lt
⊢ zoom cut l✝ (left c✝ path v✝ r✝) = (t', path... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.zoom) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26623) ((:c Batteries.RBNode.Path.left) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26205) (:fv _uniq.26624) (:fv _uniq.2... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.zoom) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6418,"sourceStart":6413,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":6422,"sourceStart":6419,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":6424,"sourceStart":6423,"tag":"identifi... | [] | [{"source":"fun e => zoom_zoomed₂ e ⟨h, hp⟩","source_end":6456,"source_start":6419,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 14 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7893b223edf3cb059888d5700bb278fac5a7235332a0f9d54a67ffb9399d45e3 | e82702a6bb3f7a44ba373f3d5aa0a1862e087fd3cf02e494112a116480878d7b | eab082381336b8a3b1eb8ed9f6298634feb8f1006c2dce2b2916bd5949f1084d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,393 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | next h => exact fun e => zoom_zoomed₂ e ⟨h, hp⟩ | case h_2
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.gt
⊢ zoom cut r✝ (right c✝ l✝ v✝ path... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.zoom) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26625) ((:c Batteries.RBNode.Path.right) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26623) (:fv _uniq.26624) (:fv _uniq.... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.zoom) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"children":[{"children":[{"children":[{"source":"next","sourceEnd":6468,"sourceStart":6464,"tag":"atom"},{"children":[{"children":[{"contextIndex":16,"semanticRole":"local","source":"h","sourceEnd":6470,"sourceStart":6469,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"h","sourceEnd":6470,"source... | [] | [{"source":"fun e => zoom_zoomed₂ e ⟨h, hp⟩","source_end":6517,"source_start":6480,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 19 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d79e8c73b6d640b7f7e312dfff271bba8b518de49a21a0fc05422a88f001b090 | fdda888eea1b9d339c8714a8bbc6f8b0135338bb6279489eaa5fc1645eded6bf | db7bdcdcb96b50c5fffe6b3cdabdc94eb3ac0e2aeaede186d0281df55db7015c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,394 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun e => zoom_zoomed₂ e ⟨h, hp⟩ | α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
h : cut v✝ = Ordering.gt
⊢ zoom cut r✝ (right c✝ l✝ v✝ path) = (t', pat... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Batteries.RBNode.zoom) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26625) ((:c Batteries.RBNode.Path.right) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26623) (:fv _uniq.26624) (:fv _uniq.... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Batteries.RBNode.zoom) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":6479,"sourceStart":6474,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":6483,"sourceStart":6480,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":6485,"sourceStart":6484,"tag":"identifi... | [] | [{"source":"fun e => zoom_zoomed₂ e ⟨h, hp⟩","source_end":6517,"source_start":6480,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 22 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 58afc954bcee28fa3c61b55ac02ab6e18cb83a1e80c81880e0b31a9f1a784ab9 | c368af2840b080c5fe10b651e9cb3ae48884cdd7d90e92c7324fc1056d3cd669 | eab082381336b8a3b1eb8ed9f6298634feb8f1006c2dce2b2916bd5949f1084d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,395 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro e | case h_3
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.eq
⊢ (node c✝ l✝ v✝ r✝, path) = (t', ... | case h_3
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e✝ : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.eq
e : (node c✝ l✝ v✝ r✝, path) = (t... | (:forall e ((:c Eq) ((:c Prod) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202))) ((:c Prod.mk) ((:c Batteries.RBNode) (:fv _uniq.26202)) ((:c Batteries.RBNode.Path) (:fv _uniq.26202)) ((:c Batteries.RBNode.node) (:fv _uniq.26202) (:fv _uniq.26622) (:fv _uniq.26623) (:fv _uniq.266... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:forall e :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Batteries.RBNode) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Batteries.RBNode.Path) (:arg :explicit 0 (:fv FV1)))))) (:arg :explicit 1 (:app (:c Prod.mk) (:arg :implicit-type 0 (:app (:c Batteries.RBNod... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"intro","sourceEnd":6530,"sourceStart":6525,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":6532,"sourceStart":6531,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":6532,"sourceStart":6531,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"e","source_end":6532,"source_start":6531,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 29 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 56df01928d2af04bf3fb0c309fac2c434f6f33db5b28282c7b31739a436e2d76 | 200ef46cb78d2487bc873f6e61d42859a3cef2e2cb391ba21781ce10ad68b313 | d97190aa489499e2113eb2b7ebfaf49976e5a9774a652c63907edf69e5878ebb | 450a4b5eaeb67f763387fd5e2ed8aebb621b1aa14e1584ec35b718db777e216f |
cat-searcher/leandojo-benchmark-4-random | test | 3,396 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases e | case h_3
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t'✝ : RBNode α✝
path'✝ : Path α✝
e✝ : zoom cut t path = (t'✝, path'✝)
hp : Zoomed cut path
path' : Path α✝
t' : RBNode α✝
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.eq
e : (node c✝ l✝ v✝ r✝, path) = (t... | case h_3.refl
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t' : RBNode α✝
path' : Path α✝
e : zoom cut t path = (t', path')
hp : Zoomed cut path
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.eq
⊢ Zoomed cut path | ((:c Batteries.RBNode.Path.Zoomed) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26620)) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'✝","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":... | (:app (:c Batteries.RBNode.Path.Zoomed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV9))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"cases","sourceEnd":6539,"sourceStart":6534,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":17,"semanticRole":"local","source":"e","sourceEnd":6541,"sourceStart":6540,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"e","source_end":6541,"source_start":6540,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 31 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de5ce3b261297767e62912aa5618d79db31e433123f2ac7d9a64cb4b80777c22 | 450a4b5eaeb67f763387fd5e2ed8aebb621b1aa14e1584ec35b718db777e216f | e63e2afa2f9837f88e99f6ee01b0653d52a24f045157a6e8e5e4982ee92f7119 | 55efc6ef75d6efdc9dab4841be90c300ac2c3c60822b8577ae953e450ea07f0f |
cat-searcher/leandojo-benchmark-4-random | test | 3,397 | Batteries.RBNode.Path.zoom_zoomed₂ | .lake/packages/batteries/Batteries/Data/RBMap/Alter.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hp | case h_3.refl
α✝ : Type u_1
cut : α✝ → Ordering
t : RBNode α✝
path : Path α✝
t' : RBNode α✝
path' : Path α✝
e : zoom cut t path = (t', path')
hp : Zoomed cut path
c✝ : RBColor
l✝ : RBNode α✝
v✝ : α✝
r✝ : RBNode α✝
x✝ : Ordering
heq✝ : cut v✝ = Ordering.eq
⊢ Zoomed cut path | ((:c Batteries.RBNode.Path.Zoomed) (:fv _uniq.26202) (:fv _uniq.26203) (:fv _uniq.26205)) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"cut","sexp":"(:forall _ (:fv _uniq.26202) (:c Ordering))"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"path","sexp":"((:c Batteries.RBNode.Path) (:fv _uniq.26202))"},{"name":"t'","sexp":"((:c Batteries.RBNode) (:fv _uniq.26202))"},{"name":"... | (:app (:c Batteries.RBNode.Path.Zoomed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"name":"cut","sexp":"(:forall _ :explicit (:fv FV1) (:c Ordering... | {"children":[{"source":"exact","sourceEnd":6548,"sourceStart":6543,"tag":"atom"},{"contextIndex":8,"semanticRole":"local","source":"hp","sourceEnd":6551,"sourceStart":6549,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hp","sourceEnd":6551,"sourceStart":6543,"tag":"node"} | [] | [{"source":"hp","source_end":6551,"source_start":6549,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.26202","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.26203","is_instance":false,"is_let":false,"user_name":"cut"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 18 | 33 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c279834d90d11d52213798907d5012e21061c8b14bc4bda8135cbf8d022d2840 | 55efc6ef75d6efdc9dab4841be90c300ac2c3c60822b8577ae953e450ea07f0f | 83a7aa75303694d396e1f5fc213c4940596cdd40f7a7e95be81e00a5e475cb5e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,398 | Trivialization.linearMapAt_apply | Mathlib/Topology/VectorBundle/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Trivialization.coe_linearMapAt</a>] | R : Type u_1
B : Type u_2
F : Type u_3
E : B → Type u_4
inst✝⁸ : Semiring R
inst✝⁷ : TopologicalSpace F
inst✝⁶ : TopologicalSpace B
inst✝⁵ : TopologicalSpace (TotalSpace F E)
e✝ : Trivialization F TotalSpace.proj
x : TotalSpace F E
b✝ : B
y✝ : E b✝
inst✝⁴ : AddCommMonoid F
inst✝³ : Module R F
inst✝² : (x : B) → AddComm... | ((:c Eq) (:fv _uniq.39040) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.39034) (:fv _uniq.39034) (:fv _uniq.39048) (:fv _uniq.39048) ((:c RingHom.id) (:fv _uniq.39034) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.39034) (:fv _uniq.39048))) ((:fv _uniq.39045) (:fv _uniq.40459)) (:fv _uniq.39040) ((:fv _uniq.39149) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"B","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:forall _ (:fv _uniq.39037) (:sort (+ u_4 1)))"},{"name":"inst✝⁸","sexp":"((:c Semiring) (:fv _uniq.39034))"},{"name":"inst✝⁷","sexp":"((:c TopologicalSpace) (:fv _uniq.39040))"}... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv 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.39034","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39037","is_instance":false,"is_let":false,"name":"B","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":11327,"sourceStart":11325,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11329,"sourceStart":11328,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"coe_linearMapAt","source_end":11344,"source_start":11329,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.39034","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.39037","is_instance":false,"is_let":false,"user_name":"B"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 2 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d46b0fb62bf787c5d1fcdf1cd8ff5eafa84194924bb50c148d7d79457e5f0a9e | 7e1112082bc8e7a945bb00346c7945f323b77e104d9ceac08815be1333fb785f | 32d0e808fc842d855e6d6f7a89904c65b483afeb1b184546e27be5876c306f97 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,399 | Matroid.Basis.exchange | Mathlib/Data/Matroid/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨y,hy, h⟩ := hIX.restrict_base.exchange hJX.restrict_base he | α : Type u_1
M : Matroid α
R I J✝ X Y B J : Set α
e : α
hIX : M.Basis I X
hJX : M.Basis J X
he : e ∈ I \ J
⊢ ∃ f ∈ J \ I, M.Basis (insert f (I \ {e})) X | case intro.intro
α : Type u_1
M : Matroid α
R I J✝ X Y B J : Set α
e : α
hIX : M.Basis I X
hJX : M.Basis J X
he : e ∈ I \ J
y : α
hy : y ∈ J \ I
h : (M ↾ X).Base (insert y (I \ {e}))
⊢ ∃ f ∈ J \ I, M.Basis (insert f (I \ {e})) X | ((:c Exists) (:fv _uniq.78230) (:lambda f (:fv _uniq.78230) ((:c And) ((:c Membership.mem) (:fv _uniq.78230) ((:c Set) (:fv _uniq.78230)) ((:c Set.instMembership) (:fv _uniq.78230)) 0 ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.78230)) ((:c Set.instSDiff) (:fv _uniq.78230)) (:fv _uniq.78254) (:fv _uniq.78239))) ((:c Matroid... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"((:c Matroid) (:fv _uniq.78230))"},{"name":"R","sexp":"((:c Set) (:fv _uniq.78230))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.78230))"},{"name":"J✝","sexp":"((:c Set) (:fv _uniq.78230))"},{"name":"X","sexp":"((:c Set) (:fv _uniq.78230))"},{"name":"Y","sexp":... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda f :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78230","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78233","is_instance":false,"is_let":false,"name":"M","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0)... | {"children":[{"source":"obtain","sourceEnd":18972,"sourceStart":18966,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":18976,"sourceStart":18973,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEn... | [] | [{"source":"hIX.restrict_base.exchange hJX.restrict_base he","source_end":19037,"source_start":18990,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y,hy, h⟩","source_end":18986,"source_start":18973,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.78230","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.78233","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 84 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c2e2ea59b0beddb0e5c7b4591d3c021fd7d644d65cdf5c9e50f6fa7e79c532c | e026ebc1f3362ff14f115596b9fdc69d452d6dbc99cf89bf6e8175f19b4d0d66 | 362f88a52be659c8affc3631eba02edf25fa07a163cd23542616472cdcacd98e | 7660f302769c9bf1a2d4ecfb70dd02721e2c034c2b8f78ddb67d07f8de01e01c |
cat-searcher/leandojo-benchmark-4-random | test | 3,402 | Multiset.inf_union | Mathlib/Data/Multiset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Multiset.inf_dedup</a>, <a>Multiset.dedup_ext</a>.2, <a>Multiset.inf_dedup</a>, <a>Multiset.inf_add</a>] | α : Type u_1
inst✝² : SemilatticeInf α
inst✝¹ : OrderTop α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ (s₁ ∪ s₂).inf = s₁.inf ⊓ s₂.inf | α : Type u_1
inst✝² : SemilatticeInf α
inst✝¹ : OrderTop α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ ∀ (a : α), a ∈ s₁ ∪ s₂ ↔ a ∈ s₁ + s₂ | ((:c Eq) (:fv _uniq.27063) ((:c Multiset.inf) (:fv _uniq.27063) (:fv _uniq.27066) (:fv _uniq.27159) ((:c Union.union) ((:c Multiset) (:fv _uniq.27063)) ((:c Multiset.instUnion) (:fv _uniq.27063) (:fv _uniq.27166)) (:fv _uniq.27353) (:fv _uniq.27354))) ((:c Inf.inf) (:fv _uniq.27063) ((:c SemilatticeInf.toInf) (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c SemilatticeInf) (:fv _uniq.27063))"},{"name":"inst✝¹","sexp":"((:c OrderTop) (:fv _uniq.27063) ((:c Preorder.toLE) (:fv _uniq.27063) ((:c PartialOrder.toPreorder) (:fv _uniq.27063) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.27063) (:fv _uniq.270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset.inf) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c SemilatticeInf) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c OrderTop) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27063","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27066","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c SemilatticeInf) (:arg :... | {"children":[{"source":"rw","sourceEnd":5395,"sourceStart":5393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5397,"sourceStart":5396,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5400,"sourceStart":... | [] | [{"source":"inf_dedup","source_end":5410,"source_start":5401,"syntax_kind":"ident"},{"source":"dedup_ext.2","source_end":5423,"source_start":5412,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"inf_dedup","source_end":5434,"source_start":5425,"syntax_kind":"ident"},{"source":"inf_add","source_end":5443,"source_start"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27063","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27066","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 63 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e1f2de626af932b538b8fcc3d96a884c94e9e88b865cdfa5f9acb78a36b3d96 | e20292cc910f5ae6c9f2f0f28a7cb4899b2ca9baf5c266781a1561672c7823ab | d56c96ea7379632e9a3ea5eb8184f59d67bb24217236e6c4cb76635e2ee01987 | 8dc51f58c6b819a1b76e30a0920b3f20088a43d4cd09de2e2ec7bf83291fc7db |
cat-searcher/leandojo-benchmark-4-random | test | 3,403 | Multiset.inf_union | Mathlib/Data/Multiset/Lattice.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
inst✝² : SemilatticeInf α
inst✝¹ : OrderTop α
inst✝ : DecidableEq α
s₁ s₂ : Multiset α
⊢ ∀ (a : α), a ∈ s₁ ∪ s₂ ↔ a ∈ s₁ + s₂ | (:forall a (:fv _uniq.27063) ((:c Iff) ((:c Membership.mem) (:fv _uniq.27063) ((:c Multiset) (:fv _uniq.27063)) ((:c Multiset.instMembership) (:fv _uniq.27063)) 0 ((:c Union.union) ((:c Multiset) (:fv _uniq.27063)) ((:c Multiset.instUnion) (:fv _uniq.27063) (:fv _uniq.27166)) (:fv _uniq.27353) (:fv _uniq.27354))) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c SemilatticeInf) (:fv _uniq.27063))"},{"name":"inst✝¹","sexp":"((:c OrderTop) (:fv _uniq.27063) ((:c Preorder.toLE) (:fv _uniq.27063) ((:c PartialOrder.toPreorder) (:fv _uniq.27063) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.27063) (:fv _uniq.270... | (:forall a :explicit (:fv FV0) (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27063","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27066","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c SemilatticeInf) (:arg :... | {"children":[{"source":"simp","sourceEnd":5450,"sourceStart":5446,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.27063","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.27066","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index":... | 63 | 11 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 181cd3b9bf69f533784be0df69c5b70044afdc339b93d8c4eccc552f8ba4435f | 8dc51f58c6b819a1b76e30a0920b3f20088a43d4cd09de2e2ec7bf83291fc7db | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,404 | Vector.mapAccumr_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction xs | α : Type u_2
n : ℕ
xs : Vector α n
α✝ : Type
β✝ : Type u_1
f : α → α✝ → α✝ × β✝
x : α
s : α✝
⊢ mapAccumr f (xs.snoc x) s =
let q := f x s;
let r := mapAccumr f xs q.1;
(r.1, r.2.snoc q.2) | case nil
α : Type u_2
n : ℕ
xs : Vector α n
α✝ : Type
β✝ : Type u_1
f : α → α✝ → α✝ × β✝
x : α
s : α✝
⊢ mapAccumr f (nil.snoc x) s =
let q := f x s;
let r := mapAccumr f nil q.1;
(r.1, r.2.snoc q.2)
case cons
α : Type u_2
n : ℕ
xs : Vector α n
α✝ : Type
β✝ : Type u_1
f : α → α✝ → α✝ × β✝
x : α
s : α✝
n✝ : ℕ... | ((:c Eq) ((:c Prod) (:fv _uniq.3558) ((:c Vector) (:fv _uniq.3559) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.3379) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))) ((:c Vector.mapAccumr) (:fv _uniq.3374) (:fv _uniq.3559) ((:c HAdd.hAdd) (:c Nat) (... | [{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"xs","sexp":"((:c Vector) (:fv _uniq.3374) (:fv _uniq.3379))"},{"name":"α✝","sexp":"(:sort 1)"},{"name":"β✝","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.3374) (:forall _ (:fv _uniq.3558) ((:c Prod) (:fv _uniq.3558)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"source":"induction","sourceEnd":3958,"sourceStart":3949,"tag":"atom"},{"children":[{"contextIndex":2,"semanticRole":"local","source":"xs","sourceEnd":3961,"sourceStart":3959,"tag":"identifier"}],"kind":"null","source":"xs","sourceEnd":3961,"sourceStart":3959,"tag":"node"},{"children":[],"kind":"null","so... | [] | [{"source":"xs","source_end":3961,"source_start":3959,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq... | 24 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffbc1cd95e9ad8b73168931a2a1f8ce8e0b8fa8a43741c8ceb4f72a88d02a1b7 | 98757fa4d6500217b971b9b3fd43bdb5c74900f474091be3048a0a9213ad4e4b | df4518c3b8c7e1ad20f1ceccf1a92d2abf718eeb26ab8af30df8d7fc6269c3b2 | 641935190904a349783548898a0f39ea53bdb1e9e7cc40e834f8b4a0dff67882 |
cat-searcher/leandojo-benchmark-4-random | test | 3,405 | Vector.mapAccumr_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case nil
α : Type u_2
n : ℕ
xs : Vector α n
α✝ : Type
β✝ : Type u_1
f : α → α✝ → α✝ × β✝
x : α
s : α✝
⊢ mapAccumr f (nil.snoc x) s =
let q := f x s;
let r := mapAccumr f nil q.1;
(r.1, r.2.snoc q.2) | ((:c Eq) ((:c Prod) (:fv _uniq.3558) ((:c Vector) (:fv _uniq.3559) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))) ((:c Vector.mapAccumr) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"xs","sexp":"((:c Vector) (:fv _uniq.3374) (:fv _uniq.3379))"},{"name":"α✝","sexp":"(:sort 1)"},{"name":"β✝","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.3374) (:forall _ (:fv _uniq.3558) ((:c Prod) (:fv _uniq.3558)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":3970,"sourceStart":3967,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":3970,"sourceStart":3967,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":3970,"sourceStart":3967,"tag":"node"}],"kind":"Lean.Pars... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq... | 24 | 7 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 09b0313d6eb2b9265c1d88b407d1540327800b1198e27a22a3f85164a04b835e | 8e552f0f56beda553e67dcf0f6e3a5b64574d5a08b5e3723259af720ab5c1eab | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,406 | Vector.mapAccumr_snoc | Mathlib/Data/Vector/Snoc.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [*] | case cons
α : Type u_2
n : ℕ
xs : Vector α n
α✝ : Type
β✝ : Type u_1
f : α → α✝ → α✝ × β✝
x : α
s : α✝
n✝ : ℕ
x✝ : α
w✝ : Vector α n✝
a✝ :
mapAccumr f (w✝.snoc x) s =
let q := f x s;
let r := mapAccumr f w✝ q.1;
(r.1, r.2.snoc q.2)
⊢ mapAccumr f ((x✝ ::ᵥ w✝).snoc x) s =
let q := f x s;
