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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 | 1,248 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | match <a>Batteries.RBNode.ins</a> cmp v a, ihl with | _, .balanced .nil => exact .balanced (.red .nil hr) | _, .balanced (.red ha hb) => exact .redred <a>rfl</a> (.red ha hb) hr | _, .balanced (.black ha hb) => exact .balanced (.red (.black ha hb) hr) | _, .redred h .. => cases hl <;> cases h | case red.h_1
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt
⊢ RedRed ((node red a... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"match","sourceEnd":11730,"sourceStart":11725,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"child... | [] | [{"source":"match ins cmp v a, ihl with\n | _, .balanced .nil => ? rhs | _, .balanced (.red ha hb) => ? rhs | _, .balanced (.black ha hb) => ? rhs | _, .redred h .. => ? rhs","source_end":12011,"source_start":11725,"syntax_kind":"Lean.Parser.Term.match"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 18 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 160fe77c653599b42be47eefe066dbdca2052632df8475d723f90258f37ca423 | 37bf65d0cac61b3b0111c366317579daeeca3264ec423c428fbf46f4b8a5cc98 | 7c5e32379d054f10219eaaff84c0e7fbbaf331b0a99b2112247acb7b7017467f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,249 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red .nil hr) | α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
ihl : RedRed (a.isRed = red) (ins cmp v a) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt
hl : a.Balanced black 0
hr : b.Balanced black 0
ihr : RedRed (b.isRed = red) (ins cmp v b) 0
⊢ RedRed ((node red a x b).isRed =... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":11787,"sourceStart":11782,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":11789,"sourceStart":11788,"tag":"atom"},{"source":"balanced","sourceEnd":11797,"sourceStart":11789,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red .nil hr)","source_end":11812,"source_start":11788,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 22 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 771e6a9a30dcefaca90a546303438ae56db3663742e8a197f32d82a78cef5a23 | c7ab69b908e98a7af2f24ddc962a529caf8ba991f9144b499f5850a72dc01ca3 | 416f2796ddb2aeb75bc0d2d1eb0620405aea32234cd7b6a5289d279abd148304 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,250 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .redred <a>rfl</a> (.red ha hb) hr | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n✝ : Nat
b : RBNode α
x : α
ihl : RedRed (a.isRed = red) (ins cmp v a) n✝
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt
n : Nat
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
ha : l✝.Balanced black n
hb : r✝.Balanced black n
hl : a.Balanced black n
hr : b.... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":11855,"sourceStart":11850,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":11857,"sourceStart":11856,"tag":"atom"},{"source":"redred","sourceEnd":11863,"sourceStart":11857,"tag":"identifier"}],"kind":"Lean.Parser.Term.dot... | [] | [{"source":".redred rfl (.red ha hb) hr","source_end":11883,"source_start":11856,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 26 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d7c6f6d5aa463690ebc644197617744ce141bc0b9611d1905889096739e10d8 | 26583fb8cd34cde3bd99a0831259d656de4f6569cf94ebc1bb38115fd7c10ed8 | a5f3c68b936888c51ff4e8442a51c35df53b88be9de08fd4b6bd2faf0ec3a708 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,251 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red (.black ha hb) hr) | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
ihl : RedRed (a.isRed = red) (ins cmp v a) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
n✝ : Nat
c₁✝ c₂✝ : RBColor
ha : l✝.Balanced c₁✝ n✝
hb : r✝.Balanced c₂✝ n✝
hl : a.Balanced ... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":11928,"sourceStart":11923,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":11930,"sourceStart":11929,"tag":"atom"},{"source":"balanced","sourceEnd":11938,"sourceStart":11930,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red (.black ha hb) hr)","source_end":11963,"source_start":11929,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 30 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54c3252f1cc8c34b58cb6bec470b436a8bb5a961d399d4d32f4bd57c3e1c399b | 72e6b5e530deb7a75ab04b83ed0881c24bfda2c4109a11afac31c23bb0c0498c | 305a3a6ed5179dfacb1c76c6dddb345de95da63ef76cdd4e1eeb72447906637f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,252 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases hl <;> cases h | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n✝ : Nat
b : RBNode α
x : α
ihl : RedRed (a.isRed = red) (ins cmp v a) n✝
x✝¹ : Ordering
heq✝ : cmp v x = Ordering.lt
n : Nat
a✝² : RBNode α
c₁✝ : RBColor
b✝ : RBNode α
c₂✝ : RBColor
x✝ : α
h : a.isRed = red
a✝¹ : a✝².Balanced c₁✝ n
a✝ : b✝.... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":11996,"sourceStart":11991,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":23,"semanticRole":"local","source":"hl","sourceEnd":11999,"sourceStart":11997,"tag":"ide... | [] | [{"source":"hl","source_end":11999,"source_start":11997,"syntax_kind":"ident"},{"source":"h","source_end":12011,"source_start":12010,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 34 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 64b26c13541192dde80da57441f01619d69324448c82a76b6bcc06510fd50300 | b91b64bdd5a3dd9fefa51ae0d88b0861722741c4dc61c35d10aadaf119d6fa90 | 79e518598881fa840768c7fdf0da24947c892b88a5c071ef0d544ea595e0f871 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,253 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | match <a>Batteries.RBNode.ins</a> cmp v b, ihr with | _, .balanced .nil => exact .balanced (.red hl .nil) | _, .balanced (.red ha hb) => exact .redred <a>rfl</a> hl (.red ha hb) | _, .balanced (.black ha hb) => exact .balanced (.red hl (.black ha hb)) | _, .redred h .. => cases hr <;> cases h | case red.h_2
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.gt
⊢ RedRed ((node red a... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"match","sourceEnd":12024,"sourceStart":12019,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"child... | [] | [{"source":"match ins cmp v b, ihr with\n | _, .balanced .nil => ? rhs | _, .balanced (.red ha hb) => ? rhs | _, .balanced (.black ha hb) => ? rhs | _, .redred h .. => ? rhs","source_end":12305,"source_start":12019,"syntax_kind":"Lean.Parser.Term.match"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 43 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37e537ace0ad4c414325d5199c21f893d82781a42187964c9608432c4f5f7867 | 1c343df8cb4206e606702bdc387e224e476aa4ba6bfde961aea0ba13845cc5d5 | c3914cc1125778cfb217014a70b36866bd30ca4cd03a15ede96fd0fe81dbec5d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,254 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red hl .nil) | α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.gt
hl : a.Balanced black 0
hr : b.Balanced black 0
ihl : RedRed (a.isRed = red) (ins cmp v a) 0
⊢ RedRed ((node red a x b).isRed =... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12081,"sourceStart":12076,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":12083,"sourceStart":12082,"tag":"atom"},{"source":"balanced","sourceEnd":12091,"sourceStart":12083,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red hl .nil)","source_end":12106,"source_start":12082,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 47 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a0905b91ba15896528238da358a6ac240d3978b775aaedde927c11ec6e444e48 | 2f604f8440cb80ef25b0b788de9738bead36f1b1c219aee11ace7e976062bb2c | ff9e9e481f2d47b3ab63edc89c67521b3d5c170a89da3284d39386285d92293b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,255 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .redred <a>rfl</a> hl (.red ha hb) | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n✝ : Nat
b : RBNode α
x : α
ihr : RedRed (b.isRed = red) (ins cmp v b) n✝
x✝ : Ordering
heq✝ : cmp v x = Ordering.gt
n : Nat
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
ha : l✝.Balanced black n
hb : r✝.Balanced black n
hl : a.Balanced black n
hr : b.... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12149,"sourceStart":12144,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":12151,"sourceStart":12150,"tag":"atom"},{"source":"redred","sourceEnd":12157,"sourceStart":12151,"tag":"identifier"}],"kind":"Lean.Parser.Term.dot... | [] | [{"source":".redred rfl hl (.red ha hb)","source_end":12177,"source_start":12150,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 51 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dfe524bcb4995f72a5a35c866723669a350ee80de05bada2a3362f77cedb7edf | df9b4c45141d5eb8c91a0e772ae43a9c663662ae96be39a83b330dd1562d68b1 | 087cc8a5509bd48e6423162ed65e43e700ae9cb5699fc31c22a740857acc6369 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,256 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red hl (.black ha hb)) | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.gt
l✝ : RBNode α
v✝ : α
r✝ : RBNode α
n✝ : Nat
c₁✝ c₂✝ : RBColor
ha : l✝.Balanced c₁✝ n✝
hb : r✝.Balanced c₂✝ n✝
hl : a.Balanced ... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12222,"sourceStart":12217,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":12224,"sourceStart":12223,"tag":"atom"},{"source":"balanced","sourceEnd":12232,"sourceStart":12224,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red hl (.black ha hb))","source_end":12257,"source_start":12223,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 55 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aec632a52d0db6bca0511a598a136255aabd9d1c71f1f8e7dd9f71a7d3de8c68 | e4a72a6939b124072aa9014eb55d81372b93575cfc21e43058089c6ec8819c2d | 841a29ff8a71b703f216aa4618b4dbe0b97fab13ce615ed4e179edff913d92e1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,257 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases hr <;> cases h | α : Type u_1
c : RBColor
n✝¹ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n✝ : Nat
b : RBNode α
x : α
ihr : RedRed (b.isRed = red) (ins cmp v b) n✝
x✝¹ : Ordering
heq✝ : cmp v x = Ordering.gt
n : Nat
a✝² : RBNode α
c₁✝ : RBColor
b✝ : RBNode α
c₂✝ : RBColor
x✝ : α
h : b.isRed = red
a✝¹ : a✝².Balanced c₁✝ n
a✝ : b✝.... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝¹","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"}... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":12290,"sourceStart":12285,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":24,"semanticRole":"local","source":"hr","sourceEnd":12293,"sourceStart":12291,"tag":"ide... | [] | [{"source":"hr","source_end":12293,"source_start":12291,"syntax_kind":"ident"},{"source":"h","source_end":12305,"source_start":12304,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 59 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3ee405bb29f79580e5e1c05ca88369da4cea59aef9fd997a606d7ee94c3842f8 | 17fb94577a962c59799be142c91d02f3f98e82adfc7453c05ce4e5e75abccc0f | 83ecf5b802650374274f1bc2b240be0c86e6fe5d062de51224549cacdb07a7b6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,258 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.red hl hr) | case red.h_3
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
n : Nat
b : RBNode α
x : α
hl : a.Balanced black n
hr : b.Balanced black n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.eq
⊢ RedRed ((node red a... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.red) (:fv _uniq.70065) (:fv _uniq.70068) (:fv _uniq.70067))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _un... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12318,"sourceStart":12313,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":12320,"sourceStart":12319,"tag":"atom"},{"source":"balanced","sourceEnd":12328,"sourceStart":12320,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.red hl hr)","source_end":12341,"source_start":12319,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 68 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 28cd92b07f83d5c0641214e9a5051b4a16b854ae5fab424ee3aa19024e12bf82 | 7ad329ac72ebd9a20944e54891e4702f7d46072d88c046785ab81f5a03ce2259 | bb4fc1c73334443cbb0f5e66f56bb248e77a8bf2126273d6f55aff78e073c6cd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,259 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | unfold <a>Batteries.RBNode.ins</a> | case black
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node black a x b).isRed = red) (ins... | case black
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node black a x b).isRed = red)
... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.black) (:fv _uniq.78967) (:fv _uniq.78972) (:fv _uniq.78970))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.ins) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"source":"unfold","sourceEnd":12394,"sourceStart":12388,"tag":"atom"},{"children":[{"name":"Batteries.RBNode.ins","semanticRole":"global","source":"ins","sourceEnd":12398,"sourceStart":12395,"tag":"identifier"}],"kind":"null","source":"ins","sourceEnd":12398,"sourceStart":12395,"tag":"node"},{"children":[... | [] | [{"source":"ins","source_end":12398,"source_start":12395,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 74 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4527810cf92218f4fe5bcb1cfd9ed8e8b850f15f0f8be494e258964076060cc9 | dbca19af521b419d88125e836e57c2ec94643afa1171d1af41e7086eb52355c7 | 1f65e6bfeed629bfe8364ce0534222ae5ddc0fa2bdbd994c1c5c731e84ae8ffc | 309e35683a932ff66544b6ead4e2c77a2d2f2ab7136257a7e9b04b21e4fe4cc1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,260 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split | case black
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
⊢ RedRed ((node black a x b).isRed = red)
... | case black.h_1
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.black) (:fv _uniq.78967) (:fv _uniq.78972) (:fv _uniq.78970))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.ins.match_1)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"source":"split","sourceEnd":12405,"sourceStart":12400,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.split","source":"split","sourceEnd":12405,"sourceStart":12400,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 76 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 409c3996ec483f58268ca86fa5149311e31474b3df72e83af235286890c7fef5 | 309e35683a932ff66544b6ead4e2c77a2d2f2ab7136257a7e9b04b21e4fe4cc1 | ad1a64057f9ab34fecfe3f4ee78660bb0316dbda9370581ffbeb1e8bddf3d598 | 6d111cbbc55439799d1829f06aee3cd6fb57365bcb19147d2445bd6eddb680dd |
cat-searcher/leandojo-benchmark-4-random | test | 1,261 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact have ⟨c, h⟩ := ihl.balance1 hr; .balanced h | case black.h_1