let r := ma... | ((:c Eq) ((:c Prod) (:fv _uniq.3558) ((:c Vector) (:fv _uniq.3559) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c Nat.succ) (:fv _uniq.3591)) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))) ((:c Vector.mapAccumr) (:fv _uniq.3374) (:fv _uniq.3559) ((:c HAdd.... | [{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"xs","sexp":"((:c Vector) (:fv _uniq.3374) (:fv _uniq.3379))"},{"name":"α✝","sexp":"(:sort 1)"},{"name":"β✝","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.3374) (:forall _ (:fv _uniq.3558) ((:c Prod) (:fv _uniq.3558)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c Vector) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_i... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":3980,"sourceStart":3976,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3374","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3379","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq... | 24 | 12 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4eb488f517689de24300039e864b3a6e8197b880daf335bfff24343d105b4ccc | c2a5e83ce66340ab40cc525b8dbfff7cc65def67d62b137755146c92fbf90ea8 | 903cd004ebbac27d656bf09f5687e829125364c7514b78ed1bfc22dadd4b3fee | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,407 | orthogonalProjection_eq_self_iff | Mathlib/Analysis/InnerProductSpace/Projection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h => ?_, fun h => <a>eq_orthogonalProjection_of_mem_of_inner_eq_zero</a> h ?_⟩ | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
⊢ ↑((orthogonalProjection K) v) = v ↔ v ∈ K | case refine_1
𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
h : ↑((orthogonalProjection K) v) = v
⊢ v ∈ K
case refine_... | ((:c Iff) ((:c Eq) (:fv _uniq.383016) ((:c Subtype.val) (:fv _uniq.383016) (:lambda x (:fv _uniq.383016) ((:c Membership.mem) (:fv _uniq.383016) ((:c Set) (:fv _uniq.383016)) ((:c Set.instMembership) (:fv _uniq.383016)) 0 ((:c SetLike.coe) ((:c Submodule) (:fv _uniq.383013) (:fv _uniq.383016) ((:c DivisionSemiring.toSe... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.383013))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.383016))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.38301... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":27579,"sourceStart":27573,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":27583,"sourceStart":27580,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":27586,"sourceStart":27583,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun h => ?_, fun h => eq_orthogonalProjection_of_mem_of_inner_eq_zero h ?_⟩","source_end":27660,"source_start":27580,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb55e4d6feaff7eff536d44cd72b00daf4da5caafa6b016f3d0645d98f269302 | 588cc3ec7950ad9381e8eed4ea429f64f916e1c184b370f2ae89c27111e258b9 | 53844819e27fabd919a268aa3eb4dad57c2ea9a7901278d878b7202c6c1e49c9 | 8d0175169bb4cf000a908f7c9d1a14323c457cd2a545993125ce10b90e9edb4e |
cat-searcher/leandojo-benchmark-4-random | test | 3,408 | orthogonalProjection_eq_self_iff | Mathlib/Analysis/InnerProductSpace/Projection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← h] | case refine_1
𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
h : ↑((orthogonalProjection K) v) = v
⊢ v ∈ K | case refine_1
𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
h : ↑((orthogonalProjection K) v) = v
⊢ ↑((orthogonalProje... | ((:c Membership.mem) (:fv _uniq.383016) ((:c Submodule) (:fv _uniq.383013) (:fv _uniq.383016) ((:c DivisionSemiring.toSemiring) (:fv _uniq.383013) ((:c Semifield.toDivisionSemiring) (:fv _uniq.383013) ((:c Field.toSemifield) (:fv _uniq.383013) ((:c NormedField.toField) (:fv _uniq.383013) ((:c DenselyNormedField.toNorme... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.383013))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.383016))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.38301... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":27668,"sourceStart":27666,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27670,"sourceStart":27669,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":27673,"sourceSt... | [] | [{"source":"h","source_end":27675,"source_start":27674,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 9 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 629a2131ff0418c73b035b65c7472c9f6824d44641596fd6b59182e1ba46efa3 | 5f24c5c5caf14622f9ded514b80c9798c45d0446245ab79d5e7c4b695da02417 | b8f7ba4ddf00851760c0b1131d01447fed956b4cd76dde607f7e82015e941b84 | b93b97c3a6cad1b67142df0e0f94fdf8684e3aeefa2c0c34d4b0417bd17ab496 |
cat-searcher/leandojo-benchmark-4-random | test | 3,409 | orthogonalProjection_eq_self_iff | Mathlib/Analysis/InnerProductSpace/Projection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case refine_1
𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
h : ↑((orthogonalProjection K) v) = v
⊢ ↑((orthogonalProje... | ((:c Membership.mem) (:fv _uniq.383016) ((:c Submodule) (:fv _uniq.383013) (:fv _uniq.383016) ((:c DivisionSemiring.toSemiring) (:fv _uniq.383013) ((:c Semifield.toDivisionSemiring) (:fv _uniq.383013) ((:c Field.toSemifield) (:fv _uniq.383013) ((:c NormedField.toField) (:fv _uniq.383013) ((:c DenselyNormedField.toNorme... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.383013))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.383016))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.38301... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":27685,"sourceStart":27681,"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":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 12 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e29ef177c2c25a3084b822a7504e0d5cfe24913eb85838f21f9b2ef999642a4 | b93b97c3a6cad1b67142df0e0f94fdf8684e3aeefa2c0c34d4b0417bd17ab496 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,410 | orthogonalProjection_eq_self_iff | Mathlib/Analysis/InnerProductSpace/Projection.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case refine_2
𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁵ : _root_.RCLike 𝕜
inst✝⁴ : NormedAddCommGroup E
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace 𝕜 E
inst✝¹ : InnerProductSpace ℝ F
K : Submodule 𝕜 E
inst✝ : HasOrthogonalProjection K
v : E
h : v ∈ K
⊢ ∀ w ∈ K, ⟪v - v, w⟫_𝕜 = 0 | (:forall w (:fv _uniq.383016) (:forall _ ((:c Membership.mem) (:fv _uniq.383016) ((:c Submodule) (:fv _uniq.383013) (:fv _uniq.383016) ((:c DivisionSemiring.toSemiring) (:fv _uniq.383013) ((:c Semifield.toDivisionSemiring) (:fv _uniq.383013) ((:c Field.toSemifield) (:fv _uniq.383013) ((:c NormedField.toField) (:fv _uni... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁵","sexp":"((:c RCLike) (:fv _uniq.383013))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.383016))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.38301... | (:forall w :explicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.383013","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":27695,"sourceStart":27691,"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.383013","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.383016","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 15 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | da4849cfe276fcc508756023e3e3816e9bed81eab919514336d53bdcbd8303c2 | 1c2d4ea627566618ab45cb2bd702750be1bda7319b7f163808260bad718c5cc5 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,411 | OrthonormalBasis.coe_toBasis | Mathlib/Analysis/InnerProductSpace/PiL2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>OrthonormalBasis.toBasis</a>] | ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝² : Nor... | ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝² : Nor... | ((:c Eq) (:forall a (:fv _uniq.260464) (:fv _uniq.260512)) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.260464) (:fv _uniq.260470) (:fv _uniq.260512) ((:c DivisionSemiring.toSemiring) (:fv _uniq.260470) ((:c Semifield.toDivisionSemiring) (:fv _uniq.260470) ((:c Field.toSemifield) (:fv _uniq.260470) ((:c NormedField.toFiel... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.260470))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.260512))"},{"name":"inst✝⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:fv FV4))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Basis) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":19456,"sourceStart":19454,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19458,"sourceStart":19457,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"OrthonormalBasis... | [] | [{"source":"OrthonormalBasis.toBasis","source_end":19482,"source_start":19458,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 115 | 4 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67d51168c4331521b62769ef6f0a3d90b30bc05bd4debb20bc0c6de2ba44906b | c5d90a28a48a8f8cfda38e6822cf924bb51c6eee4730a66be97fb358e147325d | 4566263c4a686ff90e1b0f23fd3381bfd03fc2b4c8d3c566e5cfc0996691ad24 | 55d4488493cf275f42e182050213fb5734d0f83a72817bda455f0ebaafd5ff72 |
cat-searcher/leandojo-benchmark-4-random | test | 3,412 | OrthonormalBasis.coe_toBasis | Mathlib/Analysis/InnerProductSpace/PiL2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext j | ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝² : Nor... | case h
ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝... | ((:c Eq) (:forall a (:fv _uniq.260464) (:fv _uniq.260512)) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.260464) (:fv _uniq.260470) (:fv _uniq.260512) ((:c DivisionSemiring.toSemiring) (:fv _uniq.260470) ((:c Semifield.toDivisionSemiring) (:fv _uniq.260470) ((:c Field.toSemifield) (:fv _uniq.260470) ((:c NormedField.toFiel... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.260470))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.260512))"},{"name":"inst✝⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:fv FV4))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Basis) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext","sourceEnd":19519,"sourceStart":19516,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":19521,"sourceStart":19520,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"j","sourceEnd":19521,"sourceStart":19520,"tag... | [{"role":"fresh_name","source":"j","source_end":19521,"source_start":19520,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 115 | 7 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5763e0f4ad68ae06c55548beed6329fa9b0b5155170cad07759efa4a48cf9589 | 55d4488493cf275f42e182050213fb5734d0f83a72817bda455f0ebaafd5ff72 | 541ea80d14360c000487eaabc2fb2dba269e64d03da1f54c11f36fec1cd0ca44 | 958ba8d46d6dc20011f649e2381ff3b469024b13aa6d71463d59321c0141e9b9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,413 | OrthonormalBasis.coe_toBasis | Mathlib/Analysis/InnerProductSpace/PiL2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | classical rw [<a>Basis.coe_ofEquivFun</a>] congr | case h
ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝... | ((:c Eq) (:fv _uniq.260512) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.260464) (:fv _uniq.260470) (:fv _uniq.260512) ((:c DivisionSemiring.toSemiring) (:fv _uniq.260470) ((:c Semifield.toDivisionSemiring) (:fv _uniq.260470) ((:c Field.toSemifield) (:fv _uniq.260470) ((:c NormedField.toField) (:fv _uniq.260470) ((:c Dens... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.260470))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.260512))"},{"name":"inst✝⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Basis) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"classical","sourceEnd":19533,"sourceStart":19524,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":19540,"sourceStart":19538,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19542,"sourceStart":... | [] | [{"source":"Basis.coe_ofEquivFun","source_end":19562,"source_start":19542,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 115 | 8 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f68cebdbc573f7905105b8066ff26e09e50f1fa9f7a3ae0e469331354943f963 | 958ba8d46d6dc20011f649e2381ff3b469024b13aa6d71463d59321c0141e9b9 | 1945706c6878c90aae338c4e2e65614403f05aa08179634dfaecb8832e344046 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,414 | OrthonormalBasis.coe_toBasis | Mathlib/Analysis/InnerProductSpace/PiL2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Basis.coe_ofEquivFun</a>] | case h
ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝... | case h
ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝... | ((:c Eq) (:fv _uniq.260512) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.260464) (:fv _uniq.260470) (:fv _uniq.260512) ((:c DivisionSemiring.toSemiring) (:fv _uniq.260470) ((:c Semifield.toDivisionSemiring) (:fv _uniq.260470) ((:c Field.toSemifield) (:fv _uniq.260470) ((:c NormedField.toField) (:fv _uniq.260470) ((:c Dens... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.260470))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.260512))"},{"name":"inst✝⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Basis) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV4)) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":19540,"sourceStart":19538,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19542,"sourceStart":19541,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Basis.coe_ofEqui... | [] | [{"source":"Basis.coe_ofEquivFun","source_end":19562,"source_start":19542,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 115 | 11 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c2ef98a2de62b76a5e77f62f1ce97f5b71c30088a4e1d9b82c831ab8856c8b75 | 958ba8d46d6dc20011f649e2381ff3b469024b13aa6d71463d59321c0141e9b9 | 25934e1cb346512ee3a4ba8cda5b054938a84203f29bd54d577edf2511720237 | 3cbee1e4a1d2d803b1f3cd345d3fb0d914a8eed629cf43a0f1037a98fd37b906 |
cat-searcher/leandojo-benchmark-4-random | test | 3,415 | OrthonormalBasis.coe_toBasis | Mathlib/Analysis/InnerProductSpace/PiL2.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case h
ι : Type u_1
ι' : Type u_2
𝕜 : Type u_3
inst✝⁹ : _root_.RCLike 𝕜
E : Type u_4
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : InnerProductSpace 𝕜 E
E' : Type u_5
inst✝⁶ : NormedAddCommGroup E'
inst✝⁵ : InnerProductSpace 𝕜 E'
F : Type u_6
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
F' : Type u_7
inst✝... | ((:c Eq) (:fv _uniq.260512) ((:lambda i (:fv _uniq.260464) ((:c DFunLike.coe) ((:c LinearEquiv) (:fv _uniq.260470) (:fv _uniq.260470) ((:c DivisionSemiring.toSemiring) (:fv _uniq.260470) ((:c Semifield.toDivisionSemiring) (:fv _uniq.260470) ((:c Field.toSemifield) (:fv _uniq.260470) ((:c NormedField.toField) (:fv _uniq... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"𝕜","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.260470))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.260512))"},{"name":"inst✝⁷","sexp":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV4)) (:arg :explicit 1 (:app (:lambda i :explicit (:fv FV0) (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearEquiv) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"congr","sourceEnd":19573,"sourceStart":19568,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":19573,"sourceStart":19568,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.260464","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.260467","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 115 | 14 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4915c5cfdfa613a9d789e77a48948da9fb22ef3f54c38889b05301cad84956d | 3cbee1e4a1d2d803b1f3cd345d3fb0d914a8eed629cf43a0f1037a98fd37b906 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,416 | Finset.preimage_union | Mathlib/Data/Finset/Preimage.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u
β : Type v
ι : Sort w
γ : Type x
inst✝¹ : DecidableEq α
inst✝ : DecidableEq β
f : α → β
s t : Finset β
hst : InjOn f (f ⁻¹' ↑(s ∪ t))
⊢ ↑((s ∪ t).preimage f hst) = ↑(s.preimage f ⋯ ∪ t.preimage f ⋯) | ((:c Eq) ((:c Set) (:fv _uniq.4775)) ((:c Finset.toSet) (:fv _uniq.4775) ((:c Finset.preimage) (:fv _uniq.4775) (:fv _uniq.4777) ((:c Union.union) ((:c Finset) (:fv _uniq.4777)) ((:c Finset.instUnion) (:fv _uniq.4777) (:fv _uniq.5349)) (:fv _uniq.5351) (:fv _uniq.5352)) (:fv _uniq.5350) (:fv _uniq.5353))) ((:c Finset.t... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort w)"},{"name":"γ","sexp":"(:sort (+ x 1))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.4775))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.4777))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.4775) ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Finset.toSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset.preimage) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Union.union) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4777","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2480,"sourceStart":2476,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4777","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 20 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8744dd73fdb4baafedcc68e9e4e1d2408536ad0cfede9907ce12f5bd24723e3 | 1b7cb3eb6b49efe5e4353f6bd5845d3988836a35cc3cd7225bbe44e0cd3b5be6 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,417 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hf := <a>LSeriesSummable_logMul_of_lt_re</a> (show <a>LSeries.abscissaOfAbsConv</a> 1 < s.re by rw [<a>LSeries.abscissaOfAbsConv_one</a>]; exact_mod_cast hs) | s : ℂ
hs : 1 < s.re
⊢ LSeriesSummable (fun n => ↑(Λ n)) s | s : ℂ
hs : 1 < s.re
hf : LSeriesSummable (logMul 1) s
⊢ LSeriesSummable (fun n => ↑(Λ n)) s | ((:c LSeriesSummable) (:lambda _ (:c Nat) ((:c Complex.ofReal') ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c ArithmeticFunction.vonMangoldt) 0))) (:fv _uniq.69165)) | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"}] | (:app (:c LSeriesSummable) (:arg :explicit 0 (:lambda _ :explicit (:c Nat) (:app (:c Complex.ofReal') (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Real))))))) (:arg :impli... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"have","sourceEnd":15380,"sourceStart":15376,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf","sourceEnd":15383,"sourceStart":15381,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf","sourceEnd":15383,"sourceStart":15381,"tag":"nod... | [] | [{"source":"LSeriesSummable_logMul_of_lt_re\n (show abscissaOfAbsConv 1 < s.re by rw [abscissaOfAbsConv_one]; exact_mod_cast hs)","source_end":15505,"source_start":15387,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"}] | 65 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 28728a1f792435254f41e3b3944d58d14b93bf8142e91152f3b33ac4e9c20686 | 507ae0617f3af7f05dfb57f7df6f3ad4627708d1242011d2d6a879b7c4f16b2c | f3e34efa7998905d2c3d49d4e71ed639505851af98a97710b3b2c41855d416f7 | 9853afe26ccf3276ad2923a0739fef57f6582885dfe0c2d4fe888537ac212a32 |
cat-searcher/leandojo-benchmark-4-random | test | 3,418 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LSeriesSummable</a>, ← <a>summable_norm_iff</a>] at hf ⊢ | s : ℂ
hs : 1 < s.re
hf : LSeriesSummable (logMul 1) s
⊢ LSeriesSummable (fun n => ↑(Λ n)) s | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
⊢ Summable fun x => ‖term (fun n => ↑(Λ n)) s x‖ | ((:c LSeriesSummable) (:lambda _ (:c Nat) ((:c Complex.ofReal') ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c ArithmeticFunction.vonMangoldt) 0))) (:fv _uniq.69165)) | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c LSeriesSummable) ((:c LSeries.logMul) ((:c OfNat.ofNat) (:forall _ (:c Na... | (:app (:c LSeriesSummable) (:arg :explicit 0 (:lambda _ :explicit (:c Nat) (:app (:c Complex.ofReal') (:arg :explicit 0 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:c Real))))))) (:arg :impli... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"rw","sourceEnd":15510,"sourceStart":15508,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15512,"sourceStart":15511,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LSeriesSummable"... | [] | [{"source":"LSeriesSummable","source_end":15527,"source_start":15512,"syntax_kind":"ident"},{"source":"hf","source_end":15557,"source_start":15555,"syntax_kind":"ident"},{"source":"summable_norm_iff","source_end":15550,"source_start":15533,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 12 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 897061ce9b92e5671b1f31942d5eba9d93407ef545d5ee11eba2a6496adffddc | 9853afe26ccf3276ad2923a0739fef57f6582885dfe0c2d4fe888537ac212a32 | c530dcb6c55d0c1f83d464d0b03c5974aa28ea7507600aa11dd27e0bf6e102ed | 1087ec18f9973265b39bcd113b3445b34d11f0dd714fccf206279c37f7724c3d |
cat-searcher/leandojo-benchmark-4-random | test | 3,419 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Summable.of_nonneg_of_le</a> (fun _ ↦ <a>norm_nonneg</a> _) (fun n ↦ <a>LSeries.norm_term_le</a> s ?_) hf | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
⊢ Summable fun x => ‖term (fun n => ↑(Λ n)) s x‖ | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
⊢ ‖↑(Λ n)‖ ≤ ‖logMul 1 n‖ | ((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:lambda x (:c Nat) ((:c Norm.norm) (:c Complex) ((:c NormedAddCommGroup.toNorm) (:c Complex) (:c Complex.instNormedAddCommGroup)) ... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c Summable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (: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 (:lambda x :explicit (:c Nat) (:ap... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"refine","sourceEnd":15570,"sourceStart":15564,"tag":"atom"},{"children":[{"name":"Summable.of_nonneg_of_le","semanticRole":"global","source":"Summable.of_nonneg_of_le","sourceEnd":15595,"sourceStart":15571,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":15597,"sourceStart... | [] | [{"source":"Summable.of_nonneg_of_le (fun _ ↦ norm_nonneg _) (fun n ↦ norm_term_le s ?_) hf","source_end":15654,"source_start":15571,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 16 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71ecfe62cd54cbf958369bd0677d0dc6925d243a415d9f2b56605bc8ae18ff3f | 1087ec18f9973265b39bcd113b3445b34d11f0dd714fccf206279c37f7724c3d | a504d1ce7da50b9828bcbc783660fb0a39b1a17635b914913283da5def93d066 | ca8058d57d7a0dd1123a349c74cd452d2265d5e338bce378225e2b38958696ce |
cat-searcher/leandojo-benchmark-4-random | test | 3,420 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hΛ : ‖↗Λ n‖ ≤ ‖<a>Complex.log</a> n‖ := by simp only [<a>Complex.norm_eq_abs</a>, <a>Complex.abs_ofReal</a>, <a>abs_of_nonneg</a> <a>ArithmeticFunction.vonMangoldt_nonneg</a>, ← <a>Complex.natCast_log</a>, <a>abs_of_nonneg</a> <| <a>Real.log_natCast_nonneg</a> n] exact <a>ArithmeticFunction.vonMangoldt_le_log</a> | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
⊢ ‖↑(Λ n)‖ ≤ ‖logMul 1 n‖ | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
hΛ : ‖(fun n => ↑(Λ n)) n‖ ≤ ‖Complex.log ↑n‖
⊢ ‖↑(Λ n)‖ ≤ ‖logMul 1 n‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Complex) (:c Complex.instNorm) ((:c Complex.ofReal') ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c ArithmeticFunction.v... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c Comp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"have","sourceEnd":15661,"sourceStart":15657,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hΛ","sourceEnd":15665,"sourceStart":15662,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hΛ","sourceEnd":15665,"sourceStart":15662,"tag":"nod... | [] | [{"source":"‖↗Λ n‖ ≤ ‖Complex.log n‖","source_end":15705,"source_start":15668,"syntax_kind":"«term_≤_»"},{"source":"norm_eq_abs","source_end":15738,"source_start":15727,"syntax_kind":"ident"},{"source":"abs_ofReal","source_end":15750,"source_start":15740,"syntax_kind":"ident"},{"source":"_root_.abs_of_nonneg vonMangold... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 17 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42106b3c28f65abaa5dce4a34969408d996faa96c3d5abf8b149b0162e24e00f | ca8058d57d7a0dd1123a349c74cd452d2265d5e338bce378225e2b38958696ce | 4478e861a6a8273a08a29d8ebe43a192ae90cc75513ef90685a57a92c7fe917b | 31500306682beed6357082f884855cf3947987609a820536bfc863fcf48fa68d |
cat-searcher/leandojo-benchmark-4-random | test | 3,421 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hΛ.trans <| by simp only [<a>Complex.norm_eq_abs</a>, <a>norm_mul</a>, <a>Pi.one_apply</a>, <a>NormOneClass.norm_one</a>, <a>mul_one</a>, <a>le_refl</a>] | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
hΛ : ‖(fun n => ↑(Λ n)) n‖ ≤ ‖Complex.log ↑n‖
⊢ ‖↑(Λ n)‖ ≤ ‖logMul 1 n‖ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Complex) (:c Complex.instNorm) ((:c Complex.ofReal') ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c ArithmeticFunction.v... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c Comp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"exact","sourceEnd":15930,"sourceStart":15925,"tag":"atom"},{"children":[{"source":"hΛ.trans","sourceEnd":15940,"sourceStart":15931,"tag":"identifier"},{"source":"<|","sourceEnd":15943,"sourceStart":15941,"tag":"atom"},{"children":[{"source":"by","sourceEnd":15946,"sourceStart":15944,"tag":"atom"... | [] | [{"source":"hΛ.trans <| by simp only [norm_eq_abs, norm_mul, Pi.one_apply, norm_one, mul_one, le_refl]","source_end":16022,"source_start":15931,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 21 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c3dcdbf59ece57f69861dd9a5bac6f4e5206de2a6c44913cb8c88049b3bd413c | 31500306682beed6357082f884855cf3947987609a820536bfc863fcf48fa68d | 5b54c1dd2723d31d51e6f0b27d93dd1db304bc1097fa7db62a442b5233ed3e29 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,422 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LSeries.abscissaOfAbsConv_one</a>] | s : ℂ
hs : 1 < s.re
⊢ abscissaOfAbsConv 1 < ↑s.re | s : ℂ
hs : 1 < s.re
⊢ 1 < ↑s.re | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c LSeries.abscissaOfAbsConv) ((:c OfNat.ofNat) (:forall _ (:c Nat) (:c Complex)) (:lit 1) ((:c One.toOfNat1) (:forall _ (:c Nat) (:c Complex)) ((:c Pi.instOne) (:c Nat) (:lambda _ (:c Nat) (:c ... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c LSeries.abscissaOfAbsConv) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:c Complex))) (:arg :explicit 1 (:lit 1... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"rw","sourceEnd":15461,"sourceStart":15459,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15463,"sourceStart":15462,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LSeries.abscissa... | [] | [{"source":"abscissaOfAbsConv_one","source_end":15484,"source_start":15463,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"}] | 65 | 7 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50a31d3cf9646e7a6d40698261b23785f5e1edb7c02dfbe8d328f279e67cd517 | be09e4f24ab205b7bd191b545fa700b7d3dc3feb673f355cd91152015685d460 | e1592c77174422f8f00039e7c152dd292f249c19c6e2a337114cf92136044004 | db0759df83ec3c603275dfa9fc620b522cf555bfa817105f4af6f609b556ee73 |
cat-searcher/leandojo-benchmark-4-random | test | 3,423 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hs | s : ℂ
hs : 1 < s.re
⊢ 1 < ↑s.re | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 1) ((:c One.toOfNat1) (:c EReal) (:c instERealOne))) ((:c Real.toEReal) ((:c Complex.re) (:fv _uniq.69165)))) | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"exact_mod_cast","sourceEnd":15501,"sourceStart":15487,"tag":"atom"},{"contextIndex":2,"semanticRole":"local","source":"hs","sourceEnd":15504,"sourceStart":15502,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.tacticExact_mod_cast_","source":"exact_mod_cast hs","sourceEnd":15504,"sourceStart":154... | [] | [{"source":"hs","source_end":15504,"source_start":15502,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"}] | 65 | 11 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2aad01be9ff693dafd47acaef2a90bd0fe186fd32accd44471830fdfc081247 | db0759df83ec3c603275dfa9fc620b522cf555bfa817105f4af6f609b556ee73 | aff1b04bd507eed84531e5236aca67b736a1086f13e874b36cccefc9a3a8f5fb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,424 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.norm_eq_abs</a>, <a>Complex.abs_ofReal</a>, <a>abs_of_nonneg</a> <a>ArithmeticFunction.vonMangoldt_nonneg</a>, ← <a>Complex.natCast_log</a>, <a>abs_of_nonneg</a> <| <a>Real.log_natCast_nonneg</a> n] | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
⊢ ‖(fun n => ↑(Λ n)) n‖ ≤ ‖Complex.log ↑n‖ | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
⊢ Λ n ≤ Real.log ↑n | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Complex) (:c Complex.instNorm) ((:lambda _ (:c Nat) ((:c Complex.ofReal') ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:lambda... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"simp","sourceEnd":15720,"sourceStart":15716,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15725,"sourceStart":15721,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":157... | [] | [{"source":"norm_eq_abs","source_end":15738,"source_start":15727,"syntax_kind":"ident"},{"source":"abs_ofReal","source_end":15750,"source_start":15740,"syntax_kind":"ident"},{"source":"_root_.abs_of_nonneg vonMangoldt_nonneg","source_end":15791,"source_start":15752,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Compl... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 19 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9d2a2c548ea363874d89093b8094f078426011363350d1af71452f2bc36070d6 | 5c3aedaa679f3731b8df08ca98eb9b1c95209f6d75da9448be9a9b612dbaa1b4 | 6483f1bcecb0c8f9abab57d29ef13bf5b0be698f1579873cde56ceda9e97e634 | e43cd2d5480011d8ed7dc200ac77a01b5a29afcfd4ecd9ae05c0a4ccc66e803c |
cat-searcher/leandojo-benchmark-4-random | test | 3,425 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>ArithmeticFunction.vonMangoldt_le_log</a> | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
⊢ Λ n ≤ Real.log ↑n | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c DFunLike.coe) ((:c ArithmeticFunction) (:c Real) (:c Real.instZero)) (:c Nat) (:lambda _ (:c Nat) (:c Real)) ((:c ArithmeticFunction.instFunLikeNat) (:c Real) (:c Real.instZero)) (:c ArithmeticFunction.vonMangoldt) (:fv _uniq.71635)) ((:c Real.log) ((:c Nat.cast) (:c Real) (:... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c ArithmeticFunction) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Zero) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"source":"exact","sourceEnd":15884,"sourceStart":15879,"tag":"atom"},{"name":"ArithmeticFunction.vonMangoldt_le_log","semanticRole":"global","source":"ArithmeticFunction.vonMangoldt_le_log","sourceEnd":15922,"sourceStart":15885,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact Arithme... | [] | [{"source":"ArithmeticFunction.vonMangoldt_le_log","source_end":15922,"source_start":15885,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 20 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53566b01790fec95b2a5a3579fdef4b9df12637ab4eadcff5fe0566642874780 | e43cd2d5480011d8ed7dc200ac77a01b5a29afcfd4ecd9ae05c0a4ccc66e803c | 5ab6c457af2652cede9a06563eae7a5009835d45a942056d69752e4b7a353134 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,426 | ArithmeticFunction.LSeriesSummable_vonMangoldt | Mathlib/NumberTheory/LSeries/Dirichlet.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Complex.norm_eq_abs</a>, <a>norm_mul</a>, <a>Pi.one_apply</a>, <a>NormOneClass.norm_one</a>, <a>mul_one</a>, <a>le_refl</a>] | s : ℂ
hs : 1 < s.re
hf : Summable fun x => ‖term (logMul 1) s x‖
n : ℕ
hΛ : ‖(fun n => ↑(Λ n)) n‖ ≤ ‖Complex.log ↑n‖
⊢ ‖Complex.log ↑n‖ ≤ ‖logMul 1 n‖ | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Norm.norm) (:c Complex) (:c Complex.instNorm) ((:c Complex.log) ((:c Nat.cast) (:c Complex) ((:c Semiring.toNatCast) (:c Complex) (:c Complex.instSemiring)) (:fv _uniq.71635)))) ((:c Norm.norm) (:c Complex) (:c Complex.instNorm) ((:c LSeri... | [{"name":"s","sexp":"(:c Complex)"},{"name":"hs","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Complex.re) (:fv _uniq.69165)))"},{"name":"hf","sexp":"((:c Summable) (:c Real) (:c Nat) (:c Real.instAddCommMonoid) ((:c UniformSpac... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c Comp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"name":"hs","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (:c R... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":15951,"sourceStart":15947,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":15956,"sourceStart":15952,"tag":"atom"}],"kind"... | [] | [{"source":"norm_eq_abs","source_end":15969,"source_start":15958,"syntax_kind":"ident"},{"source":"norm_mul","source_end":15979,"source_start":15971,"syntax_kind":"ident"},{"source":"Pi.one_apply","source_end":15993,"source_start":15981,"syntax_kind":"ident"},{"source":"norm_one","source_end":16003,"source_start":15995... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69165","is_instance":false,"is_let":false,"user_name":"s"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.69166","is_instance":false,"is_let":false,"user_name":"hs"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 65 | 24 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 756f08889cd42e2ed8c0f1cb3e188844184a8af9e0268009bc60fa1b41cf1e2a | 5b00c3bb13a0ebeabce0ba8107069000becce1f61709ba8829024f83319ff897 | 4871f23f6ac31fc84485199f155d666a67a2b5b4cb4eaee46f427bbc1b105d01 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,427 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>nilpotent_iff_finite_ascending_central_series</a>] | G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ Group.IsNilpotent G ↔ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) ↔ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | ((:c Iff) ((:c Group.IsNilpotent) (:fv _uniq.35059) (:fv _uniq.35062)) ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsDescendingCentralSer... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Group.IsNilpotent) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :impl... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":12450,"sourceStart":12448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12452,"sourceStart":12451,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"nilpotent_iff_fi... | [] | [{"source":"nilpotent_iff_finite_ascending_central_series","source_end":12497,"source_start":12452,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 268977003dc6c645f68a989c5cf06acce7106d0ca03ab39efe39f3fdce37cdbb | 617318a41a3ef490f857503a49b313e3babc7f3d43f322157ed1ca6497361d3f | e6345ab4e75f03ec1c69c88dbcad97e0e53f9a1ac395dff321daebedcfd66443 | af4ee7deec5c4b4cbb92751dce7d5f1bd83d17f4dfdb4fb5fbb33bc5ccc13dbc |
cat-searcher/leandojo-benchmark-4-random | test | 3,428 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) ↔ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | case mp
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) → ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥
case mpr
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥) → ∃ n H, IsAscendingCentralSeries H... | ((:c Iff) ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsAscendingCentralSeries) (:fv _uniq.35059) (:fv _uniq.35062) 0) ((:c Eq) ((:c Subg... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"constructor","sourceEnd":12512,"sourceStart":12501,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":12512,"sourceStart":12501,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 7 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b31b201a4fe913f4b7e3329275a47d337a1a3f3f87394fc466452b7b81e41af6 | af4ee7deec5c4b4cbb92751dce7d5f1bd83d17f4dfdb4fb5fbb33bc5ccc13dbc | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 88522a3bc4d5e7ac817d7754992234f0f851ce3b9cca8328464df6fbcb4e0b9d |
cat-searcher/leandojo-benchmark-4-random | test | 3,429 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨n, H, hH, hn⟩ | case mp
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) → ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | (:forall _ ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsAscendingCentralSeries) (:fv _uniq.35059) (:fv _uniq.35062) 0) ((:c Eq) ((:c Sub... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"}] | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0)))))... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"rintro","sourceEnd":12524,"sourceStart":12518,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12528,"sourceStart":12525,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":12529,"sou... | [{"role":"fresh_name","source":"n","source_end":12529,"source_start":12528,"syntax_kind":"ident"},{"role":"fresh_name","source":"H","source_end":12532,"source_start":12531,"syntax_kind":"ident"},{"role":"fresh_name","source":"hH","source_end":12536,"source_start":12534,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [{"source":"⟨n, H, hH, hn⟩","source_end":12543,"source_start":12525,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 12 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9fb7ba0f545fe19c89ea5c550f6e72dfe0eae71632319cc991f0d0c1e6f6041 | c3ef3e15cac333b5cacf2bfbfedb5687f61aae20c7bf019c9abd1d91548ab762 | 84c6f7c21bd9af8f41f0f9f7f8e75d553c34fc0f60f17eb7cdf5c7f11d1b3e42 | 7c09467d6efc90d8d12853f3e6e6feee9dfeb1871b49f16fe0badcded3bad39f |
cat-searcher/leandojo-benchmark-4-random | test | 3,430 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨n, fun m => H (n - m), <a>is_decending_rev_series_of_is_ascending</a> G hn hH, ?_⟩ | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥ | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ (fun m => H (n - m)) n = ⊥ | ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsDescendingCentralSeries) (:fv _uniq.35059) (:fv _uniq.35062) 0) ((:c Eq) ((:c Subgroup) (:f... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0)))))))) (:arg :explicit 1... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"refine","sourceEnd":12554,"sourceStart":12548,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":12558,"sourceStart":12555,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"n","sourceEnd":12559,"sourceStart":12558,"tag":"identifier"},{"source":",","sourceEnd":12560,... | [] | [{"source":"⟨n, fun m => H (n - m), is_decending_rev_series_of_is_ascending G hn hH, ?_⟩","source_end":12635,"source_start":12555,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 13 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8eabce27ee7cf7c8ea85de825dd5fe44404b6cb4760eb2914afff82dd9035ccb | 7c09467d6efc90d8d12853f3e6e6feee9dfeb1871b49f16fe0badcded3bad39f | 572647d4412f9f994fded651b41a051640696989bc8cb3606cd87163ad901698 | d1fbd2b40c6a018eec78a20026fa2ac488d94af9c081011990c832a506b54c26 |
cat-searcher/leandojo-benchmark-4-random | test | 3,431 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ (fun m => H (n - m)) n = ⊥ | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ H (n - n) = ⊥ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:lambda m (:c Nat) ((:fv _uniq.36484) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.36466) 0))) (:fv _uniq.36466)) ((:c Bot.bot) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:c Subgroup.instBot) (:fv... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:lambda m :explicit (:c Nat) (:app (:fv FV6) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :im... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"dsimp","sourceEnd":12645,"sourceStart":12640,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12650,"sourceStart":12646,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":12... | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 14 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 923d7530c23049d30b1bb1d5f8e10821bb06bf13e868fecd77b3e302c9e2e6aa | d1fbd2b40c6a018eec78a20026fa2ac488d94af9c081011990c832a506b54c26 | a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273 | 36c444ef5db5e18702d09127a0b6aa72ade64cea27bc466dcd803407d6f7ac56 |
cat-searcher/leandojo-benchmark-4-random | test | 3,432 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>tsub_self</a>] | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ H (n - n) = ⊥ | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ H 0 = ⊥ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:fv _uniq.36484) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.36466) (:fv _uniq.36466))) ((:c Bot.bot) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:c Subgroup.instBot) (:fv _uniq.35059) (:fv _uniq.... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impli... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":12657,"sourceStart":12655,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12659,"sourceStart":12658,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"tsub_self","sema... | [] | [{"source":"tsub_self","source_end":12668,"source_start":12659,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 15 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1e72b4782a739686712395733a1e5c26bd689d108bc06d33ee2e33be4571f790 | 36c444ef5db5e18702d09127a0b6aa72ade64cea27bc466dcd803407d6f7ac56 | 75b0e79463e619544371ec41256c1720886cffdf5fb76cef108d695d57263faf | 3c6d72e23e6f58e30ecd1ee1c44c8980b7f608b7cf136c19896c004ecd48e4a1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,433 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hH.1 | case mp.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsAscendingCentralSeries H
hn : H n = ⊤
⊢ H 0 = ⊥ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:fv _uniq.36484) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c Zero.toOfNat0) (:c Nat) ((:c AddMonoid.toZero) (:c Nat) ((:c AddCommMonoid.toAddMonoid) (:c Nat) ((:c OrderedAddCommMonoid.toAddCommMonoid) (:c Nat) ((:c CanonicallyOrderedAddCommMonoid.toOrderedAddC... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":12679,"sourceStart":12674,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"hH","sourceEnd":12682,"sourceStart":12680,"tag":"identifier"},{"source":".","sourceEnd":12683,"sourceStart":12682,"tag":"atom"},{"children":[{"source":"1","sourceEnd":12684,... | [] | [{"source":"hH.1","source_end":12684,"source_start":12680,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 18 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11a880a66cbefaf5899debe1200d0a8ef2b8f6712aeb010ee99a5e3f72896626 | 3c6d72e23e6f58e30ecd1ee1c44c8980b7f608b7cf136c19896c004ecd48e4a1 | 775d4d6008c6532336f69f1c80d62fdd0b5b4a91d1a95466107ae3aae46b429c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,434 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨n, H, hH, hn⟩ | case mpr
G : Type u_1
inst✝¹ : Group G
H : Subgroup G
inst✝ : H.Normal