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.lt... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.black) (:fv _uniq.78967) (:fv _uniq.78972) (:fv _uniq.78970))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.balance1) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12418,"sourceStart":12413,"tag":"atom"},{"children":[{"source":"have","sourceEnd":12423,"sourceStart":12419,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12427,"sourceStart":12424,"tag":"atom"},{"children"... | [] | [{"source":"have ⟨c, h⟩ := ihl.balance1 hr; .balanced h","source_end":12466,"source_start":12419,"syntax_kind":"Lean.Parser.Term.have"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 79 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b1257ec2bf48640461784b6828f79691c4c2cb4d1563722145d3acfb6b7b433 | 2e85d37d20e8d844e5ef01a3820cf06d4f9f40d6befbd8ecb0ed6a91f856e3e7 | afbdd8482d599aa49bec3b2ab4374e882d09d4ee8aa9a5ee783f115c8c2c1aa2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,262 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact have ⟨c, h⟩ := ihr.balance2 hl; .balanced h | case black.h_2
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.gt... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.black) (:fv _uniq.78967) (:fv _uniq.78972) (:fv _uniq.78970))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.balance2) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12479,"sourceStart":12474,"tag":"atom"},{"children":[{"source":"have","sourceEnd":12484,"sourceStart":12480,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12488,"sourceStart":12485,"tag":"atom"},{"children"... | [] | [{"source":"have ⟨c, h⟩ := ihr.balance2 hl; .balanced h","source_end":12527,"source_start":12480,"syntax_kind":"Lean.Parser.Term.have"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 84 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db69cc9358e581cd73a8df34a2daad531efee0b6b5ddf87244d504d573643449 | e8ca54c07b8741b8a3f93efe0cf0254376020349f92b604bbe68fbc50e8d145d | 5c66e9e596e48d15e95fd524c1b9f67d420a0fbdc4c4b2d9053a7422bfcef88b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,263 | Batteries.RBNode.Balanced.ins | .lake/packages/batteries/Batteries/Data/RBMap/WF.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact .balanced (.black hl hr) | case black.h_3
α : Type u_1
c : RBColor
n✝ : Nat
cmp : α → α → Ordering
v : α
t a : RBNode α
ca : RBColor
n : Nat
b : RBNode α
cb : RBColor
x : α
hl : a.Balanced ca n
hr : b.Balanced cb n
ihl : RedRed (a.isRed = red) (ins cmp v a) n
ihr : RedRed (b.isRed = red) (ins cmp v b) n
x✝ : Ordering
heq✝ : cmp v x = Ordering.eq... | ((:c Batteries.RBNode.RedRed) ((:c Eq) (:c Batteries.RBColor) ((:c Batteries.RBNode.isRed) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _uniq.69971) (:c Batteries.RBColor.black) (:fv _uniq.78967) (:fv _uniq.78972) (:fv _uniq.78970))) (:c Batteries.RBColor.red)) (:fv _uniq.69971) ((:c Batteries.RBNode.node) (:fv _... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"c","sexp":"(:c Batteries.RBColor)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"cmp","sexp":"(:forall _ (:fv _uniq.69971) (:forall _ (:fv _uniq.69971) (:c Ordering)))"},{"name":"v","sexp":"(:fv _uniq.69971)"},{"name":"t","sexp":"((:c Batteries.RBNode) (:fv _uniq.69971))"},... | (:app (:c Batteries.RBNode.RedRed) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Batteries.RBColor)) (:arg :explicit 1 (:app (:c Batteries.RBNode.isRed) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Batteries.RBNode.node) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:c Batteries.RBC... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"name":"c","sexp":"(:c Batteries.RBColor)"},{"binder_role":":impl... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":12540,"sourceStart":12535,"tag":"atom"},{"children":[{"children":[{"source":".","sourceEnd":12542,"sourceStart":12541,"tag":"atom"},{"source":"balanced","sourceEnd":12550,"sourceStart":12542,"tag":"identifier"}],"kind":"Lean.Parser.Term.d... | [] | [{"source":".balanced (.black hl hr)","source_end":12565,"source_start":12541,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69971","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.69972","is_instance":false,"is_let":false,"user_name":"c"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 46 | 89 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f604c4347ee44d3343352bb1fb967fe7b96a65169738c024646443c49b91cf4 | d8c9855de785978e22bc547e8742bea520d53b4b70ef3bd3ec47b703746e8f28 | 2fef2d5400c56e2bdac62c0e8e3f01da8415201bf4700efee6bca98b91cb6a63 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,264 | Filter.exists_eventually_atBot | Mathlib/Order/Filter/AtTopBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Filter.eventually_atBot</a>, ← <a>exists_swap</a> (α := α)] | ι : Type u_1
ι' : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
inst✝¹ : SemilatticeInf α
inst✝ : Nonempty α
r : α → β → Prop
⊢ (∃ b, ∀ᶠ (a : α) in atBot, r a b) ↔ ∀ᶠ (a₀ : α) in atBot, ∃ b, ∀ a ≤ a₀, r a b | ι : Type u_1
ι' : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
inst✝¹ : SemilatticeInf α
inst✝ : Nonempty α
r : α → β → Prop
⊢ (∃ x y, ∀ b ≤ x, r b y) ↔ ∃ a, ∀ b ≤ a, ∃ b_1, ∀ a ≤ b, r a b_1 | ((:c Iff) ((:c Exists) (:fv _uniq.38390) (:lambda b (:fv _uniq.38390) ((:c Filter.Eventually) (:fv _uniq.38387) (:lambda a (:fv _uniq.38387) ((:fv _uniq.39187) 0 1)) ((:c Filter.atBot) (:fv _uniq.38387) ((:c PartialOrder.toPreorder) (:fv _uniq.38387) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.38387) (:fv _uniq.3918... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c SemilatticeInf) (:fv _uniq.38387))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.3... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda b :explicit (:fv FV3) (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda a :explicit (:fv FV2) (:app (:fv FV8) (:arg :explicit 0 0) (:arg :explicit 1 1)))) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38381","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38384","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simp_rw","sourceEnd":17352,"sourceStart":17345,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17354,"sourceStart":17353,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.even... | [] | [{"source":"eventually_atBot","source_end":17370,"source_start":17354,"syntax_kind":"ident"},{"source":"exists_swap (α := α)","source_end":17398,"source_start":17376,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38381","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38384","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 123 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 64415d49347d081459f9cc01d32b786438a18304176915a9e9c03802cb682ca3 | 041c4e9fdf267691e2ba20739cd4d42afee49a22a749fb60f936b6d259c0ea7c | 5c913971439850912d40100d44a60e59f87a4443842dd1e623e24dbc5727040c | f31de27d2baa4f40bb4fb2a0a5fd911669e8c587dcd3244e56d78cb1a2767fbc |
cat-searcher/leandojo-benchmark-4-random | test | 1,265 | Filter.exists_eventually_atBot | Mathlib/Order/Filter/AtTopBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>exists_congr</a> fun a ↦ .symm <| <a>forall_le_iff</a> <| <a>Antitone.exists</a> fun _ _ _ hb H n hn ↦ H n (hn.trans hb) | ι : Type u_1
ι' : Type u_2
α : Type u_3
β : Type u_4
γ : Type u_5
inst✝¹ : SemilatticeInf α
inst✝ : Nonempty α
r : α → β → Prop
⊢ (∃ x y, ∀ b ≤ x, r b y) ↔ ∃ a, ∀ b ≤ a, ∃ b_1, ∀ a ≤ b, r a b_1 | ((:c Iff) ((:c Exists) (:fv _uniq.38387) (:lambda x (:fv _uniq.38387) ((:c Exists) (:fv _uniq.38390) (:lambda y (:fv _uniq.38390) (:forall b (:fv _uniq.38387) (:forall _ ((:c LE.le) (:fv _uniq.38387) ((:c Preorder.toLE) (:fv _uniq.38387) ((:c PartialOrder.toPreorder) (:fv _uniq.38387) ((:c SemilatticeInf.toPartialOrder... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"β","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c SemilatticeInf) (:fv _uniq.38387))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.3... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Exists) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:lambda x :explicit (:fv FV2) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:lambda y :explicit (:fv FV3) (:forall b :explicit (:fv FV2) (:forall _ :explicit (:app (:c LE.le) (:arg :implicit-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38381","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38384","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"exact","sourceEnd":17407,"sourceStart":17402,"tag":"atom"},{"children":[{"name":"exists_congr","semanticRole":"global","source":"exists_congr","sourceEnd":17420,"sourceStart":17408,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":17424,"sourceStart":17421,"tag":"atom"},{... | [] | [{"source":"exists_congr fun a ↦ .symm <| forall_le_iff <| Antitone.exists fun _ _ _ hb H n hn ↦\n H n (hn.trans hb)","source_end":17518,"source_start":17408,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38381","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38384","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 123 | 8 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52c469e50465b7e6b1b61edaf6ef3f627d9f1f5d3ce962ad235d523ff9e8e051 | f31de27d2baa4f40bb4fb2a0a5fd911669e8c587dcd3244e56d78cb1a2767fbc | 1932ac8bed7497e4e9df8ff2a00953def2504b1aa119f5d007af9b85e51076fe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,266 | Matroid.Base.inter_basis_iff_compl_inter_basis_dual | Mathlib/Data/Matroid/Dual.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨hB.compl_inter_basis_of_inter_basis, fun h ↦ ?_⟩ | α : Type u_1
M : Matroid α
I B X : Set α
hB : M.Base B
hX : autoParam (X ⊆ M.E) _auto✝
⊢ M.Basis (B ∩ X) X ↔ M✶.Basis (M.E \ B ∩ (M.E \ X)) (M.E \ X) | α : Type u_1
M : Matroid α
I B X : Set α
hB : M.Base B
hX : autoParam (X ⊆ M.E) _auto✝
h : M✶.Basis (M.E \ B ∩ (M.E \ X)) (M.E \ X)
⊢ M.Basis (B ∩ X) X | ((:c Iff) ((:c Matroid.Basis) (:fv _uniq.30377) (:fv _uniq.30380) ((:c Inter.inter) ((:c Set) (:fv _uniq.30377)) ((:c Set.instInter) (:fv _uniq.30377)) (:fv _uniq.30386) (:fv _uniq.30389)) (:fv _uniq.30389)) ((:c Matroid.Basis) (:fv _uniq.30377) ((:c Matroid.dual) (:fv _uniq.30377) (:fv _uniq.30380)) ((:c Inter.inter) ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"((:c Matroid) (:fv _uniq.30377))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"B","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"X","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"hB","sexp":"((:c Matroid.Base) (:fv _uniq.30377) (:fv _uniq.30... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Matroid.Basis) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30377","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30380","is_instance":false,"is_let":false,"name":"M","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0)... | {"children":[{"source":"refine","sourceEnd":9790,"sourceStart":9784,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9794,"sourceStart":9791,"tag":"atom"},{"children":[{"name":"Matroid.Base.compl_inter_basis_of_inter_basis","semanticRole":"global","source":"hB.compl_inter_basis_of_inter_basis","sourceEnd":9829,"sou... | [] | [{"source":"⟨hB.compl_inter_basis_of_inter_basis, fun h ↦ ?_⟩","source_end":9846,"source_start":9791,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30377","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30380","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f7053ab75323a65fd67eae4bbb28e853a988c68054c7eb5b553cc987f098fd3e | a5b2c3efd6392aa3f91623a8eeb5c96649eefd2961e578397d80c133205f64f0 | 519689a682a9a0240d7f41e6cafa00f9754cf99e3f2cb1252b6dc6bb5440a538 | 861792b08718c0d83f2e159f79439cd8842b1447bb9b99f1eac9e15defeca91a |
cat-searcher/leandojo-benchmark-4-random | test | 1,267 | Matroid.Base.inter_basis_iff_compl_inter_basis_dual | Mathlib/Data/Matroid/Dual.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Set.inter_eq_self_of_subset_right</a> hX, <a>Set.inter_eq_self_of_subset_right</a> hB.subset_ground] using hB.compl_base_dual.compl_inter_basis_of_inter_basis h | α : Type u_1
M : Matroid α
I B X : Set α
hB : M.Base B
hX : autoParam (X ⊆ M.E) _auto✝
h : M✶.Basis (M.E \ B ∩ (M.E \ X)) (M.E \ X)
⊢ M.Basis (B ∩ X) X | ((:c Matroid.Basis) (:fv _uniq.30377) (:fv _uniq.30380) ((:c Inter.inter) ((:c Set) (:fv _uniq.30377)) ((:c Set.instInter) (:fv _uniq.30377)) (:fv _uniq.30386) (:fv _uniq.30389)) (:fv _uniq.30389)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"M","sexp":"((:c Matroid) (:fv _uniq.30377))"},{"name":"I","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"B","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"X","sexp":"((:c Set) (:fv _uniq.30377))"},{"name":"hB","sexp":"((:c Matroid.Base) (:fv _uniq.30377) (:fv _uniq.30... | (:app (:c Matroid.Basis) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c Inter) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30377","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30380","is_instance":false,"is_let":false,"name":"M","sexp":"(:app (:c Matroid) (:arg :explicit 0 (:fv FV0)... | {"children":[{"source":"simpa","sourceEnd":9854,"sourceStart":9849,"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":"inter_eq_self_of_subset_right hX","source_end":9888,"source_start":9856,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inter_eq_self_of_subset_right hB.subset_ground","source_end":9936,"source_start":9890,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hB.compl_base_dual.compl_inter_basis_of_inter_basis ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30377","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30380","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 26 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2375cf5c8e6f0ab2eb63fcb485240f2fedbfb27f8e332d7f848bfe1e94fe1701 | 861792b08718c0d83f2e159f79439cd8842b1447bb9b99f1eac9e15defeca91a | a85633e00c60cc2f26abef978753bccb2374ab4c451fbb00cc871289e9f1ce5b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,268 | Rat.not_countably_generated_nhds_infty_opc | Mathlib/Topology/Instances/RatLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro | p q : ℚ
s t : Set ℚ
⊢ ¬(𝓝 ∞).IsCountablyGenerated | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
⊢ False | ((:c Not) ((:c Filter.IsCountablyGenerated) ((:c OnePoint) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c UniformSpace.toTopologicalSpace) (:c Rat) ((:c PseudoMetricSpace.toUniformSpace) (:c Rat) ((:c MetricSpace.toPseudoMetricSpace) (:c Rat) (:c Rat.instMetricSpace)))))... | [{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"s","sexp":"((:c Set) (:c Rat))"},{"name":"t","sexp":"((:c Set) (:c Rat))"}] | (:app (:c Not) (:arg :explicit 0 (:app (:c Filter.IsCountablyGenerated) (:arg :implicit-type 0 (:app (:c OnePoint) (:arg :explicit 0 (:c Rat)))) (:arg :explicit 1 (:app (:c nhds) (:arg :implicit-type 0 (:app (:c OnePoint) (:arg :explicit 0 (:c Rat)))) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"intro","sourceEnd":2509,"sourceStart":2504,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"intro","sourceEnd":2509,"sourceStart":2504,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9a369293e1b7de3effc38a85b78ab0f64ae863cf4e9b338f069a72828e682ff | 63c547f3d51a6654ee2c1911305f1860b74f1e4a351c0b8cab6b8d28d7ca5cb5 | c432b372e0e30267e65e26a12a42c7957ab52e25dfe3c6d4b929213d88965e45 | 99f3af8c829ccdf70cb9d1d7f6c6c4a41868bf909c2387d968faea20b1166bbb |
cat-searcher/leandojo-benchmark-4-random | test | 1,269 | Rat.not_countably_generated_nhds_infty_opc | Mathlib/Topology/Instances/RatLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Filter.IsCountablyGenerated</a> (<a>Filter.comap</a> (<a>OnePoint.some</a> : ℚ → ℚ∞) (𝓝 ∞)) := by infer_instance | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
⊢ False | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
this : (comap OnePoint.some (𝓝 ∞)).IsCountablyGenerated
⊢ False | (:c False) | [{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"s","sexp":"((:c Set) (:c Rat))"},{"name":"t","sexp":"((:c Set) (:c Rat))"},{"name":"a✝","sexp":"((:c Filter.IsCountablyGenerated) ((:c OnePoint) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c Uniform... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"have","sourceEnd":2516,"sourceStart":2512,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":2517,"sourceStart":2517,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":2517,"sourceStart":2517,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"IsCountablyGenerated (comap (OnePoint.some : ℚ → ℚ∞) (𝓝 ∞))","source_end":2591,"source_start":2519,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 5 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1342c17c2b6a78c49852b263f100bf2c5e3e84a940d043dedc65a3c8f29ab2cf | 99f3af8c829ccdf70cb9d1d7f6c6c4a41868bf909c2387d968faea20b1166bbb | 016e5ee3c58ed5beafdabb3c4d104ee3c4788747ace47ed47dfd5db19fc15e04 | bd4deb78283f6bc8cb38f48bd6e87b9be3541dd9df5eb55d37bd76e3f03937af |
cat-searcher/leandojo-benchmark-4-random | test | 1,270 | Rat.not_countably_generated_nhds_infty_opc | Mathlib/Topology/Instances/RatLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>OnePoint.comap_coe_nhds_infty</a>, <a>Filter.coclosedCompact_eq_cocompact</a>] at this | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
this : (comap OnePoint.some (𝓝 ∞)).IsCountablyGenerated
⊢ False | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
this : (cocompact ℚ).IsCountablyGenerated
⊢ False | (:c False) | [{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"s","sexp":"((:c Set) (:c Rat))"},{"name":"t","sexp":"((:c Set) (:c Rat))"},{"name":"a✝","sexp":"((:c Filter.IsCountablyGenerated) ((:c OnePoint) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c Uniform... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"rw","sourceEnd":2617,"sourceStart":2615,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2619,"sourceStart":2618,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"OnePoint.comap_coe_n... | [] | [{"source":"OnePoint.comap_coe_nhds_infty","source_end":2648,"source_start":2619,"syntax_kind":"ident"},{"source":"this","source_end":2687,"source_start":2683,"syntax_kind":"ident"},{"source":"coclosedCompact_eq_cocompact","source_end":2678,"source_start":2650,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 8 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | acf1124b55665ecf4a80ee9f090be04028f06ea5ba6d8df0c046003079fa71ae | bd4deb78283f6bc8cb38f48bd6e87b9be3541dd9df5eb55d37bd76e3f03937af | 759dbd982a898bdeab03c2947477e05687d4dc0aeec67bec98fa1e23c6b88ced | 3a0292ecb635fbe99540176561c63aeab06521e7000ee48a9ecb20752b74e9b1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,271 | Rat.not_countably_generated_nhds_infty_opc | Mathlib/Topology/Instances/RatLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Rat.not_countably_generated_cocompact</a> this | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
this : (cocompact ℚ).IsCountablyGenerated
⊢ False | (:c False) | [{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"s","sexp":"((:c Set) (:c Rat))"},{"name":"t","sexp":"((:c Set) (:c Rat))"},{"name":"a✝","sexp":"((:c Filter.IsCountablyGenerated) ((:c OnePoint) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c Uniform... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"exact","sourceEnd":2695,"sourceStart":2690,"tag":"atom"},{"children":[{"name":"Rat.not_countably_generated_cocompact","semanticRole":"global","source":"not_countably_generated_cocompact","sourceEnd":2729,"sourceStart":2696,"tag":"identifier"},{"children":[{"contextIndex":6,"semanticRole":"local"... | [] | [{"source":"not_countably_generated_cocompact this","source_end":2734,"source_start":2696,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 12 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e8e02f6a5e9358aada54583e6fb1f15864d56163af7177d51fb36a7f70ebd3c | 3a0292ecb635fbe99540176561c63aeab06521e7000ee48a9ecb20752b74e9b1 | 1111974b3312a54ca9ac552a1a260694581c09a7801670ec65229af38a2065e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,272 | Rat.not_countably_generated_nhds_infty_opc | Mathlib/Topology/Instances/RatLemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | infer_instance | p q : ℚ
s t : Set ℚ
a✝ : (𝓝 ∞).IsCountablyGenerated
⊢ (comap OnePoint.some (𝓝 ∞)).IsCountablyGenerated | ((:c Filter.IsCountablyGenerated) (:c Rat) ((:c Filter.comap) (:c Rat) ((:c OnePoint) (:c Rat)) ((:c OnePoint.some) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c UniformSpace.toTopologicalSpace) (:c Rat) ((:c PseudoMetricSpace.toUniformSpace) (:c Rat) ((:c MetricSpace.t... | [{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"s","sexp":"((:c Set) (:c Rat))"},{"name":"t","sexp":"((:c Set) (:c Rat))"},{"name":"a✝","sexp":"((:c Filter.IsCountablyGenerated) ((:c OnePoint) (:c Rat)) ((:c nhds) ((:c OnePoint) (:c Rat)) ((:c OnePoint.instTopologicalSpace) (:c Rat) ((:c Uniform... | (:app (:c Filter.IsCountablyGenerated) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c Filter.comap) (:arg :implicit-type 0 (:c Rat)) (:arg :implicit-type 1 (:app (:c OnePoint) (:arg :explicit 0 (:c Rat)))) (:arg :explicit 2 (:app (:c OnePoint.some) (:arg :implicit-type 0 (:c Rat)))) (:arg :explicit 3 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"name":"q","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index... | {"children":[{"source":"infer_instance","sourceEnd":2612,"sourceStart":2598,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticInfer_instance","source":"infer_instance","sourceEnd":2612,"sourceStart":2598,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3108","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3110","is_instance":false,"is_let":false,"user_name":"q"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 7 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e40730c9f291ae39dbd0e67c26026e5d355558a6ec76a94e9de3d1f0b5582437 | 1a64b5b5443a0d3ffd2cc78b263918973b1a6c4c329971ec50b868267449e549 | 1be023dbb859162463cfcba2e9fc80f1c85bab9d31edeb816d1518206e2b70fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,273 | List.takeWhile_cons_of_neg | Mathlib/Data/List/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>List.takeWhile_cons</a>, h] | ι : Type u_1
α : Type u
β : Type v
γ : Type w
l₁ l₂ : List α
p : α → Bool
l : List α
x : α
h : ¬p x = true
⊢ takeWhile p (x :: l) = [] | ((:c Eq) ((:c List) (:fv _uniq.221536)) ((:c List.takeWhile) (:fv _uniq.221536) (:fv _uniq.221550) ((:c List.cons) (:fv _uniq.221536) (:fv _uniq.221678) (:fv _uniq.221553))) ((:c List.nil) (:fv _uniq.221536))) | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"l₁","sexp":"((:c List) (:fv _uniq.221536))"},{"name":"l₂","sexp":"((:c List) (:fv _uniq.221536))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.221536) (:c Boo... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c List.takeWhile) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:app (:c List.cons) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV9)) (:arg :explicit 2 (:fv FV7)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221534","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221536","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":116649,"sourceStart":116645,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sour... | [] | [{"source":"takeWhile_cons","source_end":116665,"source_start":116651,"syntax_kind":"ident"},{"source":"h","source_end":116668,"source_start":116667,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.221534","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.221536","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,040 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f9245a515c0c54d0207b673d628de4d0c19984bbbfbd355f16d6e64ca423c99 | ac0cdcd8ad6b7823ec9e708c0a83bf7f41308452c3d4410b1219c10d16f9285d | 06c708dec5546a92109a632ccc5e8de6a6d9e60b3dc70b7975c5378ef781c871 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,278 | Con.sup_def | Mathlib/GroupTheory/Congruence/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Con.sup_eq_conGen</a>] | M : Type u_1
N : Type u_2
P : Type u_3
inst✝² : Mul M
inst✝¹ : Mul N
inst✝ : Mul P
c✝ c d : Con M
⊢ c ⊔ d = conGen (⇑c ⊔ ⇑d) | M : Type u_1
N : Type u_2
P : Type u_3
inst✝² : Mul M
inst✝¹ : Mul N
inst✝ : Mul P
c✝ c d : Con M
⊢ (conGen fun x y => c x y ∨ d x y) = conGen (⇑c ⊔ ⇑d) | ((:c Eq) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) ((:c Sup.sup) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) ((:c SemilatticeSup.toSup) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) ((:c Lattice.toSemilatticeSup) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) ((:c CompleteLattice.toLattice) ((:c Con) (:fv _uni... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Mul) (:fv _uniq.24883))"},{"name":"inst✝¹","sexp":"((:c Mul) (:fv _uniq.24886))"},{"name":"inst✝","sexp":"((:c Mul) (:fv _uniq.24889))"},{"name":"c✝","sexp":"((:c Con) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Con) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c Sup.sup) (:arg :implicit-type 0 (:app (:c Con) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24883","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24886","is_instance":false,"is_let":false,"name":"N","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":26705,"sourceStart":26703,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":26707,"sourceStart":26706,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Con.sup_eq_conGe... | [] | [{"source":"sup_eq_conGen","source_end":26720,"source_start":26707,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24883","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24886","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 157 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68ebd82cd1f84018fd0aced88bb6d226e07792790a1142c483470c0c82ea2130 | 258c2cf89aa57fcc72f8187f6a766a4619b048e8bf435ad8bcef2b689e361d09 | 928c9b325cf2086b6428697168611545a46cce282ebfcb4470748d4f336d5763 | cb35231c37144ace9b24e71e27166ff4b0cb2f7b95e0e42898c7ad831130ba6f |
cat-searcher/leandojo-benchmark-4-random | test | 1,279 | Con.sup_def | Mathlib/GroupTheory/Congruence/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | M : Type u_1
N : Type u_2
P : Type u_3
inst✝² : Mul M
inst✝¹ : Mul N
inst✝ : Mul P
c✝ c d : Con M
⊢ (conGen fun x y => c x y ∨ d x y) = conGen (⇑c ⊔ ⇑d) | ((:c Eq) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) ((:c conGen) (:fv _uniq.24883) (:fv _uniq.24892) (:lambda x (:fv _uniq.24883) (:lambda y (:fv _uniq.24883) ((:c Or) ((:c DFunLike.coe) ((:c Con) (:fv _uniq.24883) (:fv _uniq.24892)) (:fv _uniq.24883) (:lambda _ (:fv _uniq.24883) (:forall _ (:fv _uniq.24883) (:sort... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"N","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Mul) (:fv _uniq.24883))"},{"name":"inst✝¹","sexp":"((:c Mul) (:fv _uniq.24886))"},{"name":"inst✝","sexp":"((:c Mul) (:fv _uniq.24889))"},{"name":"c✝","sexp":"((:c Con) (... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Con) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c conGen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Mul) (:arg :explicit 0 (:fv FV0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24883","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24886","is_instance":false,"is_let":false,"name":"N","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":26726,"sourceStart":26723,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":26726,"sourceStart":26723,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.24883","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.24886","is_instance":false,"is_let":false,"user_name":"N"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 157 | 8 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 82632b6a64626d68abf3a43ce74929f0debdde13e1e1ec3831d6352e7c857916 | cb35231c37144ace9b24e71e27166ff4b0cb2f7b95e0e42898c7ad831130ba6f | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,280 | Part.some_ne_none | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro h | α : Type u_1
β : Type u_2
γ : Type u_3
x : α
⊢ some x ≠ none | α : Type u_1
β : Type u_2
γ : Type u_3
x : α
h : some x = none
⊢ False | ((:c Ne) ((:c Part) (:fv _uniq.5003)) ((:c Part.some) (:fv _uniq.5003) (:fv _uniq.5022)) ((:c Part.none) (:fv _uniq.5003))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"x","sexp":"(:fv _uniq.5003)"}] | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Part.some) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)))) (:arg :explicit 2 (:app (:c Part.none) (:arg :implicit-type 0 (:fv FV0))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5003","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5006","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"intro","sourceEnd":7474,"sourceStart":7469,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":7476,"sourceStart":7475,"tag":"identifier"}],"kind":"null","source":"h","sourceEnd":7476,"sourceStart":7475,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"int... | [{"role":"fresh_name","source":"h","source_end":7476,"source_start":7475,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5003","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5006","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 62 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c95123069db5a6eb28427b095dea8bbfb0b93ef2912cd8dded6c21688437733 | fc4a3a0d5a21c88e3044297314ffbb378b5bab529f4a8f6dc0617253062709f8 | 5cf42e5c5e9faf9804f4b8005e32168f3a46b38347377087a457c72b727740cb | 28d8dd9247553d81c46a84aa246f1e010bb356e05848421788662adeab256371 |
cat-searcher/leandojo-benchmark-4-random | test | 1,281 | Part.some_ne_none | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>true_ne_false</a> (<a>congr_arg</a> <a>Part.Dom</a> h) | α : Type u_1
β : Type u_2
γ : Type u_3
x : α
h : some x = none
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"x","sexp":"(:fv _uniq.5003)"},{"name":"h","sexp":"((:c Eq) ((:c Part) (:fv _uniq.5003)) ((:c Part.some) (:fv _uniq.5003) (:fv _uniq.5022)) ((:c Part.none) (:fv _uniq.5003)))"}] | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5003","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5006","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":7484,"sourceStart":7479,"tag":"atom"},{"children":[{"name":"true_ne_false","semanticRole":"global","source":"true_ne_false","sourceEnd":7498,"sourceStart":7485,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":7500,"sourceStart":7499,"tag":"atom"},{"child... | [] | [{"source":"true_ne_false (congr_arg Dom h)","source_end":7516,"source_start":7485,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.5003","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.5006","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 62 | 5 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 89f0643955fc28f5e325f39851840bdb2e419296779cd806c921c5eabfdf2688 | 28d8dd9247553d81c46a84aa246f1e010bb356e05848421788662adeab256371 | 0640cb870846c0eaf627f68cfc6c49bbc1fac4bd560813e6a6bb3d4b1a3c0a92 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,282 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>, well_def f ha, well_def f hb] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a✝ b✝ a'✝ b'✝ : PreEnvelGroup R