⊢ (∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥) → ∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤ | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ ∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤ | (:forall _ ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsDescendingCentralSeries) (:fv _uniq.35059) (:fv _uniq.35062) 0) ((:c Eq) ((:c Su... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"}] | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0)))))... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"rintro","sourceEnd":12696,"sourceStart":12690,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12700,"sourceStart":12697,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":12701,"sou... | [{"role":"fresh_name","source":"n","source_end":12701,"source_start":12700,"syntax_kind":"ident"},{"role":"fresh_name","source":"H","source_end":12704,"source_start":12703,"syntax_kind":"ident"},{"role":"fresh_name","source":"hH","source_end":12708,"source_start":12706,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [{"source":"⟨n, H, hH, hn⟩","source_end":12715,"source_start":12697,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 23 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 932bc08ab8d898a4b975f410a246c99f9e67ec6bf89542e38ce4c77fd983a49e | 24ae4fbb1f4af5dbfad92a2227ee0a2696a4d80a434c3e1a2bcbddc2e95cc330 | 84c6f7c21bd9af8f41f0f9f7f8e75d553c34fc0f60f17eb7cdf5c7f11d1b3e42 | 21901ae15ba18c554fb0ea3af755fd46d52e149e58455e15ce7b6fb603bf7833 |
cat-searcher/leandojo-benchmark-4-random | test | 3,435 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨n, fun m => H (n - m), <a>is_ascending_rev_series_of_is_descending</a> G hn hH, ?_⟩ | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ ∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤ | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ (fun m => H (n - m)) n = ⊤ | ((:c Exists) (:c Nat) (:lambda n (:c Nat) ((:c Exists) (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) (:lambda H (:forall _ (:c Nat) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))) ((:c And) ((:c IsAscendingCentralSeries) (:fv _uniq.35059) (:fv _uniq.35062) 0) ((:c Eq) ((:c Subgroup) (:fv... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Exists) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0)))))))) (:arg :explicit 1... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"refine","sourceEnd":12726,"sourceStart":12720,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":12730,"sourceStart":12727,"tag":"atom"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"n","sourceEnd":12731,"sourceStart":12730,"tag":"identifier"},{"source":",","sourceEnd":12732,... | [] | [{"source":"⟨n, fun m => H (n - m), is_ascending_rev_series_of_is_descending G hn hH, ?_⟩","source_end":12808,"source_start":12727,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 24 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 432b4a6edde337b901e4806b6769537671932638ab8d7588ec61e56b35e34a26 | 21901ae15ba18c554fb0ea3af755fd46d52e149e58455e15ce7b6fb603bf7833 | 7e350037419f3198d37e06b27100cb84e59ab763ce7eb7d74408532511082052 | 7fa63e8356c225f22868a848fdf53933ec99b3e7e70af15d7086e7cd93c16872 |
cat-searcher/leandojo-benchmark-4-random | test | 3,436 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ (fun m => H (n - m)) n = ⊤ | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ H (n - n) = ⊤ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:lambda m (:c Nat) ((:fv _uniq.36877) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.36859) 0))) (:fv _uniq.36859)) ((:c Top.top) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:c Subgroup.instTop) (:fv... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:lambda m :explicit (:c Nat) (:app (:fv FV6) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :im... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"dsimp","sourceEnd":12818,"sourceStart":12813,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12823,"sourceStart":12819,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":12... | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 25 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a2dc75255a13b6f926105e1a80d6205cda2ce247ec548ccf981c8135a358f76 | 7fa63e8356c225f22868a848fdf53933ec99b3e7e70af15d7086e7cd93c16872 | a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273 | 97f3c08a6088690258d86880399096f898c2fe12ce1cd881efa2e23c91d33ccd |
cat-searcher/leandojo-benchmark-4-random | test | 3,437 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>tsub_self</a>] | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ H (n - n) = ⊤ | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ H 0 = ⊤ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:fv _uniq.36877) ((:c HSub.hSub) (:c Nat) (:c Nat) (:c Nat) ((:c instHSub) (:c Nat) (:c instSubNat)) (:fv _uniq.36859) (:fv _uniq.36859))) ((:c Top.top) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:c Subgroup.instTop) (:fv _uniq.35059) (:fv _uniq.... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :impli... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"rw","sourceEnd":12830,"sourceStart":12828,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12832,"sourceStart":12831,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"tsub_self","sema... | [] | [{"source":"tsub_self","source_end":12841,"source_start":12832,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 26 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3707c1743a80f1060f0863f15ab4bcabf5c18e725be8d164e0b36bffc04958e9 | 97f3c08a6088690258d86880399096f898c2fe12ce1cd881efa2e23c91d33ccd | 75b0e79463e619544371ec41256c1720886cffdf5fb76cef108d695d57263faf | 4e0e710bcc541a3eb1bc89bfbdeb93353fda3d2692a3164a0696d9d6c293c178 |
cat-searcher/leandojo-benchmark-4-random | test | 3,438 | nilpotent_iff_finite_descending_central_series | Mathlib/GroupTheory/Nilpotent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hH.1 | case mpr.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
H✝ : Subgroup G
inst✝ : H✝.Normal
n : ℕ
H : ℕ → Subgroup G
hH : IsDescendingCentralSeries H
hn : H n = ⊥
⊢ H 0 = ⊤ | ((:c Eq) ((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062)) ((:fv _uniq.36877) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c Zero.toOfNat0) (:c Nat) ((:c AddMonoid.toZero) (:c Nat) ((:c AddCommMonoid.toAddMonoid) (:c Nat) ((:c OrderedAddCommMonoid.toAddCommMonoid) (:c Nat) ((:c CanonicallyOrderedAddCommMonoid.toOrderedAddC... | [{"name":"G","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.35059))"},{"name":"H✝","sexp":"((:c Subgroup) (:fv _uniq.35059) (:fv _uniq.35062))"},{"name":"inst✝","sexp":"((:c Subgroup.Normal) (:fv _uniq.35059) (:fv _uniq.35062) (:fv _uniq.35070))"},{"name":"n","sexp":"(:c Nat)"},{"name":"H",... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subgroup) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Group) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:fv FV6) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":12852,"sourceStart":12847,"tag":"atom"},{"children":[{"contextIndex":7,"semanticRole":"local","source":"hH","sourceEnd":12855,"sourceStart":12853,"tag":"identifier"},{"source":".","sourceEnd":12856,"sourceStart":12855,"tag":"atom"},{"children":[{"source":"1","sourceEnd":12857,... | [] | [{"source":"hH.1","source_end":12857,"source_start":12853,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.35059","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.35062","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"intern... | 47 | 29 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04ba13851c6d6532d9fb24ee28aad57f1303355d79a64b8e125a350199a88add | 4e0e710bcc541a3eb1bc89bfbdeb93353fda3d2692a3164a0696d9d6c293c178 | 775d4d6008c6532336f69f1c80d62fdd0b5b4a91d1a95466107ae3aae46b429c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,439 | mulIndicator_biUnion_finset_eventuallyEq | Mathlib/Order/Filter/IndicatorFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.iUnion_eq_iUnion_finset</a> s] | α : Type u_1
β : Type u_2
M : Type u_3
E : Type u_4
ι : Type u_5
inst✝ : One β
s : ι → Set α
f : α → β
a : α
⊢ (fun n => (⋃ i ∈ n, s i).mulIndicator f a) =ᶠ[atTop] fun x => (iUnion s).mulIndicator f a | α : Type u_1
β : Type u_2
M : Type u_3
E : Type u_4
ι : Type u_5
inst✝ : One β
s : ι → Set α
f : α → β
a : α
⊢ (fun n => (⋃ i ∈ n, s i).mulIndicator f a) =ᶠ[atTop] fun x => (⋃ t, ⋃ i ∈ t, s i).mulIndicator f a | ((:c Filter.EventuallyEq) ((:c Finset) (:fv _uniq.6205)) (:fv _uniq.5894) ((:c Filter.atTop) ((:c Finset) (:fv _uniq.6205)) ((:c PartialOrder.toPreorder) ((:c Finset) (:fv _uniq.6205)) ((:c Finset.partialOrder) (:fv _uniq.6205)))) (:lambda n ((:c Finset) (:fv _uniq.6205)) ((:c Set.mulIndicator) (:fv _uniq.5891) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝","sexp":"((:c One) (:fv _uniq.5894))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.6205) ((:c Set) (:fv _u... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":3571,"sourceStart":3569,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3573,"sourceStart":3572,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Set.iUn... | [] | [{"source":"iUnion_eq_iUnion_finset s","source_end":3598,"source_start":3573,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 25 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d815dfae75093f633ec4a637c4b86edf81b09ff0ff3e276eac6f96e3afe993ae | 68d6dc1305b0da764ca9193cce81a662ac910fe1abb72859fedc88f336770613 | e46b5f4ae88a667f236ef03e1ca72af4f6a4c9fe4d49453afb9b84ef55fd3448 | 241578474a6501afd1dc16151035f404eefdaeede4c14ba823dc9a526164a121 |
cat-searcher/leandojo-benchmark-4-random | test | 3,440 | mulIndicator_biUnion_finset_eventuallyEq | Mathlib/Order/Filter/IndicatorFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Monotone.mulIndicator_eventuallyEq_iUnion</a> | α : Type u_1
β : Type u_2
M : Type u_3
E : Type u_4
ι : Type u_5
inst✝ : One β
s : ι → Set α
f : α → β
a : α
⊢ (fun n => (⋃ i ∈ n, s i).mulIndicator f a) =ᶠ[atTop] fun x => (⋃ t, ⋃ i ∈ t, s i).mulIndicator f a | case hs
α : Type u_1
β : Type u_2
M : Type u_3
E : Type u_4
ι : Type u_5
inst✝ : One β
s : ι → Set α
f : α → β
a : α
⊢ Monotone fun i => ⋃ i_1 ∈ i, s i_1 | ((:c Filter.EventuallyEq) ((:c Finset) (:fv _uniq.6205)) (:fv _uniq.5894) ((:c Filter.atTop) ((:c Finset) (:fv _uniq.6205)) ((:c PartialOrder.toPreorder) ((:c Finset) (:fv _uniq.6205)) ((:c Finset.partialOrder) (:fv _uniq.6205)))) (:lambda n ((:c Finset) (:fv _uniq.6205)) ((:c Set.mulIndicator) (:fv _uniq.5891) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝","sexp":"((:c One) (:fv _uniq.5894))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.6205) ((:c Set) (:fv _u... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Filter.atTop) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5)))) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"apply","sourceEnd":3607,"sourceStart":3602,"tag":"atom"},{"name":"Monotone.mulIndicator_eventuallyEq_iUnion","semanticRole":"global","source":"Monotone.mulIndicator_eventuallyEq_iUnion","sourceEnd":3649,"sourceStart":3608,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Mon... | [] | [{"source":"Monotone.mulIndicator_eventuallyEq_iUnion","source_end":3649,"source_start":3608,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 25 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de1608ff1d2fe39971ebe9032dfb1b142cabb783df12b0df490836f992bbf6b3 | 241578474a6501afd1dc16151035f404eefdaeede4c14ba823dc9a526164a121 | 00d91fa3524eb910eaf2603ea848b361e49a8ba9a0055b940c353e79e5afcbdc | 2177efd322a24b1f7f6f11ed381b9142b88c5fa5fe96a2ac6e488b02b4182ce8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,441 | mulIndicator_biUnion_finset_eventuallyEq | Mathlib/Order/Filter/IndicatorFunction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun _ _ ↦ <a>Set.biUnion_subset_biUnion_left</a> | case hs
α : Type u_1
β : Type u_2
M : Type u_3
E : Type u_4
ι : Type u_5
inst✝ : One β
s : ι → Set α
f : α → β
a : α
⊢ Monotone fun i => ⋃ i_1 ∈ i, s i_1 | ((:c Monotone) ((:c Finset) (:fv _uniq.6205)) ((:c Set) (:fv _uniq.5891)) ((:c PartialOrder.toPreorder) ((:c Finset) (:fv _uniq.6205)) ((:c Finset.partialOrder) (:fv _uniq.6205))) ((:c PartialOrder.toPreorder) ((:c Set) (:fv _uniq.5891)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.5891)) ((:c Compl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"E","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝","sexp":"((:c One) (:fv _uniq.5894))"},{"name":"s","sexp":"(:forall _ (:fv _uniq.6205) ((:c Set) (:fv _u... | (:app (:c Monotone) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:app (:c Finset) (:arg :explicit 0 (:fv FV5))))))) (:arg :instance 3 (:instance-of (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":3657,"sourceStart":3652,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":3661,"sourceStart":3658,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":3663,"sourceStart":3662,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":... | [] | [{"source":"fun _ _ ↦ biUnion_subset_biUnion_left","source_end":3697,"source_start":3658,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5891","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5894","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 25 | 8 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb94bb3caa9484faa97d7abf6c3e0c1a9febd3c371887851b624cd2ac34f5878 | 2177efd322a24b1f7f6f11ed381b9142b88c5fa5fe96a2ac6e488b02b4182ce8 | 5aff2d2afd66b77899b168c52327ce0e3e90bec693f124ba5f0822880f20c837 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,442 | InnerProductGeometry.angle_eq_pi_iff | Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>InnerProductGeometry.angle</a>, ← <a>real_inner_div_norm_mul_norm_eq_neg_one_iff</a>, <a>Real.arccos_eq_pi</a>, <a>LE.le.le_iff_eq</a>] | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ angle x y = π ↔ x ≠ 0 ∧ ∃ r < 0, y = r • x | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ -1 ≤ ⟪x, y⟫_ℝ / (‖x‖ * ‖y‖) | ((:c Iff) ((:c Eq) (:c Real) ((:c InnerProductGeometry.angle) (:fv _uniq.64563) (:fv _uniq.64566) (:fv _uniq.64579) (:fv _uniq.66593) (:fv _uniq.66594)) (:c Real.pi)) ((:c And) ((:c Ne) (:fv _uniq.64563) (:fv _uniq.66593) ((:c OfNat.ofNat) (:fv _uniq.64563) (:lit 0) ((:c Zero.toOfNat0) (:fv _uniq.64563) ((:c NegZeroCla... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.64563))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.64563) (:c Real.RCLike) (:fv _uniq.64566))"},{"name":"x✝","sexp":"(:fv _uniq.64563)"},{"name":"y✝","sexp":"(:fv _uniq.64563)"},{"name":"x",... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c InnerProductGeometry.angle) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c InnerProductS... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64563","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.64566","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"rw","sourceEnd":9871,"sourceStart":9869,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9873,"sourceStart":9872,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"InnerProductGeometry... | [] | [{"source":"angle","source_end":9878,"source_start":9873,"syntax_kind":"ident"},{"source":"real_inner_div_norm_mul_norm_eq_neg_one_iff","source_end":9927,"source_start":9884,"syntax_kind":"ident"},{"source":"Real.arccos_eq_pi","source_end":9946,"source_start":9929,"syntax_kind":"ident"},{"source":"LE.le.le_iff_eq","sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64563","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.64566","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 59 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 146eee6f2f90932c32831f9b446e896a021597cb988babb5ed0c9fc12c2ad0b1 | 9cfb0a1948f8ac802775d53daa370adfe3aa2955dd748f07983407794d4411e6 | 13c7b734e1f47d41f4df38bdb417cbe882a854d9f3fbe246be6dbc1f1c5f3915 | bd32d3e6fb6082bd585f885418be6194012e4d937b41ecfabd6ac0d1117336ad |
cat-searcher/leandojo-benchmark-4-random | test | 3,443 | InnerProductGeometry.angle_eq_pi_iff | Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (abs_le.mp (<a>abs_real_inner_div_norm_mul_norm_le_one</a> x y)).1 | V : Type u_1
inst✝¹ : NormedAddCommGroup V
inst✝ : InnerProductSpace ℝ V
x✝ y✝ x y : V
⊢ -1 ≤ ⟪x, y⟫_ℝ / (‖x‖ * ‖y‖) | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) (:c Real.partialOrder))) ((:c Neg.neg) (:c Real) (:c Real.instNeg) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne)))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.64563))"},{"name":"inst✝","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.64563) (:c Real.RCLike) (:fv _uniq.64566))"},{"name":"x✝","sexp":"(:fv _uniq.64563)"},{"name":"y✝","sexp":"(:fv _uniq.64563)"},{"name":"x",... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64563","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.64566","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"exact","sourceEnd":9972,"sourceStart":9967,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":9974,"sourceStart":9973,"tag":"atom"},{"children":[{"source":"abs_le.mp","sourceEnd":9983,"sourceStart":9974,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":9985,"... | [] | [{"source":"(abs_le.mp (abs_real_inner_div_norm_mul_norm_le_one x y)).1","source_end":10032,"source_start":9973,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.64563","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.64566","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":... | 59 | 10 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29883c78d9a2b4d59d208e997ccd54bb083797ac8cad017ec8808bb83dc21c0c | bd32d3e6fb6082bd585f885418be6194012e4d937b41ecfabd6ac0d1117336ad | 61bdbd72c0c516bb092c12e2dee89f44ea58026e926ee4eba50c23449cecff42 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,444 | CovBy.Ico_eq | Mathlib/Order/Cover.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.Ioo_union_left</a> h.lt, h.Ioo_eq, <a>Set.empty_union</a>] | α : Type u_1
β : Type u_2
inst✝ : PartialOrder α
a b c : α
h : a ⋖ b
⊢ Ico a b = {a} | ((:c Eq) ((:c Set) (:fv _uniq.24203)) ((:c Set.Ico) (:fv _uniq.24203) ((:c PartialOrder.toPreorder) (:fv _uniq.24203) (:fv _uniq.24209)) (:fv _uniq.24211) (:fv _uniq.24213)) ((:c Singleton.singleton) (:fv _uniq.24203) ((:c Set) (:fv _uniq.24203)) ((:c Set.instSingletonSet) (:fv _uniq.24203)) (:fv _uniq.24211))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PartialOrder) (:fv _uniq.24203))"},{"name":"a","sexp":"(:fv _uniq.24203)"},{"name":"b","sexp":"(:fv _uniq.24203)"},{"name":"c","sexp":"(:fv _uniq.24203)"},{"name":"h","sexp":"((:c CovBy) (:fv _uniq.24203) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.Ico) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV4)))) (:arg :explicit 2 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24203","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24206","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":16089,"sourceStart":16087,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16091,"sourceStart":16090,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"Ioo_union_left h.lt","source_end":16114,"source_start":16095,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h.Ioo_eq","source_end":16124,"source_start":16116,"syntax_kind":"ident"},{"source":"empty_union","source_end":16137,"source_start":16126,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24203","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24206","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 182 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c0c619c51792463db021037502ea29c1cb45bed7d08ac7da431aa4b4765c7749 | 61855ddcd271c77b99ca61c8cab6f9bcaefec353852998506dd34720adfcf2af | b2f6fa1604fb26f0e779a51a75a9fbf6543b0ae47df37017eb21fb29a98efd03 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,447 | IsSubmonoid.multiset_prod_mem | Mathlib/Deprecated/Submonoid.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Quotient.inductionOn</a> m fun l hl => ?_ | M✝ : Type u_1
inst✝² : Monoid M✝
s✝ : Set M✝
A : Type u_2
inst✝¹ : AddMonoid A
t : Set A
M : Type u_3
inst✝ : CommMonoid M
s : Set M
hs : IsSubmonoid s
m : Multiset M
⊢ (∀ a ∈ m, a ∈ s) → m.prod ∈ s | M✝ : Type u_1
inst✝² : Monoid M✝
s✝ : Set M✝
A : Type u_2
inst✝¹ : AddMonoid A
t : Set A
M : Type u_3
inst✝ : CommMonoid M
s : Set M
hs : IsSubmonoid s
m : Multiset M
l : List M
hl : ∀ a ∈ ⟦l⟧, a ∈ s
⊢ Multiset.prod ⟦l⟧ ∈ s | (:forall _ (:forall a (:fv _uniq.16405) (:forall _ ((:c Membership.mem) (:fv _uniq.16405) ((:c Multiset) (:fv _uniq.16405)) ((:c Multiset.instMembership) (:fv _uniq.16405)) 0 (:fv _uniq.16409)) ((:c Membership.mem) (:fv _uniq.16405) ((:c Set) (:fv _uniq.16405)) ((:c Set.instMembership) (:fv _uniq.16405)) 1 (:fv _uniq.1... | [{"name":"M✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.16112))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.16112))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddMonoid) (:fv _uniq.16121))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16121))"},{"name":"M","s... | (:forall _ :explicit (:forall a :explicit (:fv FV7) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Mu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Monoid) (:arg :explici... | {"children":[{"source":"refine","sourceEnd":11442,"sourceStart":11436,"tag":"atom"},{"children":[{"name":"Quotient.inductionOn","semanticRole":"global","source":"Quotient.inductionOn","sourceEnd":11463,"sourceStart":11443,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"m","sourceEnd... | [] | [{"source":"Quotient.inductionOn m fun l hl => ?_","source_end":11480,"source_start":11443,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter... | 64 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb9ceb81ccafea6acf786a628a669e5f034397d8a1a1a8e45d71986a7a5812fa | 6380fb3348597769a5bc7bf74f7e8485ff771cfe0d7574356f6bc25d49776ef9 | 7147b54741a90cae48db25f43d06e25f4a5eeb44668bb77d24ca1b74f70b7669 | ef9350e1bef83e27915d4885dc1b6a7b31d377844f30cb421d0d11145967945c |