ha : PreEnvelGroupRel' R a✝ a'✝
hb : PreEnvelGroupRel' R b✝ b'✝
⊢ mapAux f (a✝.mul b✝) = mapAux f (a'✝.mul b'✝) | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) (:fv _uniq.42975) (:fv _uniq.42976))) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26592,"sourceStart":26588,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":26613,"source_start":26594,"syntax_kind":"ident"},{"source":"well_def f ha","source_end":26628,"source_start":26615,"syntax_kind":"Lean.Parser.Term.app"},{"source":"well_def f hb","source_end":26643,"source_start":26630,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4fc5763d306c8234768d84e9a68d132dfa0b8d78549d2fcfe279242216fa3a61 | b292ceea4102fbb9521394503ee838488e0d350838fafc1fa80495c4d27426e8 | a6c80e72387cd2d9eed396fe70986aab1f916984297e97019caccf8cfd5dfc3b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,283 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>, well_def f ha] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a✝ a'✝ : PreEnvelGroup R
ha : PreEnvelGroupRel' R a✝ a'✝
⊢ mapAux f a✝.inv = mapAux f a'✝.inv | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.inv) (:fv _uniq.42700) (:fv _uniq.43027))) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26678,"sourceStart":26674,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":26699,"source_start":26680,"syntax_kind":"ident"},{"source":"well_def f ha","source_end":26714,"source_start":26701,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 7 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c4cd5f70f59daf486eb96a966c01fd4e4449f50968d5980ad8244e4a2ffb45b | 83101da49e746aa6e1dd5d42ea3c4240432bdc2d92fb19584bc1da013e735f02 | c466783b0f1e4edac17643887e8e814a8c25af8f3f71f1c305fcb42594cacd81 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,284 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>mul_assoc</a> | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a b c : PreEnvelGroup R
⊢ mapAux f ((a.mul b).mul c) = mapAux f (a.mul (b.mul c)) | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) (:fv _uniq.43073) (:fv _uniq.43074)) (:fv _uniq.43075))) ((:c Rack.toEnvelGrou... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"apply","sourceEnd":26749,"sourceStart":26744,"tag":"atom"},{"name":"mul_assoc","semanticRole":"global","source":"mul_assoc","sourceEnd":26759,"sourceStart":26750,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply mul_assoc","sourceEnd":2... | [] | [{"source":"mul_assoc","source_end":26759,"source_start":26750,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 12 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 61f2c4a90394e8afcff417c3b9ec5790c35b3e50c8bcdb8687b1687ab84abf30 | 8708a77afd3f7d06b910da0b1bb864974ead1562ac539842029249e5590500cf | 8f45dc59f3274f8640e6d1ca124dcc483c4c483cb8e11c36316f0b53fcdd0e55 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,285 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a : PreEnvelGroup R
⊢ mapAux f (unit.mul a) = mapAux f a | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) ((:c Rack.PreEnvelGroup.unit) (:fv _uniq.42700)) (:fv _uniq.43109))) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26808,"sourceStart":26804,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":26829,"source_start":26810,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 17 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b061d3985402ae61688031c01c8a4efe16025d29a50d1ed61f039e5b1b4187fe | 3f04d11822136bde3883608bd1d202db44f52802ad7d6b66431703aa11cc0f1d | 39d2bf395dcf0d5832e11dac3be0470223b7bac5dd72b4aff1b400614bba1920 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,286 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a : PreEnvelGroup R
⊢ mapAux f (a.mul unit) = mapAux f a | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) (:fv _uniq.43143) ((:c Rack.PreEnvelGroup.unit) (:fv _uniq.42700)))) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _u... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26879,"sourceStart":26875,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":26900,"source_start":26881,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 22 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ba286d01b23eee21a67a03aec433644a0f53e70151fe6477466756db185c2e8 | d9ce0139ff8924ac2cde72702570786967163abf8273623a7d286f442b134340 | 39d2bf395dcf0d5832e11dac3be0470223b7bac5dd72b4aff1b400614bba1920 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,287 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
a : PreEnvelGroup R
⊢ mapAux f (a.inv.mul a) = mapAux f unit | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) ((:c Rack.PreEnvelGroup.inv) (:fv _uniq.42700) (:fv _uniq.43177)) (:fv _uniq.43177))) ((:c Rack.toEnvelGroup.mapAux) (:fv _un... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":26955,"sourceStart":26951,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":26976,"source_start":26957,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 27 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aca1e420d5fa678853d970c5ea395d3cee0849337003aa024516d44cd91fbac1 | 9c715ea2586f0547360c2d5a2bfe38339e06130af75b3bbf3b3f9fd1efc20380 | 39d2bf395dcf0d5832e11dac3be0470223b7bac5dd72b4aff1b400614bba1920 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,288 | Rack.toEnvelGroup.mapAux.well_def | Mathlib/Algebra/Quandle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Rack.toEnvelGroup.mapAux</a>] | R : Type u_1
inst✝¹ : Rack R
G : Type u_2
inst✝ : Group G
f : R →◃ Quandle.Conj G
x y : R
⊢ mapAux f (((incl x).mul (incl y)).mul (incl x).inv) = mapAux f (incl (x ◃ y)) | ((:c Eq) (:fv _uniq.42702) ((:c Rack.toEnvelGroup.mapAux) (:fv _uniq.42700) (:fv _uniq.42701) (:fv _uniq.42702) (:fv _uniq.42703) (:fv _uniq.42704) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) ((:c Rack.PreEnvelGroup.mul) (:fv _uniq.42700) ((:c Rack.PreEnvelGroup.incl) (:fv _uniq.42700) (:fv _uniq.43215)) ((:c Rack.P... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Rack) (:fv _uniq.42700))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.42702))"},{"name":"f","sexp":"((:c ShelfHom) (:fv _uniq.42700) ((:c Quandle.Conj) (:fv _uniq.42702)) ((:c Rack.toShelf) (:fv _uniq.4270... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Rack.toEnvelGroup.mapAux) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Rack) (:arg :explicit 0 (:fv FV1))))) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c Group) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Rack) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":27011,"sourceStart":27007,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"toEnvelGroup.mapAux","source_end":27032,"source_start":27013,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.42700","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.42701","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":implicit","context_index":3,"intern... | 164 | 32 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf9de7483b0decfaea0d1e6b9134272179a52bcd51622399d388515795979e6c | 30198c0a5eac02718df4f4446ce6fdf39173e91e42618dd586bf9b18e947a41a | 39d2bf395dcf0d5832e11dac3be0470223b7bac5dd72b4aff1b400614bba1920 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,289 | Set.left_mem_Ioc | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>lt_irrefl</a>] | α : Type u_1
β : Type u_2
inst✝ : Preorder α
a a₁ a₂ b b₁ b₂ c x : α
⊢ a ∈ Ioc a b ↔ False | ((:c Iff) ((:c Membership.mem) (:fv _uniq.3847) ((:c Set) (:fv _uniq.3847)) ((:c Set.instMembership) (:fv _uniq.3847)) (:fv _uniq.3855) ((:c Set.Ioc) (:fv _uniq.3847) (:fv _uniq.3853) (:fv _uniq.3855) (:fv _uniq.3861))) (:c False)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.3847))"},{"name":"a","sexp":"(:fv _uniq.3847)"},{"name":"a₁","sexp":"(:fv _uniq.3847)"},{"name":"a₂","sexp":"(:fv _uniq.3847)"},{"name":"b","sexp":"(:fv _uniq.3847)"},{"name":"b₁","sexp":"(... | (:app (:c Iff) (: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) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3847","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3850","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implici... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":5510,"sourceStart":5506,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"lt_irrefl","source_end":5521,"source_start":5512,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.3847","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.3850","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 78 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f8b5d2c38da357561cc9b50788c5d304ed9d44c9e162964ecaff0b796ba946a | 61a39f6f94a3f1fa81b94478825a653aaed2b522a1cbbbeae786b6a3d0e47a5c | 5ec2a7f0e0a624ac7a70284dcdc158051fac28c9794783da5c0c8dde04f78828 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,290 | Finset.affineCombination_vsub | Mathlib/LinearAlgebra/AffineSpace/Combination.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>AffineMap.linearMap_vsub</a>, <a>Finset.affineCombination_linear</a>, <a>vsub_eq_sub</a>] | k : Type u_1
V : Type u_2
P : Type u_3
inst✝² : Ring k
inst✝¹ : AddCommGroup V
inst✝ : Module k V
S : AffineSpace V P
ι : Type u_4
s : Finset ι
ι₂ : Type u_5
s₂ : Finset ι₂
w₁ w₂ : ι → k
p : ι → P
⊢ (affineCombination k s p) w₁ -ᵥ (affineCombination k s p) w₂ = (s.weightedVSub p) (w₁ - w₂) | ((:c Eq) (:fv _uniq.214032) ((:c VSub.vsub) (:fv _uniq.214032) (:fv _uniq.214035) ((:c AddTorsor.toVSub) (:fv _uniq.214032) (:fv _uniq.214035) ((:c AddCommGroup.toAddGroup) (:fv _uniq.214032) (:fv _uniq.214041)) (:fv _uniq.214717)) ((:c DFunLike.coe) ((:c AffineMap) (:fv _uniq.214029) (:forall _ (:fv _uniq.214720) (:fv... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Ring) (:fv _uniq.214029))"},{"name":"inst✝¹","sexp":"((:c AddCommGroup) (:fv _uniq.214032))"},{"name":"inst✝","sexp":"((:c Module) (:fv _uniq.214029) (:fv _uniq.214032) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c VSub.vsub) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c VSub) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2))))) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.214029","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.214032","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":22791,"sourceStart":22789,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22793,"sourceStart":22792,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"AffineMap.linearMap_vsub","source_end":22821,"source_start":22797,"syntax_kind":"ident"},{"source":"affineCombination_linear","source_end":22847,"source_start":22823,"syntax_kind":"ident"},{"source":"vsub_eq_sub","source_end":22860,"source_start":22849,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.214029","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.214032","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 98 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 035d941d0ee8470a9a00a4be01bf46c74f62f9682e1dc862a3aa8b4b45d35b5e | c23d85fc8c851cf996bd0a0654354a40d345fafb5f99bde40e525923bf948143 | 8868083f57a7cf22f97a719d750db0f535765a8b1deef0c48c3132fa1141f503 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,291 | Matrix.isUnit_det_transpose | Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Matrix.det_transpose</a>] | l : Type u_1
m : Type u
n : Type u'
α : Type v
inst✝² : Fintype n
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A B : Matrix n n α
h : IsUnit A.det
⊢ IsUnit Aᵀ.det | l : Type u_1
m : Type u
n : Type u'
α : Type v
inst✝² : Fintype n
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A B : Matrix n n α
h : IsUnit A.det
⊢ IsUnit A.det | ((:c IsUnit) (:fv _uniq.53307) ((:c MonoidWithZero.toMonoid) (:fv _uniq.53307) ((:c Semiring.toMonoidWithZero) (:fv _uniq.53307) ((:c CommSemiring.toSemiring) (:fv _uniq.53307) ((:c CommRing.toCommSemiring) (:fv _uniq.53307) (:fv _uniq.53322))))) ((:c Matrix.det) (:fv _uniq.53305) (:fv _uniq.53317) (:fv _uniq.53310) (:... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u 1))"},{"name":"n","sexp":"(:sort (+ u' 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.53305))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.53305))"},{"name":"inst✝","sexp":"((:c CommRing) (... | (:app (:c IsUnit) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 2 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.53301","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53303","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":8453,"sourceStart":8451,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8455,"sourceStart":8454,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Matrix.det_transpose... | [] | [{"source":"det_transpose","source_end":8468,"source_start":8455,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.53301","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53303","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 59 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a60e5e64ec651ccd95953e368dc97d9d72f94ff90356dc025daf6a8b93ac7165 | 30c208e955929a2f57a4f86a58f82438850710019d968eae0bfd1296afccdffe | b7410964710b3b45a23814b43414112154816f8e41ef8be4c545925c9b067168 | c9ca7ffc33637f595682ebbc0e61b361b5e651c75bd0b249a2be2a1d32621a72 |
cat-searcher/leandojo-benchmark-4-random | test | 1,292 | Matrix.isUnit_det_transpose | Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h | l : Type u_1
m : Type u
n : Type u'
α : Type v
inst✝² : Fintype n
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A B : Matrix n n α
h : IsUnit A.det
⊢ IsUnit A.det | ((:c IsUnit) (:fv _uniq.53307) ((:c MonoidWithZero.toMonoid) (:fv _uniq.53307) ((:c Semiring.toMonoidWithZero) (:fv _uniq.53307) ((:c CommSemiring.toSemiring) (:fv _uniq.53307) ((:c CommRing.toCommSemiring) (:fv _uniq.53307) (:fv _uniq.53322))))) ((:c Matrix.det) (:fv _uniq.53305) (:fv _uniq.53317) (:fv _uniq.53310) (:... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u 1))"},{"name":"n","sexp":"(:sort (+ u' 1))"},{"name":"α","sexp":"(:sort (+ v 1))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.53305))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.53305))"},{"name":"inst✝","sexp":"((:c CommRing) (... | (:app (:c IsUnit) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c Matrix.det) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 2 (:insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.53301","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53303","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":8477,"sourceStart":8472,"tag":"atom"},{"contextIndex":10,"semanticRole":"local","source":"h","sourceEnd":8479,"sourceStart":8478,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact h","sourceEnd":8479,"sourceStart":8472,"tag":"node"} | [] | [{"source":"h","source_end":8479,"source_start":8478,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.53301","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.53303","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 59 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07eaa84c50f3f509fddc187a21043058e01da9a1b2544d8fb31e673351604909 | c9ca7ffc33637f595682ebbc0e61b361b5e651c75bd0b249a2be2a1d32621a72 | c2ce0e21ffddde69d6a80e187a5bf12b7761df4be076519945be8ed7a7a77294 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,293 | Submodule.ker_inclusion | Mathlib/Algebra/Module/Submodule/Ker.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Submodule.inclusion</a>, <a>LinearMap.ker_codRestrict</a>, <a>Submodule.ker_subtype</a>] | R : Type u_1
R₁ : Type u_2
R₂ : Type u_3
R₃ : Type u_4
K : Type u_5
M : Type u_6
M₁ : Type u_7
M₂ : Type u_8
M₃ : Type u_9
V : Type u_10
V₂ : Type u_11
inst✝⁷ : Semiring R
inst✝⁶ : Semiring R₂
inst✝⁵ : AddCommMonoid M
inst✝⁴ : AddCommMonoid M₂
inst✝³ : Module R M
inst✝² : Module R₂ M₂
p✝ p'✝ : Submodule R M
q : Submodu... | ((:c Eq) ((:c Submodule) (:fv _uniq.172888) ((:c Subtype) (:fv _uniq.172903) (:lambda x (:fv _uniq.172903) ((:c Membership.mem) (:fv _uniq.172903) ((:c Submodule) (:fv _uniq.172888) (:fv _uniq.172903) (:fv _uniq.172921) (:fv _uniq.172927) (:fv _uniq.172954)) ((:c SetLike.instMembership) ((:c Submodule) (:fv _uniq.17288... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₁","sexp":"(:sort (+ u_2 1))"},{"name":"R₂","sexp":"(:sort (+ u_3 1))"},{"name":"R₃","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₁","sexp":"(:sort (+ u_7 1))"},{"name":"M₂","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV5)) (:arg :explicit 1 (:lambda x :explicit (:fv FV5) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV5)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172888","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.172891","is_instance":false,"is_let":false,"name":"R₁","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10585,"sourceStart":10583,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10587,"sourceStart":10586,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"inclusion","source_end":10596,"source_start":10587,"syntax_kind":"ident"},{"source":"ker_codRestrict","source_end":10613,"source_start":10598,"syntax_kind":"ident"},{"source":"ker_subtype","source_end":10626,"source_start":10615,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.172888","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.172891","is_instance":false,"is_let":false,"user_name":"R₁"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 108 | 2 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6c2e1efb6a1bb72428aaf085d3b1d0ce741241b51f0e9bec901780004ac897e8 | 035fb0c07d20d76d28216ae468934803044b80a7c9e8789813e6a1a21f3b8533 | 0c8291e200be004eaa620c1e68819c65abe802085d962082aa5ce0b3615777f4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,294 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | generalize ef : @<a>TypeVec.splitFun</a> n _ (<a>TypeVec.append1</a> α (<a>MvPFunctor.M</a> P α)) f' f₁' = ff at e₁ | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', splitFun f' f₁'⟩
⊢ ∃ g₁',
∃ (e₁' : PFunctor.M.dest a₁ = ⟨a', g₁'⟩),
f' = pathDestLeft P e₁' f₁ ∧ f₁' = fun x => ⟨g₁' x, pathDestRight P e₁' ... | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
⊢ ∃ g₁',
∃ (e₁' : PFunctor.M.dest a₁ = ⟨a', g₁'⟩),
f' = pathDestLeft P e₁' f₁ ∧ f₁' ... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"generalize","sourceEnd":9224,"sourceStart":9214,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ef","sourceEnd":9227,"sourceStart":9225,"tag":"identifier"},{"source":":","sourceEnd":9229,"sourceStart":9228,"tag":"atom"}],"kind":"null","source":"ef :"... | [] | [{"source":"@splitFun n _ (append1 α (M P α)) f' f₁'","source_end":9274,"source_start":9230,"syntax_kind":"Lean.Parser.Term.app"},{"source":"e₁","source_end":9287,"source_start":9283,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3f13a6e2a736d36b0eed6a9fa318449f23b6440654e5ae6e809e07aede9f654 | 0be7aba34460fa269a3f8a44fd8f10692a103ad90f3b3951b4974607907dbe4e | 037173cfe443db7740066cc4dc2839b6c02bc0bc79660f405f363969bd85e7f4 | 83473f49a68782c1c7e50bb2909914f4174ce213f31db4f9da0b00c6694e3da9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,295 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let he₁' := <a>PFunctor.M.dest</a> a₁ | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
⊢ ∃ g₁',
∃ (e₁' : PFunctor.M.dest a₁ = ⟨a', g₁'⟩),
f' = pathDestLeft P e₁' f₁ ∧ f₁' ... | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
⊢ ∃ g₁',
∃ (e₁' : PFunctor.M.dest a₁ = ⟨a', ... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"let","sourceEnd":9293,"sourceStart":9290,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"he₁'","sourceEnd":9300,"sourceStart":9294,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"... | [] | [{"source":"PFunctor.M.dest a₁","source_end":9324,"source_start":9304,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19463918e630aa11f97c1590640cc28b5ff2963ae3bc2e3ce6c87cd1f533c86a | 83473f49a68782c1c7e50bb2909914f4174ce213f31db4f9da0b00c6694e3da9 | 34c91c8c604b4597a09f013c2a0d66fa2e11385549119d30c19da7836a2ff9d1 | bde8cb18a622a8579c4ae0911337de66102422ee9dbc646f4f4c56fbe115f6aa |
cat-searcher/leandojo-benchmark-4-random | test | 1,296 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases e₁' : he₁' with ⟨a₁', g₁'⟩ | n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
⊢ ∃ g₁',
∃ (e₁' : PFunctor.M.dest a₁ = ⟨a', ... | case mk
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
a₁' : P.last.A
g₁' : P.last.B a₁' → P.la... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"rcases","sourceEnd":9334,"sourceStart":9328,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"e₁'","sourceEnd":9340,"sourceStart":9335,"tag":"identifier"},{"source":":","sourceEnd":9342,"sourceStart":9341,"tag":"atom"}],"kind":"null","source":"e₁' :","... | [] | [{"source":"he₁'","source_end":9349,"source_start":9343,"syntax_kind":"ident"},{"source":"⟨a₁', g₁'⟩","source_end":9373,"source_start":9355,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 7 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5891b44b016c67cdbd74f0d878383d9a43dfbb7cd659c2737f3758fe2393651e | bde8cb18a622a8579c4ae0911337de66102422ee9dbc646f4f4c56fbe115f6aa | edd96ab39876c22eea8ca5925d5bae824b743b25dcc1bddfdef6563ba64b6b71 | a95bf1a2fe23e2c907b09a20bcbed6a018374f53febc01b13075dc5a6ab3d44e |
cat-searcher/leandojo-benchmark-4-random | test | 1,297 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MvPFunctor.M.dest_eq_dest'</a> _ e₁'] at e₁ | case mk
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
e₁ : dest P ⟨a₁, f₁⟩ = ⟨a', ff⟩
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
a₁' : P.last.A
g₁' : P.last.B a₁' → P.la... | case mk
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
a₁' : P.last.A
g₁' : P.last.B a₁' → P.last.M
e₁' : he₁' = ⟨a₁', g₁'⟩
e₁ ... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"rw","sourceEnd":9379,"sourceStart":9377,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9381,"sourceStart":9380,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"MvPFunc... | [] | [{"source":"e₁","source_end":9413,"source_start":9409,"syntax_kind":"ident"},{"source":"M.dest_eq_dest' _ e₁'","source_end":9404,"source_start":9381,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 9 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 575f0d8474baf6b25eefd631f64cc9139ec127bec48994bd3379552d30f011ce | a95bf1a2fe23e2c907b09a20bcbed6a018374f53febc01b13075dc5a6ab3d44e | 22f3e1520618fb79d6e24afaaf86a4d3f325aeac3b4c82efc93f0bff18bb0b99 | 3bd51a5754489f5c9444b7d1e29cbc9906dd46201c8e56f66f15b48c8513adc4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,298 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases e₁ | case mk
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
ff : P.B a' ⟹ α ::: P.M α
ef : splitFun f' f₁' = ff
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
a₁' : P.last.A
g₁' : P.last.B a₁' → P.last.M
e₁' : he₁' = ⟨a₁', g₁'⟩
e₁ ... | case mk.refl
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
g₁' : P.last.B a' → P.last.M
e₁' : he₁' = ⟨a', g₁'⟩
ef : splitFun f' f₁' = splitFun (pathDestLeft P e₁' f₁) fun x => ⟨g... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"cases","sourceEnd":9421,"sourceStart":9416,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":15,"semanticRole":"local","source":"e₁","sourceEnd":9426,"sourceStart":9422,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sour... | [] | [{"source":"e₁","source_end":9426,"source_start":9422,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 12 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3bc68231613a970f8777ad6d638a193ba6d1d2a893a5a2a213eb68330e7d5064 | 3bd51a5754489f5c9444b7d1e29cbc9906dd46201c8e56f66f15b48c8513adc4 | 6bc86210baf544e464884dc092263a7e7751807ccf850a5215d05bf7d4137d99 | d8a37f2b4e7dae7953cc505c8615dc81520e5bc96ab3792746c94883bca5788f |
cat-searcher/leandojo-benchmark-4-random | test | 1,299 | MvPFunctor.M.bisim_lemma | Mathlib/Data/PFunctor/Multivariate/M.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨_, e₁', <a>TypeVec.splitFun_inj</a> ef⟩ | case mk.refl
n : ℕ
P : MvPFunctor.{u} (n + 1)
α : TypeVec.{u} n
a₁ : P.mp.A
f₁ : P.mp.B a₁ ⟹ α
a' : P.A
f' : (P.B a').drop ⟹ α
f₁' : (P.B a').last → P.M α
he₁' : ↑P.last P.last.M := PFunctor.M.dest a₁
g₁' : P.last.B a' → P.last.M
e₁' : he₁' = ⟨a', g₁'⟩
ef : splitFun f' f₁' = splitFun (pathDestLeft P e₁' f₁) fun x => ⟨g... | ((:c Exists) (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c PFunctor.M) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)))) (:lambda g₁' (:forall _ ((:c PFunctor.B) ((:c MvPFunctor.last) (:fv _uniq.16904) (:fv _uniq.16964)) (:fv _uniq.17516)) ((:c... | [{"name":"n","sexp":"(:c Nat)"},{"name":"P","sexp":"((:c MvPFunctor) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.16904) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))))"},{"name":"α","sexp":"((:c TypeVec) (:fv _uniq.16904))"},{"name":"a₁","sexp":"((:... | (:app (:c Exists) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c PFunctor.B) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV1)))) (:arg :explicit 1 (:fv FV6))) (:app (:c PFunctor.M) (:arg :explicit 0 (:app (:c MvPFunctor.last) (:arg :implicit 0) (:arg :explicit 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"name":"P","sexp":"(:app (:c MvPFunctor) (:arg :explicit 0 (:app (:c ... | {"children":[{"source":"exact","sourceEnd":9433,"sourceStart":9428,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":9437,"sourceStart":9434,"tag":"atom"},{"children":[{"children":[{"source":"_","sourceEnd":9438,"sourceStart":9437,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_","sourceEnd":9438,"sourceSta... | [] | [{"source":"⟨_, e₁', splitFun_inj ef⟩","source_end":9465,"source_start":9434,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16904","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.16964","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 50 | 14 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e3c9c34ac71599dd942bc9215e5d8e1f767d9bcb41f75630684ab4845a5d53f1 | d8a37f2b4e7dae7953cc505c8615dc81520e5bc96ab3792746c94883bca5788f | 88bd38a86be2fb0ed12bfd866f175db2c81ef03d4661a7942406e19872799cdb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,300 | SimpleGraph.dart_edge_eq_mk'_iff' | Mathlib/Combinatorics/SimpleGraph/Dart.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨⟨a, b⟩, h⟩ u v | V : Type u_1
G : SimpleGraph V
⊢ ∀ {d : G.Dart} {u v : V}, d.edge = s(u, v) ↔ d.toProd.1 = u ∧ d.toProd.2 = v ∨ d.toProd.1 = v ∧ d.toProd.2 = u | case mk.mk
V : Type u_1
G : SimpleGraph V
a b : V
h : G.Adj (a, b).1 (a, b).2
u v : V
⊢ { toProd := (a, b), adj := h }.edge = s(u, v) ↔
{ toProd := (a, b), adj := h }.toProd.1 = u ∧ { toProd := (a, b), adj := h }.toProd.2 = v ∨
{ toProd := (a, b), adj := h }.toProd.1 = v ∧ { toProd := (a, b), adj := h }.toPro... | (:forall d ((:c SimpleGraph.Dart) (:fv _uniq.4220) (:fv _uniq.4223)) (:forall u (:fv _uniq.4220) (:forall v (:fv _uniq.4220) ((:c Iff) ((:c Eq) ((:c Sym2) (:fv _uniq.4220)) ((:c SimpleGraph.Dart.edge) (:fv _uniq.4220) (:fv _uniq.4223) 2) ((:c Sym2.mk) (:fv _uniq.4220) ((:c Prod.mk) (:fv _uniq.4220) (:fv _uniq.4220) 1 0... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.4220))"}] | (:forall d :implicit (:app (:c SimpleGraph.Dart) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1))) (:forall u :implicit (:fv FV0) (:forall v :implicit (:fv FV0) (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym2) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4220","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"name":"G","sexp":"(:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV... | {"children":[{"source":"rintro","sourceEnd":4300,"sourceStart":4294,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4304,"sourceStart":4301,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":4307,"sourceStart":4304,"tag":"atom"},{"chil... | [{"role":"fresh_name","source":"a","source_end":4308,"source_start":4307,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":4311,"source_start":4310,"syntax_kind":"ident"},{"role":"fresh_name","source":"h","source_end":4317,"source_start":4316,"syntax_kind":"ident"},{"role":"fresh_name","source":"u",... | [{"source":"⟨⟨a, b⟩, h⟩","source_end":4320,"source_start":4301,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4220","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"user_name":"G"}] | 40 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1359599f26fca477a2401a05f2b3e66c27905e5b76012a998cf776751c56f0d6 | 86d295d21c7b955d0d10fe5115a8eb24599b4d9f5fb7ba003d5882bc34203584 | 3eb14df0704f91c09dbb1a20440688e39dc5d329cd4ab2f4d624db22cc78c003 | b2c57191651bc30eb8a044d0296f9b7758a3f697cb05de0dd880cf60113cf116 |
cat-searcher/leandojo-benchmark-4-random | test | 1,301 | SimpleGraph.dart_edge_eq_mk'_iff' | Mathlib/Combinatorics/SimpleGraph/Dart.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>SimpleGraph.dart_edge_eq_mk'_iff</a>] | case mk.mk
V : Type u_1
G : SimpleGraph V
a b : V
h : G.Adj (a, b).1 (a, b).2
u v : V
⊢ { toProd := (a, b), adj := h }.edge = s(u, v) ↔
{ toProd := (a, b), adj := h }.toProd.1 = u ∧ { toProd := (a, b), adj := h }.toProd.2 = v ∨
{ toProd := (a, b), adj := h }.toProd.1 = v ∧ { toProd := (a, b), adj := h }.toPro... | case mk.mk
V : Type u_1
G : SimpleGraph V
a b : V
h : G.Adj (a, b).1 (a, b).2
u v : V
⊢ { toProd := (a, b), adj := h }.toProd = (u, v) ∨ { toProd := (a, b), adj := h }.toProd = (u, v).swap ↔
{ toProd := (a, b), adj := h }.toProd.1 = u ∧ { toProd := (a, b), adj := h }.toProd.2 = v ∨