cat-searcher/leandojo-benchmark-4-random | test | 3,448 | IsSubmonoid.multiset_prod_mem | Mathlib/Deprecated/Submonoid.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Multiset.quot_mk_to_coe</a>, <a>Multiset.prod_coe</a>] | M✝ : Type u_1
inst✝² : Monoid M✝
s✝ : Set M✝
A : Type u_2
inst✝¹ : AddMonoid A
t : Set A
M : Type u_3
inst✝ : CommMonoid M
s : Set M
hs : IsSubmonoid s
m : Multiset M
l : List M
hl : ∀ a ∈ ⟦l⟧, a ∈ s
⊢ Multiset.prod ⟦l⟧ ∈ s | M✝ : Type u_1
inst✝² : Monoid M✝
s✝ : Set M✝
A : Type u_2
inst✝¹ : AddMonoid A
t : Set A
M : Type u_3
inst✝ : CommMonoid M
s : Set M
hs : IsSubmonoid s
m : Multiset M
l : List M
hl : ∀ a ∈ ⟦l⟧, a ∈ s
⊢ l.prod ∈ s | ((:c Membership.mem) (:fv _uniq.16405) ((:c Set) (:fv _uniq.16405)) ((:c Set.instMembership) (:fv _uniq.16405)) ((:c Multiset.prod) (:fv _uniq.16405) (:fv _uniq.16406) ((:c Quotient.mk) ((:c List) (:fv _uniq.16405)) ((:c List.isSetoid) (:fv _uniq.16405)) (:fv _uniq.16445))) (:fv _uniq.16407)) | [{"name":"M✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.16112))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.16112))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddMonoid) (:fv _uniq.16121))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16121))"},{"name":"M","s... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7))))))) (:arg :explicit 3 (:app (:c Multiset.prod... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Monoid) (:arg :explici... | {"children":[{"source":"rw","sourceEnd":11485,"sourceStart":11483,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11487,"sourceStart":11486,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Multiset.quot_mk... | [] | [{"source":"Multiset.quot_mk_to_coe","source_end":11510,"source_start":11487,"syntax_kind":"ident"},{"source":"Multiset.prod_coe","source_end":11529,"source_start":11512,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter... | 64 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e5871fd6e066fb395f0fd7004f53950afcc2b0004dde648a1e0bb4e33baa545 | ef9350e1bef83e27915d4885dc1b6a7b31d377844f30cb421d0d11145967945c | ec5d36a769bab00196a5846aa7ab7ab36db60f981e3a88f79febdc11d03fa9d0 | b5f7ff6e6c17e9071f5359f896e80870e4b802e75f123076d45ffb18d8422348 |
cat-searcher/leandojo-benchmark-4-random | test | 3,449 | IsSubmonoid.multiset_prod_mem | Mathlib/Deprecated/Submonoid.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IsSubmonoid.list_prod_mem</a> hs hl | M✝ : Type u_1
inst✝² : Monoid M✝
s✝ : Set M✝
A : Type u_2
inst✝¹ : AddMonoid A
t : Set A
M : Type u_3
inst✝ : CommMonoid M
s : Set M
hs : IsSubmonoid s
m : Multiset M
l : List M
hl : ∀ a ∈ ⟦l⟧, a ∈ s
⊢ l.prod ∈ s | ((:c Membership.mem) (:fv _uniq.16405) ((:c Set) (:fv _uniq.16405)) ((:c Set.instMembership) (:fv _uniq.16405)) ((:c List.prod) (:fv _uniq.16405) ((:c MulOneClass.toMul) (:fv _uniq.16405) ((:c Monoid.toMulOneClass) (:fv _uniq.16405) ((:c CommMonoid.toMonoid) (:fv _uniq.16405) (:fv _uniq.16406)))) ((:c Monoid.toOne) (:f... | [{"name":"M✝","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.16112))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.16112))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c AddMonoid) (:fv _uniq.16121))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16121))"},{"name":"M","s... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV7)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV7))))))) (:arg :explicit 3 (:app (:c List.prod) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"name":"M✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Monoid) (:arg :explici... | {"children":[{"source":"exact","sourceEnd":11538,"sourceStart":11533,"tag":"atom"},{"children":[{"name":"IsSubmonoid.list_prod_mem","semanticRole":"global","source":"list_prod_mem","sourceEnd":11552,"sourceStart":11539,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hs","sourceEnd":... | [] | [{"source":"list_prod_mem hs hl","source_end":11558,"source_start":11539,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16112","is_instance":false,"is_let":false,"user_name":"M✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.16115","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inter... | 64 | 9 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5dde2827adde0155ffd42d2d320f91efa758984efed1cf1815df4895053eb08c | b5f7ff6e6c17e9071f5359f896e80870e4b802e75f123076d45ffb18d8422348 | 599d12707beef61cf5df548430279c8abdcade144352d36bb2186d80c47ce84f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,450 | StructureGroupoid.restriction_in_maximalAtlas | Mathlib/Geometry/Manifold/ChartedSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro e' he' | H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
⊢ e.subtypeRest... | H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' : PartialHom... | ((:c Membership.mem) ((:c PartialHomeomorph) ((:c Subtype) (:fv _uniq.72645) (:lambda x (:fv _uniq.72645) ((:c Membership.mem) (:fv _uniq.72645) ((:c TopologicalSpace.Opens) (:fv _uniq.72645) (:fv _uniq.72657)) ((:c SetLike.instMembership) ((:c TopologicalSpace.Opens) (:fv _uniq.72645) (:fv _uniq.72657)) (:fv _uniq.726... | [{"name":"H","sexp":"(:sort (+ u 1))"},{"name":"H'","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"M'","sexp":"(:sort (+ u_3 1))"},{"name":"M''","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.72639))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PartialHomeomorph) (:arg :explicit 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 TopologicalSpace.Opens) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"name":"H'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"intro","sourceEnd":61171,"sourceStart":61166,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"e'","sourceEnd":61174,"sourceStart":61172,"tag":"identifier"},{"semanticRole":"scoped_local","source":"he'","sourceEnd":61178,"sourceStart":61175,"tag":"identifier"}],"kind":"null","s... | [{"role":"fresh_name","source":"e'","source_end":61174,"source_start":61172,"syntax_kind":"ident"},{"role":"fresh_name","source":"he'\n -- `e'` is the restriction of some chart of `M` at `x`,","source_end":61178,"source_start":61175,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"user_name":"H'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 243 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 938a294870905439fcde44511df3c42de4e1b2d8f9c1bd6a2c9774fcc84c656d | 882a0a0d00f240b871a7d59010e773e9d55442db4c2722aca2a2d934f122a3a7 | dfe3b52e67e01c7671c33a6bcc71c726a289514632bb164c758c239610eaf67d | 8fb60523dc0d272edc26b214b84f2b1997a334d020de55e091d2db5119263251 |
cat-searcher/leandojo-benchmark-4-random | test | 3,451 | StructureGroupoid.restriction_in_maximalAtlas | Mathlib/Geometry/Manifold/ChartedSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨x, this⟩ := <a>TopologicalSpace.Opens.chart_eq</a> hs he' | H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' : PartialHom... | case intro
H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' :... | ((:c And) ((:c Membership.mem) ((:c PartialHomeomorph) (:fv _uniq.72639) (:fv _uniq.72639) (:fv _uniq.72654) (:fv _uniq.72654)) ((:c StructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c instMembershipPartialHomeomorphStructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c PartialHomeomorph.trans) (:fv _uni... | [{"name":"H","sexp":"(:sort (+ u 1))"},{"name":"H'","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"M'","sexp":"(:sort (+ u_3 1))"},{"name":"M''","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.72639))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) ... | (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PartialHomeomorph) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"name":"H'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"obtain","sourceEnd":61245,"sourceStart":61239,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":61249,"sourceStart":61246,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEn... | [] | [{"source":"Opens.chart_eq hs he'","source_end":61284,"source_start":61263,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, this⟩","source_end":61259,"source_start":61246,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"user_name":"H'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 243 | 5 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 99db9c64f5c59ce063967034337438615bdf79e5d412b3d8b2470ac3fc90ea7a | 8fb60523dc0d272edc26b214b84f2b1997a334d020de55e091d2db5119263251 | 663c9c100fbb69920cbf6dea5e64f5c51d31fcea3c2041787d4299b29035a2ae | 739362f0780086d41b6671173a4ae132b57f38ff81d41d6e0405585d671c7a44 |
cat-searcher/leandojo-benchmark-4-random | test | 3,452 | StructureGroupoid.restriction_in_maximalAtlas | Mathlib/Geometry/Manifold/ChartedSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | case intro
H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' :... | case intro
H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' :... | ((:c And) ((:c Membership.mem) ((:c PartialHomeomorph) (:fv _uniq.72639) (:fv _uniq.72639) (:fv _uniq.72654) (:fv _uniq.72654)) ((:c StructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c instMembershipPartialHomeomorphStructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c PartialHomeomorph.trans) (:fv _uni... | [{"name":"H","sexp":"(:sort (+ u 1))"},{"name":"H'","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"M'","sexp":"(:sort (+ u_3 1))"},{"name":"M''","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.72639))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) ... | (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PartialHomeomorph) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"name":"H'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":61289,"sourceStart":61287,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":61291,"sourceStart":61290,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"seman... | [] | [{"source":"this","source_end":61295,"source_start":61291,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"user_name":"H'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 243 | 6 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 63048fc7b5f25fdc2d162eaeb1bcf940ee09dcdba8e451f6d32760418507e4f6 | 739362f0780086d41b6671173a4ae132b57f38ff81d41d6e0405585d671c7a44 | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | ebf5ae401ceb6c19fa863fedfa054ecb947d4d3a78d328e6a3d0c60a1fa485b8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,453 | StructureGroupoid.restriction_in_maximalAtlas | Mathlib/Geometry/Manifold/ChartedSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨G.trans_restricted he (<a>chart_mem_atlas</a> H (x : M)) hs, G.trans_restricted (<a>chart_mem_atlas</a> H (x : M)) he hs⟩ | case intro
H : Type u
H' : Type u_1
M : Type u_2
M' : Type u_3
M'' : Type u_4
inst✝⁴ : TopologicalSpace H
inst✝³ : TopologicalSpace M
inst✝² : ChartedSpace H M
e : PartialHomeomorph M H
he : e ∈ atlas H M
s : Opens M
hs : Nonempty ↥s
G : StructureGroupoid H
inst✝¹ : HasGroupoid M G
inst✝ : ClosedUnderRestriction G
e' :... | ((:c And) ((:c Membership.mem) ((:c PartialHomeomorph) (:fv _uniq.72639) (:fv _uniq.72639) (:fv _uniq.72654) (:fv _uniq.72654)) ((:c StructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c instMembershipPartialHomeomorphStructureGroupoid) (:fv _uniq.72639) (:fv _uniq.72654)) ((:c PartialHomeomorph.trans) (:fv _uni... | [{"name":"H","sexp":"(:sort (+ u 1))"},{"name":"H'","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"(:sort (+ u_2 1))"},{"name":"M'","sexp":"(:sort (+ u_3 1))"},{"name":"M''","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.72639))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) ... | (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c PartialHomeomorph) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"name":"H","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"name":"H'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"exact","sourceEnd":61484,"sourceStart":61479,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":61488,"sourceStart":61485,"tag":"atom"},{"children":[{"children":[{"source":"G.trans_restricted","sourceEnd":61506,"sourceStart":61488,"tag":"identifier"},{"children":[{"contextIndex":10,"semanticRo... | [] | [{"source":"⟨G.trans_restricted he (chart_mem_atlas H (x : M)) hs,\n G.trans_restricted (chart_mem_atlas H (x : M)) he hs⟩","source_end":61606,"source_start":61485,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.72639","is_instance":false,"is_let":false,"user_name":"H"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.72642","is_instance":false,"is_let":false,"user_name":"H'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 243 | 9 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8600f19589d366436c5944468d526bba4940c4844ab0654cfbfb66ef7eb82e25 | ebf5ae401ceb6c19fa863fedfa054ecb947d4d3a78d328e6a3d0c60a1fa485b8 | f54ca69707fe4b21cd04458f1fa25c8885bd4a9ff555fbe70d931f6ae6c2d12d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,454 | one_lt_of_lt_mul_left | Mathlib/Algebra/Order/Monoid/Unbundled/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>one_mul</a>] | α : Type u_1
β : Type u_2
inst✝² : MulOneClass α
inst✝¹ : LT α
inst✝ : ContravariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1
a b : α
h : b < a * b
⊢ 1 * ?m.28643 < a * ?m.28643 | ((:c LT.lt) (:fv _uniq.28333) (:fv _uniq.28342) ((:c HMul.hMul) (:fv _uniq.28333) (:fv _uniq.28333) (:fv _uniq.28333) ((:c instHMul) (:fv _uniq.28333) ((:c MulOneClass.toMul) (:fv _uniq.28333) (:fv _uniq.28339))) ((:c OfNat.ofNat) (:fv _uniq.28333) (:lit 1) ((:c One.toOfNat1) (:fv _uniq.28333) ((:c MulOneClass.toOne) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c MulOneClass) (:fv _uniq.28333))"},{"name":"inst✝¹","sexp":"((:c LT) (:fv _uniq.28333))"},{"name":"inst✝","sexp":"((:c ContravariantClass) (:fv _uniq.28333) (:fv _uniq.28333) ((:c Function.swap) (:fv _uniq.2833... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (: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 HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28333","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28336","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":21726,"sourceStart":21721,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"one_mul","source_end":21740,"source_start":21733,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28333","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28336","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 195 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a83c1ad991156ee6f86cf0dfca4e20416d3f2ee2a26561ed4bf0933a1d737970 | 0d60724551efffa29722a543eb9e3c4a75e690b60c3130c2df9a4217bf5990d4 | 9e69173177fc73bed92f0cb88f6805cf64d2d379025512056b808d2063d70d0c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,455 | Set.image_fst_graphOn | Mathlib/Data/Set/Function.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Set.graphOn</a>, <a>Set.image_image</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
π : α → Type u_5
s✝ s₁ s₂ : Set α
t t₁ t₂ : Set β
p : Set γ
f✝ f₁ f₂ f₃ : α → β
g g₁ g₂ : β → γ
f' f₁' f₂' : β → α
g' : γ → β
a : α
b : β
f : α → β
s : Set α
⊢ Prod.fst '' graphOn f s = s | ((:c Eq) ((:c Set) (:fv _uniq.50069)) ((:c Set.image) ((:c Prod) (:fv _uniq.50069) (:fv _uniq.50072)) (:fv _uniq.50069) ((:c Prod.fst) (:fv _uniq.50069) (:fv _uniq.50072)) ((:c Set.graphOn) (:fv _uniq.50069) (:fv _uniq.50072) (:fv _uniq.50192) (:fv _uniq.50193))) (:fv _uniq.50193)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"π","sexp":"(:forall _ (:fv _uniq.50069) (:sort (+ u_5 1)))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.50069))"},{"name":"s₁","sexp":"((:c Set) (:fv _uniq.5... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:app (:c Prod.fst) (:arg :implicit-type 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50069","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50072","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":35413,"sourceStart":35409,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"graphOn","source_end":35422,"source_start":35415,"syntax_kind":"ident"},{"source":"image_image","source_end":35435,"source_start":35424,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.50069","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50072","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 317 | 2 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc004fa500622f979dc7f2bb22b3aa63a2195bff7a7e7824fafdc6a1ccb2d87d | 1c8584744353d0aca175eb7d900a55a68bef56fc3a70c2fa1f245c86b11306b4 | 9a559659e5426bd6ed21f2422c6ab08a1b5bfc408ad41d2b5ad5b0d028488b43 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,456 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : ∀ i, ∃ g : α → ℝ, <a>LipschitzWith</a> K g ∧ <a>Set.EqOn</a> (fun x => f x i) g s := fun i => by have : <a>LipschitzOnWith</a> K (fun x : α => f x i) s := <a>LipschitzOnWith.of_dist_le_mul</a> fun x hx y hy => (<a>dist_le_pi_dist</a> _ _ i).<a>LE.le.trans</a> (hf.dist_le_mul x hx y hy) exact this.extend_real | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
this : ∀ (i : ι), ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s
⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s | ((:c Exists) (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) (:lambda g (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) ((:c And) ((:c LipschitzWith) (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real)) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.76873) (:fv ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real)))) (:arg :explicit 1 (:lambda g :explicit (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real))) (:app (:c And) (:arg :explicit 0 (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":20661,"sourceStart":20657,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":20662,"sourceStart":20662,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":20662,"sourceStart":20662,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"∀ i, ∃ g : α → ℝ, LipschitzWith K g ∧ EqOn (fun x => f x i) g s","source_end":20738,"source_start":20664,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"fun i => by\n have : LipschitzOnWith K (fun x : α => f x i) s :=\n LipschitzOnWith.of_dist_le_mul fun x hx y hy =>\n (dist_le_pi_dist _ ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 4 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7ed94988b38bb07bc8edc5b028cff7f9fddfba283a0b0d45154403867d6c912 | 3a35299edee4fbeec0c5352aa8cae12a67428b8ae6ff5c23a77f5e87699a3441 | 6d9293ec61ebe2d8b3edcc280cbb3d65140bfc166da0bdfa1bb95a29c60444c1 | f293a613d103444834579c6765cea32a57d3e8507d75432e10ed669717dc370f |
cat-searcher/leandojo-benchmark-4-random | test | 3,457 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | choose g hg using this | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
this : ∀ (i : ι), ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s
⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s | ((:c Exists) (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) (:lambda g (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) ((:c And) ((:c LipschitzWith) (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real)) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.76873) (:fv ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real)))) (:arg :explicit 1 (:lambda g :explicit (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real))) (:app (:c And) (:arg :explicit 0 (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"choose","sourceEnd":20964,"sourceStart":20958,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"g","sourceEnd":20966,"sourceStart":20965,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"g","sourceEnd":2... | [] | [{"source":"this","source_end":20980,"source_start":20976,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 11 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fede30d3d1902b389aecdf904283d3a562c04d27416224c002b5b94bb0beb6a8 | f293a613d103444834579c6765cea32a57d3e8507d75432e10ed669717dc370f | 67b34f15fb473758dfc5a067a1256bf95cac6b25c2ce7c0983ca8c53cc371b8f | 5dee377d8a505f5c830c673d8119fb970dae2b77d3efd1befda8433eac504799 |
cat-searcher/leandojo-benchmark-4-random | test | 3,458 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun x i => g i x, <a>LipschitzWith.of_dist_le_mul</a> fun x y => ?_, fun x hx ↦ ?_⟩ | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s | case refine_1
α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
x y : α
⊢ (dist (fun i => g i x)... | ((:c Exists) (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) (:lambda g (:forall _ (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real))) ((:c And) ((:c LipschitzWith) (:fv _uniq.76873) (:forall _ (:fv _uniq.76879) (:c Real)) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.76873) (:fv ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real)))) (:arg :explicit 1 (:lambda g :explicit (:forall _ :explicit (:fv FV0) (:forall _ :explicit (:fv FV3) (:c Real))) (:app (:c And) (:arg :explicit 0 (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":20989,"sourceStart":20983,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":20993,"sourceStart":20990,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":20996,"sourceStart":20993,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun x i => g i x, LipschitzWith.of_dist_le_mul fun x y => ?_, fun x hx ↦ ?_⟩","source_end":21073,"source_start":20990,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 12 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d5fe4dd4cc2be702c89d05e1988b115800a4a08825e9e7443d34f96ec90a44f | 5dee377d8a505f5c830c673d8119fb970dae2b77d3efd1befda8433eac504799 | 51a0cfba8ad80781ff2913ea731b951c7bd52893f5b9ae5b1d6e9dd808b36f15 | 50e0277ba6ff2fb4d2e2f8978eec579bdadc535c1dfd5c80da48dcf62550d9a9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,459 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>LipschitzOnWith</a> K (fun x : α => f x i) s := <a>LipschitzOnWith.of_dist_le_mul</a> fun x hx y hy => (<a>dist_le_pi_dist</a> _ _ i).<a>LE.le.trans</a> (hf.dist_le_mul x hx y hy) | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
i : ι
⊢ ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
i : ι
this : LipschitzOnWith K (fun x => f x i) s
⊢ ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s | ((:c Exists) (:forall _ (:fv _uniq.76873) (:c Real)) (:lambda g (:forall _ (:fv _uniq.76873) (:c Real)) ((:c And) ((:c LipschitzWith) (:fv _uniq.76873) (:c Real) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.76873) (:fv _uniq.76882)) ((:c EMetricSpace.toPseudoEMetricSpace) (:c Real) ((:c MetricSpace.toEMetric... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :explicit 1 (:lambda g :explicit (:forall _ :explicit (:fv FV0) (:c Real)) (:app (:c And) (:arg :explicit 0 (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":20762,"sourceStart":20758,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":20763,"sourceStart":20763,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":20763,"sourceStart":20763,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"LipschitzOnWith K (fun x : α => f x i) s","source_end":20806,"source_start":20765,"syntax_kind":"Lean.Parser.Term.app"},{"source":"LipschitzOnWith.of_dist_le_mul fun x hx y hy =>\n (dist_le_pi_dist _ _ i).trans (hf.dist_le_mul x hx y hy)","source_end":20928,"source_start":20816,"syntax_kind":"Lean.Pa... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 9 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef470968f97e8221415eddd2cca013db86a9b0bd27b3e29e6e7956f364fcf476 | bf54256bf35b5d850dd405086c1391357f80ae82ed2033a6977c76d105761000 | 4b6ab5373a6994d748b8f360c3d61dab298c5e68b6429ada346942bb264e9c01 | 04bb0db7323710d9a8b64ba84aa5a3d5f45bb755cbe35c17b8b405afb0fe394c |
cat-searcher/leandojo-benchmark-4-random | test | 3,460 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact this.extend_real | α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
i : ι
this : LipschitzOnWith K (fun x => f x i) s
⊢ ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s | ((:c Exists) (:forall _ (:fv _uniq.76873) (:c Real)) (:lambda g (:forall _ (:fv _uniq.76873) (:c Real)) ((:c And) ((:c LipschitzWith) (:fv _uniq.76873) (:c Real) ((:c PseudoMetricSpace.toPseudoEMetricSpace) (:fv _uniq.76873) (:fv _uniq.76882)) ((:c EMetricSpace.toPseudoEMetricSpace) (:c Real) ((:c MetricSpace.toEMetric... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Real))) (:arg :explicit 1 (:lambda g :explicit (:forall _ :explicit (:fv FV0) (:c Real)) (:app (:c And) (:arg :explicit 0 (:app (:c LipschitzWith) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":20938,"sourceStart":20933,"tag":"atom"},{"name":"LipschitzOnWith.extend_real","semanticRole":"global","source":"this.extend_real","sourceEnd":20955,"sourceStart":20939,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact this.extend_real","sourceEnd":20955,"s... | [] | [{"source":"this.extend_real","source_end":20955,"source_start":20939,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 10 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0ab49265d7ad027156b29f3fe7d09ce32920fbd559851da1cdb38b698dcc15e | 04bb0db7323710d9a8b64ba84aa5a3d5f45bb755cbe35c17b8b405afb0fe394c | 9fbe7d34687e16f35509c734ae46430968f53f38ff7a7c5fdc340764ce662b1b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,461 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>dist_pi_le_iff</a> (<a>mul_nonneg</a> K.2 <a>dist_nonneg</a>)).2 fun i => (hg i).1.<a>LipschitzWith.dist_le_mul</a> x y | case refine_1
α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
x y : α
⊢ (dist (fun i => g i x)... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Dist.dist) (:forall _ (:fv _uniq.76879) (:c Real)) ((:c PseudoMetricSpace.toDist) (:forall _ (:fv _uniq.76879) (:c Real)) ((:c pseudoMetricSpacePi) (:fv _uniq.76879) (:lambda _ (:fv _uniq.76879) (:c Real)) (:fv _uniq.77055) (:lambda b (:fv _uniq.76879) (:c Real.pseudoMetricSp... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Dist.dist) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV3) (:c Real))) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:forall _ :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":21084,"sourceStart":21079,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":21086,"sourceStart":21085,"tag":"atom"},{"children":[{"name":"dist_pi_le_iff","semanticRole":"global","source":"dist_pi_le_iff","sour... | [] | [{"source":"(dist_pi_le_iff (mul_nonneg K.2 dist_nonneg)).2 fun i => (hg i).1.dist_le_mul x y","source_end":21166,"source_start":21085,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 15 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ac77a2a4b3ae093e5b3d4a5c9e2fd789cb81fc5f749b3702cb193f82ad0253ed | 45d10b4a2bda716b15ed9cf3517e104a315008ba28357642dcb4b3c42bd0c2ff | 263a03813871a1a2ce2e7eafbf6366808b40553463004f462d9d5f33483bf70f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,462 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 i | case refine_2
α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
x : α
hx : x ∈ s
⊢ f x = (fun x ... | case refine_2.h
α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
x : α
hx : x ∈ s
i : ι
⊢ f x i... | ((:c Eq) (:forall _ (:fv _uniq.76879) (:c Real)) ((:fv _uniq.77056) (:fv _uniq.77710)) ((:lambda x (:fv _uniq.76873) (:lambda i (:fv _uniq.76879) ((:fv _uniq.77557) 0 1))) (:fv _uniq.77710))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Eq) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV3) (:c Real))) (:arg :explicit 1 (:app (:fv FV9) (:arg :explicit 0 (:fv FV15)))) (:arg :explicit 2 (:app (:lambda x :explicit (:fv FV0) (:lambda i :explicit (:fv FV3) (:app (:fv FV13) (:arg :explicit 0 0) (:arg :explicit 1 1)))) (:arg :explicit 0 (:fv FV1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ext1","sourceEnd":21176,"sourceStart":21172,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":21178,"sourceStart":21177,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"i","sourceEnd":21178,"sourceStart":21177,"ta... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 22 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c14e099bfda86c6407387e57b2ead3d9f6c0f4d5463a48708bc3e15181fdb2b | e4ae489b80d61b0408bf5db7ee5826f206feb99624680d39df1f02bdc01b35b7 | f0b40076b97286d3be243ab933d9a356e9b25d96ccd42e8d1daf186c9a89c085 | a45083d54d1c422fb435d1fe146bcd26bd24fd6e0a7b0b0477b917e3b5f88560 |
cat-searcher/leandojo-benchmark-4-random | test | 3,463 | LipschitzOnWith.extend_pi | Mathlib/Topology/MetricSpace/Lipschitz.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hg i).2 hx | case refine_2.h
α : Type u
β : Type v
γ : Type w
ι : Type x
inst✝² : PseudoMetricSpace α
inst✝¹ : PseudoMetricSpace β
f✝ : α → β
inst✝ : Fintype ι
f : α → ι → ℝ
s : Set α
K : ℝ≥0
hf : LipschitzOnWith K f s
g : ι → α → ℝ
hg : ∀ (i : ι), LipschitzWith K (g i) ∧ EqOn (fun x => f x i) (g i) s
x : α
hx : x ∈ s
i : ι
⊢ f x i... | ((:c Eq) (:c Real) ((:fv _uniq.77056) (:fv _uniq.77710) (:fv _uniq.78295)) ((:lambda x (:fv _uniq.76873) (:lambda i (:fv _uniq.76879) ((:fv _uniq.77557) 0 1))) (:fv _uniq.77710) (:fv _uniq.78295))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ x 1))"},{"name":"inst✝²","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76873))"},{"name":"inst✝¹","sexp":"((:c PseudoMetricSpace) (:fv _uniq.76875))"},{"name":"f✝","sexp":"(:fora... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV9) (:arg :explicit 0 (:fv FV15)) (:arg :explicit 1 (:fv FV17)))) (:arg :explicit 2 (:app (:lambda x :explicit (:fv FV0) (:lambda i :explicit (:fv FV3) (:app (:fv FV13) (:arg :explicit 0 0) (:arg :explicit 1 1)))) (:arg :explicit 0 (:fv FV15)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":21188,"sourceStart":21183,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":21190,"sourceStart":21189,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hg","sourceEnd":21192,"sourceStart":21190,"tag":"identifier"},{"chi... | [] | [{"source":"(hg i).2 hx","source_end":21200,"source_start":21189,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.76873","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.76875","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 132 | 23 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eab682683b6e34e59ae1b3274bdea53651a43973603b54b2dcafaf17b0d2de50 | a45083d54d1c422fb435d1fe146bcd26bd24fd6e0a7b0b0477b917e3b5f88560 | 03127dbec7b37a383069a43fdaa0694e11c6cff3db16c1be1ff462c38504852e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,464 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction' n with n ih | α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
m : Sym α n
⊢ m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
m : Sym α 0
⊢ m ∈ s.sym 0 ↔ ∀ a ∈ m, a ∈ s
case succ
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
⊢ m ∈ s.sym (n + 1) ↔ ∀ a ∈ m, a ∈ s | ((:c Iff) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) (:fv _uniq.11701)) ((:c Finset) ((:c Sym) (:fv _uniq.11680) (:fv _uniq.11701))) ((:c Finset.instMembership) ((:c Sym) (:fv _uniq.11680) (:fv _uniq.11701))) (:fv _uniq.11825) ((:c Finset.sym) (:fv _uniq.11680) (:fv _uniq.11687) (:fv _uniq.11692) (:fv _uniq.11701... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n","sexp":"(:c Nat)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV6)))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV6)))))) (:arg :instance 2 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"induction'","sourceEnd":6714,"sourceStart":6704,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":6,"semanticRole":"local","source":"n","sourceEnd":6716,"sourceStart":6715,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"n","source_end":6716,"source_start":6715,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d4d47d0fea32166ea4810c065ca2a293a0a98a4dc4293a4b08a726242a26547 | 566bd4efea92bb232628b7f3a0ba65e1f753cf4585dd41b028110498a25966cf | e9e977af13db95340b52852f9ed24a874f04a57e53bb9edd1a10e3351ff79078 | 0f64d7594b1e2d50262802a881eeed657bbfab9cbb05e025ab159f9e9e076809 |
cat-searcher/leandojo-benchmark-4-random | test | 3,465 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine mem_sup.trans ⟨?_, fun h ↦ ?_⟩ | case succ
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
⊢ m ∈ s.sym (n + 1) ↔ ∀ a ∈ m, a ∈ s | case succ.refine_1
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
⊢ (∃ v ∈ s, m ∈ image (Sym.cons v) (s.sym n)) → ∀ a ∈ m, a ∈ s
case succ.refine_2
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym ... | ((:c Iff) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.11846) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) ((:c Finset) ((:c Sym) (:fv _uniq.11680) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c in... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c Nat... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"refine","sourceEnd":6884,"sourceStart":6878,"tag":"atom"},{"children":[{"source":"mem_sup.trans","sourceEnd":6898,"sourceStart":6885,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":6902,"sourceStart":6899,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":6... | [] | [{"source":"mem_sup.trans ⟨?_, fun h ↦ ?_⟩","source_end":6921,"source_start":6885,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 12 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 322fe345b31ad3cf4c30323ba51a169c2e43563cd8466202d0605bbd99b349b8 | ec9fb72a2bffa0682e054019383985c2b347e4076bebb8b0db9d489c92f56576 | 67694745c0721668188c8ef75153e313ec48911367e1d7dd379f9bb7df9af4f7 | 3200cdded3e0a1e6ad83de01cf11db711daf5dae38c0e356db8e91bdc63a1882 |
cat-searcher/leandojo-benchmark-4-random | test | 3,466 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine mem_singleton.trans ⟨?_, fun _ ↦ <a>Sym.eq_nil_of_card_zero</a> _⟩ | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
m : Sym α 0
⊢ m ∈ s.sym 0 ↔ ∀ a ∈ m, a ∈ s | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
m : Sym α 0
⊢ m = ∅ → ∀ a ∈ m, a ∈ s | ((:c Iff) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Finset) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))) ((:c Finset.instMembership) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n","sexp":"(:c Nat)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"refine","sourceEnd":6738,"sourceStart":6732,"tag":"atom"},{"children":[{"source":"mem_singleton.trans","sourceEnd":6758,"sourceStart":6739,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":6762,"sourceStart":6759,"tag":"atom"},{"children":[{"children":[{"source":"?","source... | [] | [{"source":"mem_singleton.trans ⟨?_, fun _ ↦ Sym.eq_nil_of_card_zero _⟩","source_end":6804,"source_start":6739,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 9 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d106ed3ac9ac42fdff08f5eb001f6c7698b5af6e02152dc89930079fd1304c0d | 40f9cb39c305ad41fc023b5a3dabaec00568e7f60f007351a4a4704558a11ca3 | f0ffd826e487b6fe9b1222abf0d5f83ae531b69e408ef55f3933c1e16f37bc22 | af88287e2346ac8e4236890e2aa57a069a782c39d670e8666c7ed1cfa8adb318 |
cat-searcher/leandojo-benchmark-4-random | test | 3,467 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
m : Sym α 0
⊢ m = ∅ → ∀ a ∈ m, a ∈ s | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
⊢ ∀ a ∈ ∅, a ∈ s | (:forall _ ((:c Eq) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) (:fv _uniq.11843) ((:c EmptyCollection.emptyCollection) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Sym.instEmptyCollectionOfNatNat) (:fv _uniq.11680... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n","sexp":"(:c Nat)... | (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 0))))))))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"rintro","sourceEnd":6815,"sourceStart":6809,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":6819,"sourceStart":6816,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":6819,"sourceStart":6816,"ta... | [] | [{"source":"rfl","source_end":6819,"source_start":6816,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 10 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 738b00973f927fdb40db975fcfab96afb35fadd3f166be94dfe7f8013ef58df9 | af88287e2346ac8e4236890e2aa57a069a782c39d670e8666c7ed1cfa8adb318 | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 718d9bf1acb95aedc1a611d84b2b555635271ae8027a98c58c08ccc3bc9b5b81 |
cat-searcher/leandojo-benchmark-4-random | test | 3,468 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun a ha ↦ (<a>Finset.not_mem_empty</a> _ ha).<a>False.elim</a> | case zero
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n : ℕ
⊢ ∀ a ∈ ∅, a ∈ s | (:forall a (:fv _uniq.11680) (:forall _ ((:c Membership.mem) (:fv _uniq.11680) ((:c Sym) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c Sym.instMembership) (:fv _uniq.11680) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) 0 ((:c EmptyCollection.emptyCollecti... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n","sexp":"(:c Nat)... | (:forall a :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Sym) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"exact","sourceEnd":6829,"sourceStart":6824,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":6833,"sourceStart":6830,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":6835,"sourceStart":6834,"tag":"identifier"},{"semanticRole":"scoped_local","so... | [] | [{"source":"fun a ha ↦ (Finset.not_mem_empty _ ha).elim","source_end":6875,"source_start":6830,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 11 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9feb146ecfcbb2365cc85d161388d59c6b8755d0841e993a975671eb9316d87 | 718d9bf1acb95aedc1a611d84b2b555635271ae8027a98c58c08ccc3bc9b5b81 | 00590953fc684be5b2115312b2a45de6eab81d41c689c4ab80d40ca32d0de758 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,469 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨a, ha, he⟩ b hb | case succ.refine_1
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
⊢ (∃ v ∈ s, m ∈ image (Sym.cons v) (s.sym n)) → ∀ a ∈ m, a ∈ s | case succ.refine_1.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
a : α
ha : a ∈ s
he : m ∈ image (Sym.cons a) (s.sym n)
b : α
hb : b ∈ m
⊢ b ∈ s | (:forall _ ((:c Exists) (:fv _uniq.11680) (:lambda v (:fv _uniq.11680) ((:c And) ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) 0 (:fv _uniq.11692)) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c ins... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c Nat... | (:forall _ :explicit (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda v :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"rintro","sourceEnd":6933,"sourceStart":6927,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6937,"sourceStart":6934,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":6938,"sourceSt... | [{"role":"fresh_name","source":"a","source_end":6938,"source_start":6937,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":6942,"source_start":6940,"syntax_kind":"ident"},{"role":"fresh_name","source":"he","source_end":6946,"source_start":6944,"syntax_kind":"ident"},{"role":"fresh_name","source":"b... | [{"source":"⟨a, ha, he⟩","source_end":6949,"source_start":6934,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 17 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fed6014f024d2cc597bb88c3e926db652a0bbc85d3787fce2eb782ca152df5be | 0d5d2cc3177d9c7a71ca78e4198ee888b1e16f2b90b60739cda650fe4fb840ef | 42133b5438be34db8412a399e2656336afe9a81a2ad96591eea1fd630122ca90 | 85f66b1bd6fb8922fa885b49e55fa656a4e9e6192155ac7d925360e113d8bf3a |
cat-searcher/leandojo-benchmark-4-random | test | 3,470 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_image</a>] at he | case succ.refine_1.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
a : α
ha : a ∈ s
he : m ∈ image (Sym.cons a) (s.sym n)
b : α
hb : b ∈ m
⊢ b ∈ s | case succ.refine_1.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
a : α
ha : a ∈ s
he : ∃ a_1 ∈ s.sym n, a ::ₛ a_1 = m
b : α
hb : b ∈ m
⊢ b ∈ s | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12233) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c N... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV14)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":6961,"sourceStart":6959,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6963,"sourceStart":6962,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_image","s... | [] | [{"source":"mem_image","source_end":6972,"source_start":6963,"syntax_kind":"ident"},{"source":"he","source_end":6979,"source_start":6977,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 18 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f0b3d9ca1e3e116032232a798d39d543e14d57921b7348d23e054b3e0f758ff9 | 85f66b1bd6fb8922fa885b49e55fa656a4e9e6192155ac7d925360e113d8bf3a | cae171c9d371e829113cab8ba3195dc5c2b07020ff7a30c89d3a24ca97639839 | b0495562796a4d0b7c33d1b81786b2cd96b51fb0d3c597e975ad9a1bc59193de |
cat-searcher/leandojo-benchmark-4-random | test | 3,471 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨m, he, rfl⟩ := he | case succ.refine_1.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
a : α
ha : a ∈ s
he : ∃ a_1 ∈ s.sym n, a ::ₛ a_1 = m
b : α
hb : b ∈ m
⊢ b ∈ s | case succ.refine_1.intro.intro.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
ha : a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
hb : b ∈ a ::ₛ m
⊢ b ∈ s | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12419) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c N... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV14)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"obtain","sourceEnd":6990,"sourceStart":6984,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":6994,"sourceStart":6991,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":6... | [] | [{"source":"he","source_end":7013,"source_start":7011,"syntax_kind":"ident"},{"source":"⟨m, he, rfl⟩","source_end":7007,"source_start":6991,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 21 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb503ebd9811fc076a9f482623920df5e7020b3da06842635c8c0bc76e4eb2f5 | b0495562796a4d0b7c33d1b81786b2cd96b51fb0d3c597e975ad9a1bc59193de | b114a1838776efa9bab8459a57c43bdbc5415481b215d73fdab968319cc03624 | 18afa39fab2f291bf7b7302a3feedbaeecd0bc98e92296b8b59ef99fc41c03c6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,472 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Sym.mem_cons</a>] at hb | case succ.refine_1.intro.intro.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