{ toProd := (a, b), adj := ... | ((:c Iff) ((:c Eq) ((:c Sym2) (:fv _uniq.4220)) ((:c SimpleGraph.Dart.edge) (:fv _uniq.4220) (:fv _uniq.4223) ((:c SimpleGraph.Dart.mk) (:fv _uniq.4220) (:fv _uniq.4223) ((:c Prod.mk) (:fv _uniq.4220) (:fv _uniq.4220) (:fv _uniq.4343) (:fv _uniq.4344)) (:fv _uniq.4347))) ((:c Sym2.mk) (:fv _uniq.4220) ((:c Prod.mk) (:f... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.4220))"},{"name":"a","sexp":"(:fv _uniq.4220)"},{"name":"b","sexp":"(:fv _uniq.4220)"},{"name":"h","sexp":"((:c SimpleGraph.Adj) (:fv _uniq.4220) (:fv _uniq.4223) ((:c Prod.fst) (:fv _uniq.4220) (:fv _uniq.4220) ((:c Prod.mk) (:fv... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Sym2) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c SimpleGraph.Dart.edge) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGraph.Dart.mk) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4220","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"name":"G","sexp":"(:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV... | {"children":[{"source":"rw","sourceEnd":4329,"sourceStart":4327,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4331,"sourceStart":4330,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"SimpleGraph.dart_edg... | [] | [{"source":"dart_edge_eq_mk'_iff","source_end":4351,"source_start":4331,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4220","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 40 | 5 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 044ecbbbde01f67b08c79abf3ca3d5d833ffe0dd3255f843ad34c2d437f36fbb | b2c57191651bc30eb8a044d0296f9b7758a3f697cb05de0dd880cf60113cf116 | f5fd1ee0e7ec0d4c64a8ca4b26bac5c1914620c6fa1173657b96c70e77fdb6bb | 8ee6c797352f3408c7c6c05261fb27479bc9d025234d46f38940d2eda09b898a |
cat-searcher/leandojo-benchmark-4-random | test | 1,302 | SimpleGraph.dart_edge_eq_mk'_iff' | Mathlib/Combinatorics/SimpleGraph/Dart.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case mk.mk
V : Type u_1
G : SimpleGraph V
a b : V
h : G.Adj (a, b).1 (a, b).2
u v : V
⊢ { toProd := (a, b), adj := h }.toProd = (u, v) ∨ { toProd := (a, b), adj := h }.toProd = (u, v).swap ↔
{ toProd := (a, b), adj := h }.toProd.1 = u ∧ { toProd := (a, b), adj := h }.toProd.2 = v ∨
{ toProd := (a, b), adj := ... | ((:c Iff) ((:c Or) ((:c Eq) ((:c Prod) (:fv _uniq.4220) (:fv _uniq.4220)) ((:c SimpleGraph.Dart.toProd) (:fv _uniq.4220) (:fv _uniq.4223) ((:c SimpleGraph.Dart.mk) (:fv _uniq.4220) (:fv _uniq.4223) ((:c Prod.mk) (:fv _uniq.4220) (:fv _uniq.4220) (:fv _uniq.4343) (:fv _uniq.4344)) (:fv _uniq.4347))) ((:c Prod.mk) (:fv _... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"((:c SimpleGraph) (:fv _uniq.4220))"},{"name":"a","sexp":"(:fv _uniq.4220)"},{"name":"b","sexp":"(:fv _uniq.4220)"},{"name":"h","sexp":"((:c SimpleGraph.Adj) (:fv _uniq.4220) (:fv _uniq.4223) ((:c Prod.fst) (:fv _uniq.4220) (:fv _uniq.4220) ((:c Prod.mk) (:fv... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)))) (:arg :explicit 1 (:app (:c SimpleGraph.Dart.toProd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c SimpleGr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4220","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"name":"G","sexp":"(:app (:c SimpleGraph) (:arg :explicit 0 (:fv FV... | {"children":[{"source":"simp","sourceEnd":4359,"sourceStart":4355,"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.4220","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4223","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 40 | 8 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 825d4be9edce7f6baa9525d19873094796a3d9830e2d46925e9c10132377319f | 8ee6c797352f3408c7c6c05261fb27479bc9d025234d46f38940d2eda09b898a | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,303 | Monotone.seq_lt_seq_of_lt_of_le | Mathlib/Order/Iterate.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases n | α : Type u_1
inst✝ : Preorder α
f : α → α
x y : ℕ → α
hf : Monotone f
n : ℕ
h₀ : x 0 < y 0
hx : ∀ (k : ℕ), k < n → x (k + 1) < f (x k)
hy : ∀ (k : ℕ), k < n → f (y k) ≤ y (k + 1)
⊢ x n < y n | case zero
α : Type u_1
inst✝ : Preorder α
f : α → α
x y : ℕ → α
hf : Monotone f
h₀ : x 0 < y 0
hx : ∀ (k : ℕ), k < 0 → x (k + 1) < f (x k)
hy : ∀ (k : ℕ), k < 0 → f (y k) ≤ y (k + 1)
⊢ x 0 < y 0
case succ
α : Type u_1
inst✝ : Preorder α
f : α → α
x y : ℕ → α
hf : Monotone f
h₀ : x 0 < y 0
n✝ : ℕ
hx : ∀ (k : ℕ), k < n✝ ... | ((:c LT.lt) (:fv _uniq.1274) ((:c Preorder.toLT) (:fv _uniq.1274) (:fv _uniq.1277)) ((:fv _uniq.1285) (:fv _uniq.1490)) ((:fv _uniq.1289) (:fv _uniq.1490))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.1274))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.1274) (:fv _uniq.1274))"},{"name":"x","sexp":"(:forall _ (:c Nat) (:fv _uniq.1274))"},{"name":"y","sexp":"(:forall _ (:c Nat) (:fv _uniq.1274))"},{"name":"hf","sexp":"((:c Monoto... | (: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 (:fv FV3) (:arg :explicit 0 (:fv FV7)))) (:arg :explicit 3 (:app (:fv FV4) (:arg :explicit 0 (:fv FV7))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1274","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1277","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Preorder) (:arg :explicit ... | {"children":[{"source":"cases","sourceEnd":2899,"sourceStart":2894,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"n","sourceEnd":2901,"sourceStart":2900,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","source... | [] | [{"source":"n","source_end":2901,"source_start":2900,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1274","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1277","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"internal_... | 13 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f80dbfad1ce29369f3724a77593ea9b14495054783328503adec3a5dbc53c34 | 565e8e52451b4c9b07e213f21a6ef06244836632836ab9a8cac2fbaa5c981098 | 587af0ace40623dade91be1b78e831facc5de085c3c720b59185b89ff09878a4 | aa23b8af9a8636dfba536d339621cf9ec000c258244e44273c5e72c655e2b60a |
cat-searcher/leandojo-benchmark-4-random | test | 1,305 | Cardinal.lift_le_nat_iff | Mathlib/SetTheory/Cardinal/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Cardinal.lift_natCast</a>.{v,u}, <a>Cardinal.lift_le</a>] | α β : Type u
a : Cardinal.{u}
n : ℕ
⊢ lift.{v, u} a ≤ ↑n ↔ a ≤ ↑n | ((:c Iff) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) ((:c Cardinal.lift) (:fv _uniq.98438)) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) (:fv _uniq.98439))) ((:c LE.le) (:c Cardinal) (:c Cardinal.instLE) (:fv _uniq.98438) ((:c Nat.cast) (:c Cardinal) (:c Cardinal.instNatCast) (:fv _uniq.98439)))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ u 1))"},{"name":"a","sexp":"(:c Cardinal)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Cardinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Cardinal))))) (:arg :explicit 2 (:app (:c Cardinal.lift) (:arg :explicit 0 (:fv FV3)))) (:arg :explicit 3 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Cardinal)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98258","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98260","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":55126,"sourceStart":55124,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":55128,"sourceStart":55127,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"lift_natCast.{v,u}","source_end":55150,"source_start":55132,"syntax_kind":"Lean.Parser.Term.explicitUniv"},{"source":"lift_le","source_end":55159,"source_start":55152,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.98258","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.98260","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 403 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f95cdce29b5482d4988d7833f2745c7f70470fa71503f1616de90e24b620bd50 | f05abfe4a13fa90a3b375ff88df0a2c2084f6a9af88f2ea972f988cc678ba4af | 13b1533ac1f06a56ca57a161b1b7356d58edaeb86e2d7a774c0593096a4b2027 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,306 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Submodule.finsupp_sum_mem</a> | I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
⊢ (c.sum fun a_1 b => e (π C fun x => x ∈ s) a * b • Products.eval (π C fun x => x ∈ s) a_1... | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
⊢ ∀ (c_1 : Products I),
c c_1 ≠ 0 →
e (π C fun x => x ∈ s) a * c c_1 • Pro... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"apply","sourceEnd":22968,"sourceStart":22963,"tag":"atom"},{"name":"Submodule.finsupp_sum_mem","semanticRole":"global","source":"Submodule.finsupp_sum_mem","sourceEnd":22994,"sourceStart":22969,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Submodule.finsupp_sum_mem","sou... | [] | [{"source":"Submodule.finsupp_sum_mem","source_end":22994,"source_start":22969,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ee5571deb1c7ff6a03954504a6ac659dae04f467854f78cc90110db2959af7b | 7b0cbdf2c842abb7de076988ac64740b8488be031901fa89ab4d293d037d53ef | a87b82483d80dd192f86964686f447d546a62a01f251ad162f5ffd5b512090bf | f557ecdbdc08c3dcace539ad3241fb3296d3328af9d021ffaac89cb8d151d20b |
cat-searcher/leandojo-benchmark-4-random | test | 1,307 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro m hm | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
⊢ ∀ (c_1 : Products I),
c c_1 ≠ 0 →
e (π C fun x => x ∈ s) a * c c_1 • Pro... | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
⊢ e (π C fun x => x ∈ s) a * c m • Products.eval (π C fu... | (:forall c ((:c Profinite.NobelingProof.Products) (:fv _uniq.173400) (:fv _uniq.173403)) (:forall _ ((:c Ne) (:c Int) ((:c DFunLike.coe) ((:c Finsupp) ((:c Profinite.NobelingProof.Products) (:fv _uniq.173400) (:fv _uniq.173403)) (:c Int) ((:c CommMonoidWithZero.toZero) (:c Int) ((:c CommSemiring.toCommMonoidWithZero) (... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:forall c :explicit (:app (:c Profinite.NobelingProof.Products) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:fv FV0)))))) (:forall _ :explicit (:app (:c Ne) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"intro","sourceEnd":23002,"sourceStart":22997,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"m","sourceEnd":23004,"sourceStart":23003,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hm","sourceEnd":23007,"sourceStart":23005,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"m","source_end":23004,"source_start":23003,"syntax_kind":"ident"},{"role":"fresh_name","source":"hm","source_end":23007,"source_start":23005,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 5 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 769014c603e5a2b49d00723f1ae3c43fe100bb8043abbb40fdafc1737d69a98b | f557ecdbdc08c3dcace539ad3241fb3296d3328af9d021ffaac89cb8d151d20b | 9e2d59ed729bc2490ca5e9d22371345b111514ea6398b73a123b0c1f96bc7493 | 8afa03bb491a9a6d938f0111c23f503f6cdab2e6cfa43daef8907ee824c08eaf |
cat-searcher/leandojo-benchmark-4-random | test | 1,308 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp at hsm | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"dsimp","sourceEnd":23086,"sourceStart":23081,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"ch... | [] | [{"source":"hsm","source_end":23093,"source_start":23090,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 838448ce288b91a57e355991255225e9a1bc58d33cbc133baf8ebf4c59523cf4 | 241eb6808e88307394a6ccaed423a721a4612bd4c02914b48e66bd58c0f744e1 | d5c2e1c1d0cae8040f514fb71a40fa9e094dbe427e33ebcae74b7eec63a108b0 | 3fcfeba018a6b0a0850976ba4a2beb17c90f07d29ffff9cf37b84c834306136f |
cat-searcher/leandojo-benchmark-4-random | test | 1,309 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hsm] | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"rw","sourceEnd":23098,"sourceStart":23096,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23100,"sourceStart":23099,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"seman... | [] | [{"source":"hsm","source_end":23103,"source_start":23100,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 8 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34fdee613981a7c1d32fbb87f93dcf40fbe9494ca37c1dbdff08044786d30000 | 3fcfeba018a6b0a0850976ba4a2beb17c90f07d29ffff9cf37b84c834306136f | 3508abb74aa82d278a207781ff7b22a99141205dfbd41fce4ca41698b9a5a385 | 3b3a74ed9ef8e56759fd9e6daff193866b4f51ec3cdde1d0fb61e66cd7db00e7 |
cat-searcher/leandojo-benchmark-4-random | test | 1,310 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Submodule.smul_mem</a> | case h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | case h.h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => ... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"apply","sourceEnd":23112,"sourceStart":23107,"tag":"atom"},{"name":"Submodule.smul_mem","semanticRole":"global","source":"Submodule.smul_mem","sourceEnd":23131,"sourceStart":23113,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Submodule.smul_mem","sourceEnd":23131,"source... | [] | [{"source":"Submodule.smul_mem","source_end":23131,"source_start":23113,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 11 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4626031296b53647cb0c62059e2e001a9aed5749ba22abb3500c5cf67f3b6d66 | 3b3a74ed9ef8e56759fd9e6daff193866b4f51ec3cdde1d0fb61e66cd7db00e7 | c00a4c3ff36e4c7442af9baa29e570c0426316990c3da89f5598bd686f00916e | 7382fe8cbd2a09178779eb0c6c3da4e115d7a41c1fa23bce5a9b294b70ee66c9 |
cat-searcher/leandojo-benchmark-4-random | test | 1,311 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Submodule.subset_span</a> | case h.h
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => ... | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"apply","sourceEnd":23139,"sourceStart":23134,"tag":"atom"},{"name":"Submodule.subset_span","semanticRole":"global","source":"Submodule.subset_span","sourceEnd":23161,"sourceStart":23140,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply Submodule.subset_span","sourceEnd":2316... | [] | [{"source":"Submodule.subset_span","source_end":23161,"source_start":23140,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 12 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f65927a4ef714a0f82f1526851e92cfe2cc0497e9a7b1acfd43b4c7641d91fa2 | 7382fe8cbd2a09178779eb0c6c3da4e115d7a41c1fa23bce5a9b294b70ee66c9 | 86994d4e5b04e98f938ba8f4103e68849f5fa65eedf8bc0213a31dd701f05fba | 9d21030801b80d028f3c8115abaed72f5833c7406df4119eb586e6b6f2db28bb |
cat-searcher/leandojo-benchmark-4-random | test | 1,312 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hmas : m.val ≤ as := by apply hc simpa only [<a>Finset.mem_coe</a>, <a>Finsupp.mem_support_iff</a>] using hm | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"have","sourceEnd":23168,"sourceStart":23164,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hmas","sourceEnd":23173,"sourceStart":23169,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hmas","sourceEnd":23173,"sourceStart":23169,"tag":... | [] | [{"source":"m.val ≤ as","source_end":23188,"source_start":23176,"syntax_kind":"«term_≤_»"},{"source":"hc","source_end":23207,"source_start":23205,"syntax_kind":"ident"},{"source":"Finset.mem_coe","source_end":23238,"source_start":23224,"syntax_kind":"ident"},{"source":"Finsupp.mem_support_iff","source_end":23263,"sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 13 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dbb63d83799db0ad99246bd51addc132bce9191223b4ef1939ac19d096b5a511 | 9d21030801b80d028f3c8115abaed72f5833c7406df4119eb586e6b6f2db28bb | 9471839ad82a9e0f813b15fdc1655da63e3436d3bfd75605b3a6228d5662bd92 | 74960d7540acf57fe2bd8ca3bafd7b433af2b0db5ebcb0a6b9aa0d933a6df16c |