ha : a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
hb : b ∈ a ::ₛ m
⊢ b ∈ s | case succ.refine_1.intro.intro.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
ha : a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
hb : b = a ∨ b ∈ m
⊢ b ∈ s | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12419) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c N... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV12)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"rw","sourceEnd":7020,"sourceStart":7018,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7022,"sourceStart":7021,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Sym.mem_cons","seman... | [] | [{"source":"Sym.mem_cons","source_end":7034,"source_start":7022,"syntax_kind":"ident"},{"source":"hb","source_end":7041,"source_start":7039,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 22 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a1dedbf45b924c040f549cbbae5fc3294317698b26c99cecacde05b041a9d64 | 18afa39fab2f291bf7b7302a3feedbaeecd0bc98e92296b8b59ef99fc41c03c6 | fadc1da8df885f652490eb4bbd36881242839612a6604dcd7b9886115dc0296f | a5d2362ce49775744a11d566ca3d00a3e045ed8003efd71bcb048e38a13bc03b |
cat-searcher/leandojo-benchmark-4-random | test | 3,473 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl | hb := hb | case succ.refine_1.intro.intro.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
ha : a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
hb : b = a ∨ b ∈ m
⊢ b ∈ s | case succ.refine_1.intro.intro.intro.intro.inl
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
ha : b ∈ s
⊢ b ∈ s
case succ.refine_1.intro.intro.intro.intro.inr
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ ... | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12419) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c N... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV12)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"obtain","sourceEnd":7052,"sourceStart":7046,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":7056,"sourceStart":7053,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":7056,"sourceSt... | [] | [{"source":"hb","source_end":7067,"source_start":7065,"syntax_kind":"ident"},{"source":"rfl | hb","source_end":7061,"source_start":7053,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 25 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa0a3e271cbed8a0608eb2556abfe05a0e962feda792e5fb93e2a6e63290ae5c | a5d2362ce49775744a11d566ca3d00a3e045ed8003efd71bcb048e38a13bc03b | e07369cef260448154e30ca683bc17f8b0e84ec0a964c7c8b041a86ec8e904c0 | b7df741a87fb5e5c9b9841f8977a6666ab44ebd54edd5491e56cd4eb027e8cf4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,474 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha | case succ.refine_1.intro.intro.intro.intro.inl
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
ha : b ∈ s
⊢ b ∈ s | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12419) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c Na... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV10)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7080,"sourceStart":7075,"tag":"atom"},{"contextIndex":13,"semanticRole":"local","source":"ha","sourceEnd":7083,"sourceStart":7081,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha","sourceEnd":7083,"sourceStart":70... | [] | [{"source":"ha","source_end":7083,"source_start":7081,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 28 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0697b004c09099b86c389e35c48d1503c36790d16fbed0f87c3e9c2089c55f0f | df6caf1cbf4e5d5be326935e967d87e670ef2788e950fb25e872fc89cb1e3205 | ed7b20bfa58750585795fc60c8364f3d8cfaa54d8e6d316fdcf777f9aa77d07b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,475 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ih.1 he _ hb | case succ.refine_1.intro.intro.intro.intro.inr
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b✝ : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
ha : a ∈ s
b : α
m : Sym α n
he : m ∈ s.sym n
hb : b ∈ m
⊢ b ∈ s | ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) (:fv _uniq.12419) (:fv _uniq.11692)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b✝","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c N... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:fv FV12)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7096,"sourceStart":7091,"tag":"atom"},{"children":[{"children":[{"contextIndex":9,"semanticRole":"local","source":"ih","sourceEnd":7099,"sourceStart":7097,"tag":"identifier"},{"source":".","sourceEnd":7100,"sourceStart":7099,"tag":"atom"}... | [] | [{"source":"ih.1 he _ hb","source_end":7109,"source_start":7097,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 33 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 022b547a0f88065c394669494de80a7652f58b3296ea974164c4a042ba5b22b5 | cc0310b05f5c88b2f3dfb683a55bc41c90923bb731bfa9afd347bcbebc5d57b8 | 3d20e88ef0920c178e74cc827ca91bb946747fe3f1da7e7bcafd9cf3baff2048 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,476 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨a, m, rfl⟩ := m.exists_eq_cons_of_succ | case succ.refine_2
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
m : Sym α (n + 1)
h : ∀ a ∈ m, a ∈ s
⊢ ∃ v ∈ s, m ∈ image (Sym.cons v) (s.sym n) | case succ.refine_2.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
m : Sym α n
h : ∀ a_1 ∈ a ::ₛ m, a_1 ∈ s
⊢ ∃ v ∈ s, a ::ₛ m ∈ image (Sym.cons v) (s.sym n) | ((:c Exists) (:fv _uniq.11680) (:lambda v (:fv _uniq.11680) ((:c And) ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) 0 (:fv _uniq.11692)) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c Nat... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda v :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"obtain","sourceEnd":7121,"sourceStart":7115,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7125,"sourceStart":7122,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":7... | [] | [{"source":"m.exists_eq_cons_of_succ","source_end":7165,"source_start":7141,"syntax_kind":"ident"},{"source":"⟨a, m, rfl⟩","source_end":7137,"source_start":7122,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 40 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19c3e72bc65a97b140e8e81a95329de7b25a9ca01be6a8a7b2f4039ed8bdbc77 | d81e6e3015d88a00301d2e9bfc0b093dc1edadd0fd56c798c65b35f7f8c98240 | 4b6e5b0c8ebbf8a4a2d32d99ca0a59866cbf638b52114755d8ef8b48b8f2203d | 9cab908ad01a134d453fc6c3b72ab8b2fa530e74722b3cce6f9f3b014d37722e |
cat-searcher/leandojo-benchmark-4-random | test | 3,477 | Finset.mem_sym_iff | Mathlib/Data/Finset/Sym.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨a, h _ <| <a>Sym.mem_cons_self</a> _ _, <a>Finset.mem_image_of_mem</a> _ <| ih.2 fun b hb ↦ h _ <| <a>Sym.mem_cons_of_mem</a> hb⟩ | case succ.refine_2.intro.intro
α : Type u_1
inst✝ : DecidableEq α
s t : Finset α
a✝ b : α
n✝ n : ℕ
ih : ∀ {m : Sym α n}, m ∈ s.sym n ↔ ∀ a ∈ m, a ∈ s
a : α
m : Sym α n
h : ∀ a_1 ∈ a ::ₛ m, a_1 ∈ s
⊢ ∃ v ∈ s, a ::ₛ m ∈ image (Sym.cons v) (s.sym n) | ((:c Exists) (:fv _uniq.11680) (:lambda v (:fv _uniq.11680) ((:c And) ((:c Membership.mem) (:fv _uniq.11680) ((:c Finset) (:fv _uniq.11680)) ((:c Finset.instMembership) (:fv _uniq.11680)) 0 (:fv _uniq.11692)) ((:c Membership.mem) ((:c Sym) (:fv _uniq.11680) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.11680))"},{"name":"s","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"t","sexp":"((:c Finset) (:fv _uniq.11680))"},{"name":"a✝","sexp":"(:fv _uniq.11680)"},{"name":"b","sexp":"(:fv _uniq.11680)"},{"name":"n✝","sexp":"(:c Na... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda v :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :expl... | {"children":[{"source":"exact","sourceEnd":7175,"sourceStart":7170,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":7185,"sourceStart":7182,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"a","sourceEnd":7186,"sourceStart":7185,"tag":"identifier"},{"source":",","sourceEnd":7187,"source... | [] | [{"source":"⟨a, h _ <| Sym.mem_cons_self _ _,\n mem_image_of_mem _ <| ih.2 fun b hb ↦ h _ <| Sym.mem_cons_of_mem hb⟩","source_end":7298,"source_start":7182,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11680","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.11687","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"interna... | 57 | 41 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 814712ffee70e357da7c5a425bac3ba336cf24969293948f5242c5a8f89ec8c0 | 9cab908ad01a134d453fc6c3b72ab8b2fa530e74722b3cce6f9f3b014d37722e | c39f1598a31ed4e7c74b9bcc69d99706daba619d3bf986d6111fabab12ef7e5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,478 | OrthonormalBasis.orthonormal_adjustToOrientation | Mathlib/Analysis/InnerProductSpace/Orientation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply e.orthonormal.orthonormal_of_forall_eq_or_eq_neg | E : Type u_1
inst✝³ : NormedAddCommGroup E
inst✝² : InnerProductSpace ℝ E
ι : Type u_2
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
ne : Nonempty ι
e f : OrthonormalBasis ι ℝ E
x : Orientation ℝ E ι
⊢ Orthonormal ℝ ⇑(e.toBasis.adjustToOrientation x) | E : Type u_1
inst✝³ : NormedAddCommGroup E
inst✝² : InnerProductSpace ℝ E
ι : Type u_2
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
ne : Nonempty ι
e f : OrthonormalBasis ι ℝ E
x : Orientation ℝ E ι
⊢ ∀ (i : ι), (e.toBasis.adjustToOrientation x) i = e i ∨ (e.toBasis.adjustToOrientation x) i = -e i | ((:c Orthonormal) (:c Real) (:fv _uniq.22835) (:c Real.RCLike) (:fv _uniq.22838) (:fv _uniq.22851) (:fv _uniq.22854) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.22854) (:c Real) (:fv _uniq.22835) ((:c StrictOrderedSemiring.toSemiring) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrde... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.22835))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.22835) (:c Real.RCLike) (:fv _uniq.22838))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.228... | (:app (:c Orthonormal) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c RCLike) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c InnerProductSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22835","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22838","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"apply","sourceEnd":4576,"sourceStart":4571,"tag":"atom"},{"name":"Orthonormal.orthonormal_of_forall_eq_or_eq_neg","semanticRole":"global","source":"e.orthonormal.orthonormal_of_forall_eq_or_eq_neg","sourceEnd":4625,"sourceStart":4577,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source... | [] | [{"source":"e.orthonormal.orthonormal_of_forall_eq_or_eq_neg","source_end":4625,"source_start":4577,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22835","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22838","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 19 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 766747c4f57cecc7ad847569fbb0d7043202333e67905ffbcacd4d2b58124b06 | 90e4d1793384364b3dd41584c99b0502462d134cc8d630016a2f872d54292ab9 | 924a6e05d9612fa584149cd0c2e1910840784b5e8c76844b1ea4a021655e1e7a | 607a9b42a64ab0cca0848bfccbb405519a57410986383c6f031b052a4687ca20 |
cat-searcher/leandojo-benchmark-4-random | test | 3,479 | OrthonormalBasis.orthonormal_adjustToOrientation | Mathlib/Analysis/InnerProductSpace/Orientation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using e.toBasis.adjustToOrientation_apply_eq_or_eq_neg x | E : Type u_1
inst✝³ : NormedAddCommGroup E
inst✝² : InnerProductSpace ℝ E
ι : Type u_2
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
ne : Nonempty ι
e f : OrthonormalBasis ι ℝ E
x : Orientation ℝ E ι
⊢ ∀ (i : ι), (e.toBasis.adjustToOrientation x) i = e i ∨ (e.toBasis.adjustToOrientation x) i = -e i | (:forall i (:fv _uniq.22854) ((:c Or) ((:c Eq) (:fv _uniq.22835) ((:c DFunLike.coe) ((:c Basis) (:fv _uniq.22854) (:c Real) (:fv _uniq.22835) ((:c StrictOrderedSemiring.toSemiring) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.22835))"},{"name":"inst✝²","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.22835) (:c Real.RCLike) (:fv _uniq.22838))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.228... | (:forall i :explicit (:fv FV3) (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c Basis) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22835","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22838","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c NormedAddCommGroup) (:a... | {"children":[{"source":"simpa","sourceEnd":4633,"sourceStart":4628,"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":"e.toBasis.adjustToOrientation_apply_eq_or_eq_neg x","source_end":4690,"source_start":4640,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.22835","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.22838","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_index":... | 19 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 943c4e2120da49268cb410982ec66322d039ac83a868d800eda39003ecc78808 | 607a9b42a64ab0cca0848bfccbb405519a57410986383c6f031b052a4687ca20 | d258f4873efa7adb0f49202dc31133d889e5978f5c9ae2ca9bd41c768c6e83ae | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,480 | HurwitzZeta.completedHurwitzZetaOdd_one_sub | Mathlib/NumberTheory/LSeries/HurwitzZetaOdd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>HurwitzZeta.completedHurwitzZetaOdd</a>, <a>HurwitzZeta.completedSinZeta</a>, (by { push_cast; ring } : (1 - s + 1) / 2 = ↑(3 / 2 : ℝ) - (s + 1) / 2), ← <a>HurwitzZeta.hurwitzOddFEPair_k</a>, (<a>HurwitzZeta.hurwitzOddFEPair</a> a).<a>StrongFEPair.functional_equation</a> ((s + 1) / 2), <a>HurwitzZeta.hurwitzOddF... | a : UnitAddCircle
s : ℂ
⊢ completedHurwitzZetaOdd a (1 - s) = completedSinZeta a s | ((:c Eq) (:c Complex) ((:c HurwitzZeta.completedHurwitzZetaOdd) (:fv _uniq.126801) ((:c HSub.hSub) (:c Complex) (:c Complex) (:c Complex) ((:c instHSub) (:c Complex) (:c Complex.instSub)) ((:c OfNat.ofNat) (:c Complex) (:lit 1) ((:c One.toOfNat1) (:c Complex) (:c Complex.instOne))) (:fv _uniq.126802))) ((:c HurwitzZeta... | [{"name":"a","sexp":"(:c UnitAddCircle)"},{"name":"s","sexp":"(:c Complex)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HurwitzZeta.completedHurwitzZetaOdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:insta... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"name":"a","sexp":"(:c UnitAddCircle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":18720,"sourceStart":18718,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18722,"sourceStart":18721,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"completedHurwitzZetaOdd","source_end":18745,"source_start":18722,"syntax_kind":"ident"},{"source":"completedSinZeta","source_end":18763,"source_start":18747,"syntax_kind":"ident"},{"source":"hurwitzOddFEPair_k","source_end":18872,"source_start":18854,"syntax_kind":"ident"},{"source":"(hurwitzOddFEPair a).fu... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"user_name":"s"}] | 51 | 2 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ce281e00ca19952c270f4df865e7143e60dd3e4d592a6e2825ad1edab0870dc | 103b6ac39dbcf5f02b17498293d1da6ee02108e4b2f387af80212bf4563b926f | e1f71de745b387bc30cb953098c29821941d28e277a143d38bfabdc52e6b783f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,481 | HurwitzZeta.completedHurwitzZetaOdd_one_sub | Mathlib/NumberTheory/LSeries/HurwitzZetaOdd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | push_cast | a : UnitAddCircle
s : ℂ
⊢ (1 - s + 1) / 2 = ↑(3 / 2) - (s + 1) / 2 | a : UnitAddCircle
s : ℂ
⊢ (1 - s + 1) / 2 = 3 / 2 - (s + 1) / 2 | ((:c Eq) (:c Complex) ((:c HDiv.hDiv) (:c Complex) (:c Complex) (:c Complex) ((:c instHDiv) (:c Complex) ((:c Field.toDiv) (:c Complex) (:c Complex.instField))) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) ((:c HSub.hSub) (:c Complex) (:c Complex) (:c Complex)... | [{"name":"a","sexp":"(:c UnitAddCircle)"},{"name":"s","sexp":"(:c Complex)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"name":"a","sexp":"(:c UnitAddCircle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"}] | {"children":[{"source":"push_cast","sourceEnd":18784,"sourceStart":18775,"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":[... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"user_name":"s"}] | 51 | 13 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f99b2248173be7e043e36f3bd209936e4d50d29b034d6115b3491f826d69cca | dd51570357f9a4803f8cf4349a0a3ed73604c60e79381f509c521621df39f483 | 5189104d9b5e7264ce49402b63410b1cd440d29f098c6f68c6d5dbb0f8982ff0 | a2eb14c6d26fb5d9522571b88d683d8c29025b5944099c3b1ba32cce1ba5097f |
cat-searcher/leandojo-benchmark-4-random | test | 3,482 | HurwitzZeta.completedHurwitzZetaOdd_one_sub | Mathlib/NumberTheory/LSeries/HurwitzZetaOdd.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | a : UnitAddCircle
s : ℂ
⊢ (1 - s + 1) / 2 = 3 / 2 - (s + 1) / 2 | ((:c Eq) (:c Complex) ((:c HDiv.hDiv) (:c Complex) (:c Complex) (:c Complex) ((:c instHDiv) (:c Complex) ((:c Field.toDiv) (:c Complex) (:c Complex.instField))) ((:c HAdd.hAdd) (:c Complex) (:c Complex) (:c Complex) ((:c instHAdd) (:c Complex) (:c Complex.instAdd)) ((:c HSub.hSub) (:c Complex) (:c Complex) (:c Complex)... | [{"name":"a","sexp":"(:c UnitAddCircle)"},{"name":"s","sexp":"(:c Complex)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Complex)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Complex)) (:arg :explicit 1 (:c Complex)) (:arg :... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"name":"a","sexp":"(:c UnitAddCircle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"name":"s","sexp":"(:c Complex)"}] | {"children":[{"source":"ring","sourceEnd":18790,"sourceStart":18786,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":18790,"sourceStart":18786,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.126801","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.126802","is_instance":false,"is_let":false,"user_name":"s"}] | 51 | 15 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a4afccba0aaaa0eb94557406770bb1e5589c629f4a0346e31df5ef6dd7abd46 | a2eb14c6d26fb5d9522571b88d683d8c29025b5944099c3b1ba32cce1ba5097f | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,483 | List.cons_diff_of_mem | .lake/packages/batteries/Batteries/Data/List/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.cons_diff</a>, <a>if_pos</a> h] | α : Type u_1
inst✝¹ : BEq α
inst✝ : LawfulBEq α
a : α
l₂ : List α
h : a ∈ l₂
l₁ : List α
⊢ (a :: l₁).diff l₂ = l₁.diff (l₂.erase a) | ((:c Eq) ((:c List) (:fv _uniq.150242)) ((:c List.diff) (:fv _uniq.150242) (:fv _uniq.150245) ((:c List.cons) (:fv _uniq.150242) (:fv _uniq.150315) (:fv _uniq.150318)) (:fv _uniq.150316)) ((:c List.diff) (:fv _uniq.150242) (:fv _uniq.150245) (:fv _uniq.150318) ((:c List.erase) (:fv _uniq.150242) (:fv _uniq.150245) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c BEq) (:fv _uniq.150242))"},{"name":"inst✝","sexp":"((:c LawfulBEq) (:fv _uniq.150242) (:fv _uniq.150245))"},{"name":"a","sexp":"(:fv _uniq.150242)"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.150242))"},{"name":"h","sexp":"((:c Membership.mem) (:fv ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c List.diff) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c BEq) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV0)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.150242","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.150245","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c BEq) (:arg :explicit ... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":41554,"sourceStart":41552,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41556,"sourceStart":41555,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"cons_diff","source_end":41565,"source_start":41556,"syntax_kind":"ident"},{"source":"if_pos h","source_end":41575,"source_start":41567,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.150242","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.150245","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 243 | 2 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d42d7a37fd71e29ed1baca8b0c80fe5859e7216c75d5f7d86c27d38630680d83 | e57ddf4c3fc4fde1609b7be7b72fdb183df888ed641ca5775bfcc4b9de83e551 | 39c0ab2c05e321c8ef2ee66ea208c4d7fc16b16344cacf4a72288c9dca9e777f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,484 | Substring.Valid.next | .lake/packages/batteries/Batteries/Data/String/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ⟨l, m, r, h⟩ := h.validFor | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h : x✝.Valid
e : x✝.toString.data = m₁ ++ c :: m₂
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
e : x✝.toString.data = m₁ ++ c :: m₂
l m r : List Char
h : ValidFor l m r x✝
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | ((:c Eq) (:c String.Pos) ((:c Substring.next) (:fv _uniq.170946) ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.170907)))) ((:c String.Pos.mk) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c String.utf8Len) (:fv _uniq.170907)) ((:c Char.utf8Size) (:fv _uniq.170908))))) | [{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"c","sexp":"(:c Char)"},{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h","sexp":"((:c Substring.Valid) (:fv _uniq.170946))"},{"name":"e","sexp":"((:c Eq) ((:c List) (:c Char)) ((:c String.data) ((:c Substring.toString) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.next) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Char)"... | {"children":[{"source":"let","sourceEnd":43006,"sourceStart":43003,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":43010,"sourceStart":43007,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"l","sourceEnd":43011,"sourceStart":43010,"tag":"identifier"},{"source":",","sour... | [] | [{"source":"h.validFor","source_end":43037,"source_start":43027,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 194 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e334ac16fd4d21ae18504415a489fe31aab27777db316627c9a5ce0eacb683e3 | 82fca7a338acff4d2f36361491c3331097cd90667b91d154ec0bf84a4c489be5 | c4a49969f9a49164bed59ac3215a4a63ece5d31aa7353ba2b8ab74698e084917 | e57232589a57ef058a28e7a4e5023030aae32274b766f672cf3cfc8512f23d22 |
cat-searcher/leandojo-benchmark-4-random | test | 3,485 | Substring.Valid.next | .lake/packages/batteries/Batteries/Data/String/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [h.toString] at e | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
e : x✝.toString.data = m₁ ++ c :: m₂
l m r : List Char
h : ValidFor l m r x✝
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
l m r : List Char
h : ValidFor l m r x✝
e : m = m₁ ++ c :: m₂
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | ((:c Eq) (:c String.Pos) ((:c Substring.next) (:fv _uniq.170946) ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.170907)))) ((:c String.Pos.mk) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c String.utf8Len) (:fv _uniq.170907)) ((:c Char.utf8Size) (:fv _uniq.170908))))) | [{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"c","sexp":"(:c Char)"},{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.170946))"},{"name":"e","sexp":"((:c Eq) ((:c List) (:c Char)) ((:c String.data) ((:c Substring.toString) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.next) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Char)"... | {"children":[{"source":"simp","sourceEnd":43046,"sourceStart":43042,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":43051,"sourceStart":43047,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":430... | [] | [{"source":"h.toString","source_end":43063,"source_start":43053,"syntax_kind":"ident"},{"source":"e","source_end":43069,"source_start":43068,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 194 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7fa993d87333325720eb5c0d667b0a9e44d02199c9e2b63da04e554152f245a3 | e57232589a57ef058a28e7a4e5023030aae32274b766f672cf3cfc8512f23d22 | 4476e7a5af0943d2d57b94c7f2fbe87e3a58460521bac5dcd57f61d0c1eba4dd | a12e82e934e7e8aef9ca2f86a0a978a17c8b99752d6f4e85d9ad13dfa72751cd |
cat-searcher/leandojo-benchmark-4-random | test | 3,486 | Substring.Valid.next | .lake/packages/batteries/Batteries/Data/String/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst e | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
l m r : List Char
h : ValidFor l m r x✝
e : m = m₁ ++ c :: m₂
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
l r : List Char
h : ValidFor l (m₁ ++ c :: m₂) r x✝
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | ((:c Eq) (:c String.Pos) ((:c Substring.next) (:fv _uniq.170946) ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.170907)))) ((:c String.Pos.mk) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c String.utf8Len) (:fv _uniq.170907)) ((:c Char.utf8Size) (:fv _uniq.170908))))) | [{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"c","sexp":"(:c Char)"},{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.170946))"},{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"m","sexp":"((:c List) (:c Char))"},{"name... | (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.next) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Char)"... | {"children":[{"source":"subst","sourceEnd":43076,"sourceStart":43071,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"e","sourceEnd":43078,"sourceStart":43077,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":43078,"sourceStart":43077,"tag":"node"}],"kind":"Lean.Parser.Tactic.sub... | [] | [{"source":"e","source_end":43078,"source_start":43077,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 194 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 088b2a0232af61fc516386e72a90c59f3ada1b34ff2870bfd4b96d1f685f35c6 | a12e82e934e7e8aef9ca2f86a0a978a17c8b99752d6f4e85d9ad13dfa72751cd | 9f87dce166543dae54bdf0d93e7bf67fad5e58e02009c37a2d8eb8b1f30b1ce7 | e3c9ee4d3a70a3a51f19479e178b17eb8c174956e6dcb0fec77551e74764524c |
cat-searcher/leandojo-benchmark-4-random | test | 3,487 | Substring.Valid.next | .lake/packages/batteries/Batteries/Data/String/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h.next] | m₁ : List Char
c : Char
m₂ : List Char
x✝ : Substring
h✝ : x✝.Valid
l r : List Char
h : ValidFor l (m₁ ++ c :: m₂) r x✝
⊢ x✝.next { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + c.utf8Size } | ((:c Eq) (:c String.Pos) ((:c Substring.next) (:fv _uniq.170946) ((:c String.Pos.mk) ((:c String.utf8Len) (:fv _uniq.170907)))) ((:c String.Pos.mk) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) ((:c String.utf8Len) (:fv _uniq.170907)) ((:c Char.utf8Size) (:fv _uniq.170908))))) | [{"name":"m₁","sexp":"((:c List) (:c Char))"},{"name":"c","sexp":"(:c Char)"},{"name":"m₂","sexp":"((:c List) (:c Char))"},{"name":"x✝","sexp":"(:c Substring)"},{"name":"h✝","sexp":"((:c Substring.Valid) (:fv _uniq.170946))"},{"name":"l","sexp":"((:c List) (:c Char))"},{"name":"r","sexp":"((:c List) (:c Char))"},{"name... | (:app (:c Eq) (:arg :implicit-type 0 (:c String.Pos)) (:arg :explicit 1 (:app (:c Substring.next) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c String.utf8Len) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 2 (:app (:c String.Pos.mk) (:arg :explicit 0 (:app (:c ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"name":"m₁","sexp":"(:app (:c List) (:arg :explicit 0 (:c Char)))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Char)"... | {"children":[{"source":"simp","sourceEnd":43084,"sourceStart":43080,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43086,"sourceStart":43085,"tag":"a... | [] | [{"source":"h.next","source_end":43092,"source_start":43086,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.170907","is_instance":false,"is_let":false,"user_name":"m₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.170908","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 194 | 9 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ccb0e23fb87e00b49fbd48361e0e2385511672dda4270229a74625e9a6707ea | e3c9ee4d3a70a3a51f19479e178b17eb8c174956e6dcb0fec77551e74764524c | cdd324681f048984e4ff3499e957bdf479abf4aa06a85fe7ae0b5a6e02736820 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,488 | exists_set_linearIndependent_of_isDomain | Mathlib/LinearAlgebra/Dimension/Localization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨w, hw⟩ := <a>IsLocalizedModule.linearIndependent_lift</a> R⁰ (<a>LocalizedModule.mkLinearMap</a> R⁰ M) <a>le_rfl</a> (<a>Module.Free.chooseBasis</a> (<a>FractionRing</a> R) (<a>LocalizedModule</a> R⁰ M)).<a>Basis.linearIndependent</a> | R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
inst✝¹ : IsLocal... | case intro
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
inst✝... | ((:c Exists) ((:c Set) (:fv _uniq.108863)) (:lambda s ((:c Set) (:fv _uniq.108863)) ((:c And) ((:c Eq) (:c Cardinal) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.108863) 0)) ((:c Module.rank) (:fv _uniq.108859) (:fv _uniq.108863) ((:c CommSemiring.toSemiring) (:fv _uniq.108859) ((:c CommRing.toCommSemiring) (:fv _uniq.1... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"N","sexp":"(:sort (+ v' 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.108859))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.108861))"},{"name":"inst✝⁹","sexp":"((:c AddCommGr... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV2))) (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"obtain","sourceEnd":3819,"sourceStart":3813,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":3823,"sourceStart":3820,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"w","sourceEnd":3... | [] | [{"source":"IsLocalizedModule.linearIndependent_lift R⁰ (LocalizedModule.mkLinearMap R⁰ M) le_rfl\n (Module.Free.chooseBasis (FractionRing R) (LocalizedModule R⁰ M)).linearIndependent","source_end":4020,"source_start":3839,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨w, hw⟩","source_end":3831,"source_start":3... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 12 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb1400ea2b8283139d814306d7b93daeb1ea41ea8ebc337baaab77c303b18989 | 5308119ef9a30fa12109bcd844d0ba23149e38061dea2afee94491fd01ae5a69 | d1740496c81bf7e62a7fc6742dfb80e9419252725d86edfc1260252f84ee1e4e | 81faf97977234aefcb90c254c5cd15d9c67c382c190f14b830cf51c25d1f4a2b |
cat-searcher/leandojo-benchmark-4-random | test | 3,489 | exists_set_linearIndependent_of_isDomain | Mathlib/LinearAlgebra/Dimension/Localization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨<a>Set.range</a> w, ?_, (<a>linearIndependent_subtype_range</a> hw.injective).<a>Iff.mpr</a> hw⟩ | case intro
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
inst✝... | case intro
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
inst✝... | ((:c Exists) ((:c Set) (:fv _uniq.108863)) (:lambda s ((:c Set) (:fv _uniq.108863)) ((:c And) ((:c Eq) (:c Cardinal) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.108863) 0)) ((:c Module.rank) (:fv _uniq.108859) (:fv _uniq.108863) ((:c CommSemiring.toSemiring) (:fv _uniq.108859) ((:c CommRing.toCommSemiring) (:fv _uniq.1... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"N","sexp":"(:sort (+ v' 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.108859))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.108861))"},{"name":"inst✝⁹","sexp":"((:c AddCommGr... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:lambda s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV2))) (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"refine","sourceEnd":4029,"sourceStart":4023,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":4033,"sourceStart":4030,"tag":"atom"},{"children":[{"children":[{"name":"Set.range","semanticRole":"global","source":"Set.range","sourceEnd":4042,"sourceStart":4033,"tag":"identifier"},{"children":[{... | [] | [{"source":"⟨Set.range w, ?_, (linearIndependent_subtype_range hw.injective).mpr hw⟩","source_end":4106,"source_start":4030,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 12 | 5 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0228ac19217c511edb69ec0a4a10da28a56e7c796ec65b02965eb90dff3ecd64 | 81faf97977234aefcb90c254c5cd15d9c67c382c190f14b830cf51c25d1f4a2b | 37f21ff2f9274e57da105a34f4ae21ce17353f3fd537bb6cee5bad701d0f8a12 | 1b89bfd01f79874ae898faa23918e93c24ac56b31bc722540503630221232c27 |
cat-searcher/leandojo-benchmark-4-random | test | 3,490 | exists_set_linearIndependent_of_isDomain | Mathlib/LinearAlgebra/Dimension/Localization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Cardinal.lift_injective</a>.{max u v} | case intro
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
inst✝... | case intro.a
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
ins... | ((:c Eq) (:c Cardinal) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.108863) ((:c Set.range) (:fv _uniq.108863) ((:c Module.Free.ChooseBasisIndex) ((:c FractionRing) (:fv _uniq.108859) (:fv _uniq.108868)) ((:c LocalizedModule) (:fv _uniq.108859) ((:c CommRing.toCommSemiring) (:fv _uniq.108859) (:fv _uniq.108868)) ((:c no... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"N","sexp":"(:sort (+ v' 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.108859))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.108861))"},{"name":"inst✝⁹","sexp":"((:c AddCommGr... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Module.Free.ChooseBasisIndex) (:arg :explicit 0 (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"apply","sourceEnd":4114,"sourceStart":4109,"tag":"atom"},{"children":[{"name":"Cardinal.lift_injective","semanticRole":"global","source":"Cardinal.lift_injective","sourceEnd":4138,"sourceStart":4115,"tag":"identifier"},{"source":".{","sourceEnd":4140,"sourceStart":4138,"tag":"atom"},{"children":... | [] | [{"source":"Cardinal.lift_injective.{max u v}","source_end":4148,"source_start":4115,"syntax_kind":"Lean.Parser.Term.explicitUniv"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 12 | 6 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 458bbdb298feb87cca03fa10c9886b04601afbabceab224aba7e3c9657c9ce8c | 1b89bfd01f79874ae898faa23918e93c24ac56b31bc722540503630221232c27 | 567a4ff891d0e5d5a0cb08915caaacb52a30dfef2c24902b5ddea209f5eb7cc9 | e8cc9798a1449fd75fc1ab99fa1986134c37bdce22d25cfa230b41e909aef7d1 |
cat-searcher/leandojo-benchmark-4-random | test | 3,491 | exists_set_linearIndependent_of_isDomain | Mathlib/LinearAlgebra/Dimension/Localization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Cardinal.mk_range_eq_of_injective</a> hw.injective, ← <a>Module.Free.rank_eq_card_chooseBasisIndex</a>, <a>IsLocalizedModule.lift_rank_eq</a> (<a>FractionRing</a> R) R⁰ (<a>LocalizedModule.mkLinearMap</a> R⁰ M) <a>le_rfl</a>] | case intro.a
R : Type u
S : Type u'
M : Type v
N : Type v'
inst✝¹¹ : CommRing R
inst✝¹⁰ : CommRing S
inst✝⁹ : AddCommGroup M
inst✝⁸ : AddCommGroup N
inst✝⁷ : Module R M
inst✝⁶ : Module R N
inst✝⁵ : Algebra R S
inst✝⁴ : Module S N
inst✝³ : IsScalarTower R S N
p : Submonoid R
inst✝² : IsLocalization p S
f : M →ₗ[R] N
ins... | ((:c Eq) (:c Cardinal) ((:c Cardinal.lift) ((:c Cardinal.mk) ((:c Set.Elem) (:fv _uniq.108863) ((:c Set.range) (:fv _uniq.108863) ((:c Module.Free.ChooseBasisIndex) ((:c FractionRing) (:fv _uniq.108859) (:fv _uniq.108868)) ((:c LocalizedModule) (:fv _uniq.108859) ((:c CommRing.toCommSemiring) (:fv _uniq.108859) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ u' 1))"},{"name":"M","sexp":"(:sort (+ v 1))"},{"name":"N","sexp":"(:sort (+ v' 1))"},{"name":"inst✝¹¹","sexp":"((:c CommRing) (:fv _uniq.108859))"},{"name":"inst✝¹⁰","sexp":"((:c CommRing) (:fv _uniq.108861))"},{"name":"inst✝⁹","sexp":"((:c AddCommGr... | (:app (:c Eq) (:arg :implicit-type 0 (:c Cardinal)) (:arg :explicit 1 (:app (:c Cardinal.lift) (:arg :explicit 0 (:app (:c Cardinal.mk) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set.range) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Module... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":explicit","c... | {"children":[{"source":"rw","sourceEnd":4153,"sourceStart":4151,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4155,"sourceStart":4154,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Cardina... | [] | [{"source":"Cardinal.mk_range_eq_of_injective hw.injective","source_end":4201,"source_start":4155,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Module.Free.rank_eq_card_chooseBasisIndex","source_end":4248,"source_start":4207,"syntax_kind":"ident"},{"source":"IsLocalizedModule.lift_rank_eq (FractionRing R) R⁰ (Locali... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.108859","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.108861","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":explicit","context_index":2,"internal_name":"_... | 12 | 7 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe7307cba6a4af9913bdc9f8a9058e30729924befda0cc4b0d8a1e0c0d2f31d1 | e8cc9798a1449fd75fc1ab99fa1986134c37bdce22d25cfa230b41e909aef7d1 | 20ea13401cbc8ecadbbd33a065f937c50d1ebd5b539ba1d1f568407545b61da3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,492 | CategoryTheory.topologyOfClosureOperator_self | Mathlib/CategoryTheory/Sites/Closed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext X S | C : Type u
inst✝ : Category.{v, u} C
J₁ J₂ : GrothendieckTopology C
⊢ topologyOfClosureOperator J₁.closureOperator ⋯ = J₁ | case h.h.h
C : Type u
inst✝ : Category.{v, u} C
J₁ J₂ : GrothendieckTopology C
X : C
S : Sieve X
⊢ S ∈ (topologyOfClosureOperator J₁.closureOperator ⋯).sieves X ↔ S ∈ J₁.sieves X | ((:c Eq) ((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18809) (:fv _uniq.18812)) ((:c CategoryTheory.topologyOfClosureOperator) (:fv _uniq.18809) (:fv _uniq.18812) ((:c CategoryTheory.GrothendieckTopology.closureOperator) (:fv _uniq.18809) (:fv _uniq.18812) (:fv _uniq.18827)) (:lambda X (:fv _uniq.18809) (:lambd... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18809))"},{"name":"J₁","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18809) (:fv _uniq.18812))"},{"name":"J₂","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18809) (:fv _uniq.18812))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.GrothendieckTopology) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c CategoryTheory.topologyOfClosureOperator) (:arg :implicit-type 0 (:fv FV0)) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18809","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18812","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"ext","sourceEnd":13353,"sourceStart":13350,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"X","sourceEnd":13355,"sourceStart":13354,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"X","sourceEnd":13355,"sourceStart":13354,"tag... | [{"role":"fresh_name","source":"X","source_end":13355,"source_start":13354,"syntax_kind":"ident"},{"role":"fresh_name","source":"S","source_end":13357,"source_start":13356,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18809","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18812","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 47 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3af3ba6eb59997c6782b78863aa4fa1fe8ba787153ed67ae5d67501ab19676d0 | d0231b35a48c226cc949da85e180efc55e9ec49ed33476632a881731c06e9e45 | 2110e4421002ba6ddac019e991dbbf96f6516d5b10fe3bc69e3009b065611e8a | cb0fc062bf3d9972d4a5a88e3f0028fc5498792a3a2f50c97ab37741c15147b9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,493 | CategoryTheory.topologyOfClosureOperator_self | Mathlib/CategoryTheory/Sites/Closed.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem</a> | case h.h.h
C : Type u
inst✝ : Category.{v, u} C
J₁ J₂ : GrothendieckTopology C
X : C
S : Sieve X
⊢ S ∈ (topologyOfClosureOperator J₁.closureOperator ⋯).sieves X ↔ S ∈ J₁.sieves X | ((:c Iff) ((:c Membership.mem) ((:c CategoryTheory.Sieve) (:fv _uniq.18809) (:fv _uniq.18812) (:fv _uniq.18993)) ((:c Set) ((:c CategoryTheory.Sieve) (:fv _uniq.18809) (:fv _uniq.18812) (:fv _uniq.18993))) ((:c Set.instMembership) ((:c CategoryTheory.Sieve) (:fv _uniq.18809) (:fv _uniq.18812) (:fv _uniq.18993))) (:fv _... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.18809))"},{"name":"J₁","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18809) (:fv _uniq.18812))"},{"name":"J₂","sexp":"((:c CategoryTheory.GrothendieckTopology) (:fv _uniq.18809) (:fv _uniq.18812))"},{"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c CategoryTheory.Sieve) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV5)))) (:arg :implicit-type 1 (:app (:c Set) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18809","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18812","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"apply","sourceEnd":13365,"sourceStart":13360,"tag":"atom"},{"name":"CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem","semanticRole":"global","source":"GrothendieckTopology.close_eq_top_iff_mem","sourceEnd":13407,"sourceStart":13366,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply",... | [] | [{"source":"GrothendieckTopology.close_eq_top_iff_mem","source_end":13407,"source_start":13366,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.18809","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.18812","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 47 | 5 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4d3c2022f7f0ff66631df5815b0e507f02e55a81b98f46a35b961d4fefbffb46 | cb0fc062bf3d9972d4a5a88e3f0028fc5498792a3a2f50c97ab37741c15147b9 | 1bf46dda6e15bdab77aa4de2c8ce5c6e4a1e67a2cbfe9471fcea756248ed4786 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,494 | Nat.prime_two | Mathlib/Data/Nat/Prime.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | n : ℕ
⊢ Prime 2 | ((:c Nat.Prime) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) | [{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Nat.Prime) (:arg :explicit 0 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:lit 2)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5553","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":6251,"sourceStart":6245,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":6251,"sourceStart":6245,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":6251,"sourceStart":6245,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5553","is_instance":false,"is_let":false,"user_name":"n"}] | 42 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb894048c70c37612b8d37e45aa9745d02115e5a70d1a99419573711a5234936 | 56adfbd801ff577c992d620bbdb4efe0c0d2c940df8d9d460114a24fea92e010 | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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