cat-searcher/leandojo-benchmark-4-random | test | 1,313 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨a :: m.val, ha.cons_of_le m.prop hmas⟩, ⟨<a>List.cons_le_cons</a> a hmas, ?_⟩⟩ | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | ((:c Membership.mem) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) ... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"refine","sourceEnd":23282,"sourceStart":23276,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":23286,"sourceStart":23283,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":23289,"sourceStart":23286,"tag":"atom"},{"children":[{"children":[{"contextIndex":6,"semanticRole":"local... | [] | [{"source":"⟨⟨a :: m.val, ha.cons_of_le m.prop hmas⟩, ⟨List.cons_le_cons a hmas, ?_⟩⟩","source_end":23368,"source_start":23283,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 17 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4cbaa444d3d3c2b60c5c82e655c75bd86e8c4d508f0e1df2e5288271b69dfbda | 74960d7540acf57fe2bd8ca3bafd7b433af2b0db5ebcb0a6b9aa0d933a6df16c | ab277277e4f95b14639b266ccdc9103d011f43101f312600753f4ed913df8b96 | 92fd274dd6faab48f6f2faea44ecf15244a27ff0d2dd5256cc0a9967682475bf |
cat-searcher/leandojo-benchmark-4-random | test | 1,314 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Profinite.NobelingProof.Products.eval</a>, <a>List.map</a>, <a>List.prod_cons</a>] | case h.h.a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x =... | ((:c Eq) ((:c LocallyConstant) ((:c Set.Elem) (:forall _ (:fv _uniq.173400) (:c Bool)) ((:c Profinite.NobelingProof.π) (:fv _uniq.173400) (:fv _uniq.173910) (:lambda _ (:fv _uniq.173400) ((:c Membership.mem) (:fv _uniq.173400) ((:c Finset) (:fv _uniq.173400)) ((:c Finset.instMembership) (:fv _uniq.173400)) 0 (:fv _uniq... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LocallyConstant) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV0) (:c Bool))) (:arg :explicit 1 (:app (:c Profinite.NobelingProof.π) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:lambda _ :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"simp","sourceEnd":23375,"sourceStart":23371,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":23380,"sourceStart":23376,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":233... | [] | [{"source":"Products.eval","source_end":23395,"source_start":23382,"syntax_kind":"ident"},{"source":"List.map","source_end":23405,"source_start":23397,"syntax_kind":"ident"},{"source":"List.prod_cons","source_end":23421,"source_start":23407,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 18 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ea87b06e4c223b03444bcbe664cfe44728976840dcc2ccc12765a4a42724185 | 92fd274dd6faab48f6f2faea44ecf15244a27ff0d2dd5256cc0a9967682475bf | daf75f87fa09b32af5f1d10ce1092281e10b4a2eddcb02f7fbbf2b071af4ef2a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,315 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply hc | I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ∈ s) ℤ)... | case a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | ((:c LE.le) ((:c List) (:fv _uniq.173400)) ((:c List.LE') (:fv _uniq.173400) (:fv _uniq.173403)) ((:c Subtype.val) ((:c List) (:fv _uniq.173400)) (:lambda l ((:c List) (:fv _uniq.173400)) ((:c List.Chain') (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c GT.gt) (:fv _uniq.173400) ((:c... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c List) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Subtype.val) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"apply","sourceEnd":23204,"sourceStart":23199,"tag":"atom"},{"contextIndex":10,"semanticRole":"local","source":"hc","sourceEnd":23207,"sourceStart":23205,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply hc","sourceEnd":23207,"sourceStart":23199,"tag":"node"} | [] | [{"source":"hc","source_end":23207,"source_start":23205,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 15 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cee8515fc30bee4e2df00696041c7dab56c5c3f5065ed831ccbc05c1f8b06b04 | 1c11a0c351d84e686be5f2899fd06fa48f8b33a1e8486f6dcec203d208865181 | 51be0f2c4dd0c5ded0626ce88a07b9881d56a22cdf679bd06e7213168a5e6032 | 81ee94c8f7e05d369c0bbcea74965f8bb0f3f8e0d27f5c4239df5cbea4022ef0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,316 | Profinite.NobelingProof.GoodProducts.finsupp_sum_mem_span_eval | Mathlib/Topology/Category/Profinite/Nobeling.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Finset.mem_coe</a>, <a>Finsupp.mem_support_iff</a>] using hm | case a
I : Type u
inst✝¹ : LinearOrder I
inst✝ : IsWellOrder I fun x x_1 => x < x_1
C : Set (I → Bool)
s : Finset I
a : I
as : List I
ha : List.Chain' (fun x x_1 => x > x_1) (a :: as)
c : Products I →₀ ℤ
hc : ↑c.support ⊆ {m | ↑m ≤ as}
m : Products I
hm : c m ≠ 0
hsm :
∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x => x ... | ((:c Membership.mem) ((:c Profinite.NobelingProof.Products) (:fv _uniq.173400) (:fv _uniq.173403)) ((:c Set) ((:c Profinite.NobelingProof.Products) (:fv _uniq.173400) (:fv _uniq.173403))) ((:c Set.instMembership) ((:c Profinite.NobelingProof.Products) (:fv _uniq.173400) (:fv _uniq.173403))) (:fv _uniq.176144) ((:c Fins... | [{"name":"I","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrder) (:fv _uniq.173400))"},{"name":"inst✝","sexp":"((:c IsWellOrder) (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) (:lambda _ (:fv _uniq.173400) ((:c LT.lt) (:fv _uniq.173400) ((:c Preorder.toLT) (:fv _uniq.173400) ((:c PartialOrder.toPreor... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Profinite.NobelingProof.Products) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrder) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Profinite.NobelingProof.Products) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"name":"I","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c LinearOrder) (:arg :e... | {"children":[{"source":"simpa","sourceEnd":23217,"sourceStart":23212,"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"},{"ch... | [] | [{"source":"Finset.mem_coe","source_end":23238,"source_start":23224,"syntax_kind":"ident"},{"source":"Finsupp.mem_support_iff","source_end":23263,"source_start":23240,"syntax_kind":"ident"},{"source":"hm","source_end":23273,"source_start":23271,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.173400","is_instance":false,"is_let":false,"user_name":"I"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.173403","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 80 | 16 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b11a41bca9888cc30853e083b5ee319476838ee0ca6797c554608ff7d2aa41b | 81ee94c8f7e05d369c0bbcea74965f8bb0f3f8e0d27f5c4239df5cbea4022ef0 | cdb7a474f405f178d5f98c61adb2a1611b968f222e1d26f635cb9262666f3b1c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,317 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Finset.mul_sum</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ k ∈ Ico 2 (n + 1), a ^ k * ∑ c ∈ {c | 1 < c.length}.toFinse... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ x ∈ Ico 2 (n + 1),
∑ i ∈ {c | 1 < c.length}.toFinset,... | ((:c Eq) (:c Real) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatN... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :explicit 3 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:c Nat)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp_rw","sourceEnd":19604,"sourceStart":19597,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19606,"sourceStart":19605,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mul_... | [] | [{"source":"mul_sum","source_end":19613,"source_start":19606,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 054da256e8075759ec56ebfc632acf302619468147edc0bbbc43874d94bee85f | 28ad9e0e296c074ca007d91f880d34dd180bbe9e8dcfffa5629072c36d907942 | cf00387af5cb71127db36044dbd8d906e1f97512d920dc5152610b70e94fc9a6 | 2dcf90f02c63e578a4ee141a630d9318930631af492b80da69e0218b67f59df6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,318 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr! with k _ c | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ x ∈ Ico 2 (n + 1),
∑ i ∈ {c | 1 < c.length}.toFinset,... | case a.a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
a✝¹ : k ∈ Ico 2 (n + 1)
c : Composition k
a✝ : c... | ((:c Eq) (:c Real) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatN... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :explicit 3 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:c Nat)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"congr!","sourceEnd":19627,"sourceStart":19621,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":19632,"sourceStart":19628,"tag":"atom"},{"children":[{"children":[{"children":[{"sem... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 7 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2cc5796a4a16a9b398665d8dae6f65db435fba3afbadf17b2a00ffe701e0e151 | 2dcf90f02c63e578a4ee141a630d9318930631af492b80da69e0218b67f59df6 | 5c3b674d0077469d8c6692b3a5fa52e58aa7ce3870825db15f4227aec309519d | b403437c4e66d6ae2b38062c8f55d76b2e15fcb534a90b51011a89479c595955 |
cat-searcher/leandojo-benchmark-4-random | test | 1,319 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.prod_mul_distrib</a>, <a>Finset.prod_mul_distrib</a>, <a>Finset.prod_pow_eq_pow_sum</a>, <a>Composition.sum_blocksFun</a>, <a>Finset.prod_const</a>, <a>Finset.card_fin</a>] | case a.a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
a✝¹ : k ∈ Ico 2 (n + 1)
c : Composition k
a✝ : c... | case a.a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
a✝¹ : k ∈ Ico 2 (n + 1)
c : Composition k
a✝ : c... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c NonUnitalNonAssocSemiring.toMul) (:c Real) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Real) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring) (:c Real) ((:c NonUnitalCommRing.toNonUnital... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":19647,"sourceStart":19645,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19649,"sourceStart":19648,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.prod_mul_... | [] | [{"source":"prod_mul_distrib","source_end":19665,"source_start":19649,"syntax_kind":"ident"},{"source":"prod_mul_distrib","source_end":19683,"source_start":19667,"syntax_kind":"ident"},{"source":"prod_pow_eq_pow_sum","source_end":19704,"source_start":19685,"syntax_kind":"ident"},{"source":"Composition.sum_blocksFun","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 8 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3bcf138748dff13b12262cb5d7cc52b0fa6e9337189ab42555be4ac298011dae | b403437c4e66d6ae2b38062c8f55d76b2e15fcb534a90b51011a89479c595955 | 6cc7bf6145ac1e51bd383ac34dab31114853ae89796b38ecc54747255b86daf9 | 17e33032369b4cf3442ad6a45e226f24c574af1ca6d0b963b173ea423c71b43b |
cat-searcher/leandojo-benchmark-4-random | test | 1,320 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | case a.a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
a✝¹ : k ∈ Ico 2 (n + 1)
c : Composition k
a✝ : c... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c NonUnitalNonAssocSemiring.toMul) (:c Real) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Real) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring) (:c Real) ((:c NonUnitalCommRing.toNonUnital... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"ring","sourceEnd":19773,"sourceStart":19769,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":19773,"sourceStart":19769,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 16 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a862e25e5fa4547b9cc58fecb1611212550babc323bc79dc0b4f525a68c4fe81 | 17e33032369b4cf3442ad6a45e226f24c574af1ca6d0b963b173ea423c71b43b | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,321 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.sum_sigma'</a>] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ k ∈ Ico 2 (n + 1),
∑ c ∈ {c | 1 < c.length}.toFinset,... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ x ∈ (Ico 2 (n + 1)).sigma fun k => {c | 1 < c.length}.toFin... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Nat) (:li... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":19932,"sourceStart":19930,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19934,"sourceStart":19933,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.sum_sigma... | [] | [{"source":"sum_sigma'","source_end":19944,"source_start":19934,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 21 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d5e317e9a0a12c27e42e64167a539c7e2cc25ffbf16dafd88a2195ae3bb4778 | 19c0fdca08ee83a9f76bcf291007fe25741830d036cee84fd3616ea0348889f6 | f2166cd92e6d444ba8fc24e2ddcd32c6b93a1c675241ee6b1f2ec4dc25703d0f | 75ce7896bf25478a8503409a55f99bdc5657d9f6faa74aa1508df3fd852770ee |
cat-searcher/leandojo-benchmark-4-random | test | 1,322 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Finset.sum_le_sum_of_subset_of_nonneg</a> ?_ fun x _ _ => <a>Finset.prod_nonneg</a> fun j _ => <a>mul_nonneg</a> hr (<a>mul_nonneg</a> (<a>pow_nonneg</a> ha _) (hp _)) | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ x ∈ (Ico 2 (n + 1)).sigma fun k => {c | 1 < c.length}.toFin... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ((Ico 2 (n + 1)).sigma fun k => {c | 1 < c.length}.toFinset) ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Finset.sum) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0))) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.sigma) (:c Nat) (:c Composition) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) ... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:app (:c Composition) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"refine","sourceEnd":19958,"sourceStart":19952,"tag":"atom"},{"children":[{"name":"Finset.sum_le_sum_of_subset_of_nonneg","semanticRole":"global","source":"sum_le_sum_of_subset_of_nonneg","sourceEnd":19997,"sourceStart":19967,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd"... | [] | [{"source":"sum_le_sum_of_subset_of_nonneg ?_ fun x _ _ =>\n prod_nonneg fun j _ => mul_nonneg hr (mul_nonneg (pow_nonneg ha _) (hp _))","source_end":20098,"source_start":19967,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 24 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01c976e2f5fb44399b9e322ef27a4f42f4adfcba71cdce9a61d22ca9eabf0198 | 75ce7896bf25478a8503409a55f99bdc5657d9f6faa74aa1508df3fd852770ee | d4399e677230cd32876cf84ce31f63b17d59b13a189149088b7532fd57f2e821 | dba7e440462d5d06739dd57adbc9cb450a5f285a1cbb079d5e188a1d87ffcfad |
cat-searcher/leandojo-benchmark-4-random | test | 1,323 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨k, c⟩ hd | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ((Ico 2 (n + 1)).sigma fun k => {c | 1 < c.length}.toFinset) ... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : ⟨k, c⟩ ∈ (Ico 2 (n + 1)).s... | ((:c HasSubset.Subset) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Finset.instHasSubset) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Finset.sigma) (:c Nat) (:c Composition) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrdere... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Fin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rintro","sourceEnd":20111,"sourceStart":20105,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":20115,"sourceStart":20112,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":20116,"sou... | [{"role":"fresh_name","source":"k","source_end":20116,"source_start":20115,"syntax_kind":"ident"},{"role":"fresh_name","source":"c","source_end":20119,"source_start":20118,"syntax_kind":"ident"},{"role":"fresh_name","source":"hd","source_end":20125,"source_start":20123,"syntax_kind":"ident"}] | [{"source":"⟨k, c⟩","source_end":20122,"source_start":20112,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 25 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f1dc645cc57b9d0a00f2f9e2af638ba2ac5684df0ae4012646f2c86dc79a605 | dba7e440462d5d06739dd57adbc9cb450a5f285a1cbb079d5e188a1d87ffcfad | 7a5202387380ae573c5b490cae6626b51c2a25815b8879b7f9485edd75b8414c | 3a5a1143460d24bf8875342d3350dfa3a6bc39846ff6b9921f8e60eb4ace1d8b |
cat-searcher/leandojo-benchmark-4-random | test | 1,324 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_toFinset</a> (s := {c | 1 < <a>Composition.length</a> c}), <a>Finset.mem_Ico</a>, <a>Finset.mem_sigma</a>, <a>Set.mem_setOf_eq</a>] at hd | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : ⟨k, c⟩ ∈ (Ico 2 (n + 1)).s... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Sigma.mk) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":20136,"sourceStart":20132,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":20141,"sourceStart":20137,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":201... | [] | [{"source":"Set.mem_toFinset (s := {c | 1 < Composition.length c})","source_end":20197,"source_start":20143,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mem_Ico","source_end":20206,"source_start":20199,"syntax_kind":"ident"},{"source":"mem_sigma","source_end":20217,"source_start":20208,"syntax_kind":"ident"},{"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 26 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7414c33bf0e768122fddb06c175738e957c7f44371eb381fa2ba6c556d3fbc1 | 3a5a1143460d24bf8875342d3350dfa3a6bc39846ff6b9921f8e60eb4ace1d8b | 438affabbb4b81687e8fc7d03308f59753ab62b01659b3971e4658ec17cfbf30 | 76e7b40dd11123836e7dfdf302a0c5eb5200843c854a9045f66a0173a94fa354 |
cat-searcher/leandojo-benchmark-4-random | test | 1,325 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>FormalMultilinearSeries.mem_compPartialSumTarget_iff</a>] | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Finset.instMembership) ((:c Sigma) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)))) ((:c Sigma.mk) (:c Nat) (:lambda i (:c Nat) ((:c Composition) 0)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda i :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":20261,"sourceStart":20257,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":20266,"sourceStart":20262,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":202... | [] | [{"source":"mem_compPartialSumTarget_iff","source_end":20296,"source_start":20268,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 27 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b9b56e97ce8e2fef55627ef19d323f7bb743982a6183cb6a0ec862c432270d9 | 76e7b40dd11123836e7dfdf302a0c5eb5200843c854a9045f66a0173a94fa354 | 796a504c4bb9da746e3803ec3a9460e3853d0679ab5327510e6ea7f1f780ca0d | ada8e44911aa2ed175a12c2847eb6d72962889d8825e4c328c3c56c240d942eb |
cat-searcher/leandojo-benchmark-4-random | test | 1,326 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨hd.2, c.length_le.trans_lt hd.1.2, fun j => ?_⟩ | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c And) ((:c LE.le) (:c Nat) (:c instLENat) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c Composition.length) (:fv _uniq.399343) (:fv _uniq.399344))) ((:c And) ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.length) (:fv _uniq.399343) (:fv _uniq.399344)) ((:c HAdd.hAdd) (:c Nat) (:c Nat)... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"refine","sourceEnd":20310,"sourceStart":20304,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":20314,"sourceStart":20311,"tag":"atom"},{"children":[{"children":[{"contextIndex":18,"semanticRole":"local","source":"hd","sourceEnd":20316,"sourceStart":20314,"tag":"identifier"},{"source":".","so... | [] | [{"source":"⟨hd.2, c.length_le.trans_lt hd.1.2, fun j => ?_⟩","source_end":20363,"source_start":20311,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 28 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 46e93a0465341ccb7dfce30da909b55c225e4a36f7113f598c10c9e61763f3be | ada8e44911aa2ed175a12c2847eb6d72962889d8825e4c328c3c56c240d942eb | ae5f471697f3b8a380c14ca185fab394e575fd6b1e6b20eb583b2f2af72abb68 | 98ada0e3adf5b869fbc09234d6c09aa22a4f518fda52bfe8372c093f7f5562c4 |
cat-searcher/leandojo-benchmark-4-random | test | 1,327 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : c ≠ <a>Composition.single</a> k (zero_lt_two.trans_le hd.1.1) := by simp [<a>Composition.eq_single_iff_length</a>, <a>ne_of_gt</a> hd.2] | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.blocksFun) (:fv _uniq.399343) (:fv _uniq.399344) (:fv _uniq.400868)) (:fv _uniq.390708)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Composition.blocksFun) (:arg :implicit 0) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:fv FV19)))) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":20374,"sourceStart":20370,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":20375,"sourceStart":20375,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":20375,"sourceStart":20375,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"c ≠ Composition.single k (zero_lt_two.trans_le hd.1.1)","source_end":20433,"source_start":20377,"syntax_kind":"«term_≠_»"},{"source":"Composition.eq_single_iff_length","source_end":20486,"source_start":20454,"syntax_kind":"ident"},{"source":"ne_of_gt hd.2","source_end":20501,"source_start":20488,"syntax_kin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 29 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c8e5371a6c7acaac40de0d2bb9788a1871eebc3781d56cc7920c23ef8824f1b7 | 98ada0e3adf5b869fbc09234d6c09aa22a4f518fda52bfe8372c093f7f5562c4 | bc06a631f859470a32d204ae670f6b0a29122b404d888af3cfc787f489d5305b | 1bd237a9222fddb4f89513090ef05182ebe3b83d29e1f8470d74d3b805ad639d |
cat-searcher/leandojo-benchmark-4-random | test | 1,328 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Composition.ne_single_iff</a>] at this | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.blocksFun) (:fv _uniq.399343) (:fv _uniq.399344) (:fv _uniq.400868)) (:fv _uniq.390708)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Composition.blocksFun) (:arg :implicit 0) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:fv FV19)))) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":20511,"sourceStart":20509,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20513,"sourceStart":20512,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Composition.ne_s... | [] | [{"source":"Composition.ne_single_iff","source_end":20538,"source_start":20513,"syntax_kind":"ident"},{"source":"this","source_end":20547,"source_start":20543,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 32 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee52fbe1627dd738dab29d08db74c7b90161ab0ab1266cba50880b1a7070cee5 | 1bd237a9222fddb4f89513090ef05182ebe3b83d29e1f8470d74d3b805ad639d | e2855a64a275787092488391188a37f157f90ac68156df399ef3172136dca777 | 86832006c15ab7350e701c523f4ebcd7b7cef1be463cbeb9effc7f497c93e554 |
cat-searcher/leandojo-benchmark-4-random | test | 1,329 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (this j).<a>LT.lt.trans_le</a> (Nat.lt_succ_iff.mp hd.1.2) | case mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < ... | ((:c LT.lt) (:c Nat) (:c instLTNat) ((:c Composition.blocksFun) (:fv _uniq.399343) (:fv _uniq.399344) (:fv _uniq.400868)) (:fv _uniq.390708)) | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Composition.blocksFun) (:arg :implicit 0) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:fv FV19)))) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"exact","sourceEnd":20559,"sourceStart":20554,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":20561,"sourceStart":20560,"tag":"atom"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"this","sourceEnd":20565,"sourceStart":20561,"tag":"identifier"},{"c... | [] | [{"source":"(this j).trans_le (Nat.lt_succ_iff.mp hd.1.2)","source_end":20605,"source_start":20560,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 35 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f02509605e0281f949fb514a99e0c9637d58fe6b2ca6c87e06208e2680c728db | 86832006c15ab7350e701c523f4ebcd7b7cef1be463cbeb9effc7f497c93e554 | e736fb1f103d64018077d612ff90d29fc2a58c50c286a1ab1117af57e483d385 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,330 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Composition.eq_single_iff_length</a>, <a>ne_of_gt</a> hd.2] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
c : Composition k
hd : (2 ≤ k ∧ k < n + 1) ∧ 1 < c.length... | ((:c Ne) ((:c Composition) (:fv _uniq.399343)) (:fv _uniq.399344) ((:c Composition.single) (:fv _uniq.399343) ((:c LT.lt.trans_le) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c Zero.toOfNa... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Composition) (:arg :explicit 0 (:fv FV16)))) (:arg :explicit 1 (:fv FV17)) (:arg :explicit 2 (:app (:c Composition.single) (:arg :explicit 0 (:fv FV16)) (:arg :proof 1 (:proof-of (:app (:c LT.lt) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LT... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":20452,"sourceStart":20448,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20454,"sourceStart":20453,"tag":"a... | [] | [{"source":"Composition.eq_single_iff_length","source_end":20486,"source_start":20454,"syntax_kind":"ident"},{"source":"ne_of_gt hd.2","source_end":20501,"source_start":20488,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 31 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6cc6f1cd284882cff3ffd8f6b946b75eac6246d3dc30770112c647e42de740c3 | 21d9ea50ae169f7324cbba63be04006be4d06d5958aab3b1517c021a4d1468b9 | eb58b12eef8be466f037b30749a6b07a7ba958a704649c8840650b94aab715bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,331 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | symm | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ d ∈ compPartialSumTarget 2 (n + 1) n, ∏ j : Fin d.snd.lengt... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ e ∈ compPartialSumSource 2 (n + 1) n, ∏ j : Fin e.fst, r * ... | ((:c Eq) (:c Real) ((:c Finset.sum) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0))) (:c Real) (:c Real.instAddCommMonoid) ((:c FormalMultilinearSeries.compPartialSumTarget) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:app (:c Composition) (:arg :explicit 0 0)))))) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"symm","sourceEnd":20719,"sourceStart":20715,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.symm","source":"symm","sourceEnd":20719,"sourceStart":20715,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 40 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e75e958583d7f5bbc352011145c6e8dc431e984d5801f5513fd3da475070dc2 | 8d10b4206054df56e4e3710143c0bc4f5c55bffe170dd6e64c92f3d4ec62914d | f97373c83b943be1711d624ac8176e49b7c19e0f5ce55ad3a0ad56d8d1aae1fa | 0345f2e16f174bafc0a825de06665da8a746de038b255ca26917496432d6bbac |
cat-searcher/leandojo-benchmark-4-random | test | 1,332 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>FormalMultilinearSeries.compChangeOfVariables_sum</a> | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ e ∈ compPartialSumSource 2 (n + 1) n, ∏ j : Fin e.fst, r * ... | case h
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∀ (e : (n : ℕ) × (Fin n → ℕ)) (he : e ∈ compPartialSum... | ((:c Eq) (:c Real) ((:c Finset.sum) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat)))) (:c Real) (:c Real.instAddCommMonoid) ((:c FormalMultilinearSeries.compPartialSumSource) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 0)) (:c Nat)))))) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"apply","sourceEnd":20731,"sourceStart":20726,"tag":"atom"},{"name":"FormalMultilinearSeries.compChangeOfVariables_sum","semanticRole":"global","source":"compChangeOfVariables_sum","sourceEnd":20757,"sourceStart":20732,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply compCha... | [] | [{"source":"compChangeOfVariables_sum","source_end":20757,"source_start":20732,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 41 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bd998d02a7c5e694f0666158431e81afebc9b766cfa475900aab226227ead71e | 0345f2e16f174bafc0a825de06665da8a746de038b255ca26917496432d6bbac | b28cbd5e525ca4c6cb13623718163959896ae29b17cc06a8d564e484144b42ca | 20ddd7ad10c4d86a26308830d7a170f2d29029573f3d9d6b01aa3698087533d0 |
cat-searcher/leandojo-benchmark-4-random | test | 1,333 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨k, blocks_fun⟩ H | case h
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∀ (e : (n : ℕ) × (Fin n → ℕ)) (he : e ∈ compPartialSum... | case h.mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun⟩ ∈ co... | (:forall e ((:c Sigma) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat)))) (:forall he ((:c Membership.mem) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat)))) ((:c Finset) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))))) ((:c Finset.instMembership) ((:... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:forall e :explicit (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 0)) (:c Nat))))) (:forall he :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rintro","sourceEnd":20770,"sourceStart":20764,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":20774,"sourceStart":20771,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":20775,"sou... | [{"role":"fresh_name","source":"k","source_end":20775,"source_start":20774,"syntax_kind":"ident"},{"role":"fresh_name","source":"blocks_fun","source_end":20787,"source_start":20777,"syntax_kind":"ident"},{"role":"fresh_name","source":"H","source_end":20792,"source_start":20791,"syntax_kind":"ident"}] | [{"source":"⟨k, blocks_fun⟩","source_end":20790,"source_start":20771,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 42 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcc51e894f85a0a5981fc63fa7fbc29855f2c550e265859ff61d4a58fadf39e5 | 20ddd7ad10c4d86a26308830d7a170f2d29029573f3d9d6b01aa3698087533d0 | 4386b7e59216dd9347d5f701fc212283eb4677197215e8513ddce5a83320bd64 | 2c8db29f35b8e0e4818bd0c5accb355176d7080762e39f1fb6e242952bb2e214 |
cat-searcher/leandojo-benchmark-4-random | test | 1,334 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have K : (<a>FormalMultilinearSeries.compChangeOfVariables</a> 2 (n + 1) n ⟨k, blocks_fun⟩ H).snd.length = k := by simp | case h.mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun⟩ ∈ co... | case h.mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun⟩ ∈ co... | ((:c Eq) (:c Real) ((:c Finset.prod) ((:c Fin) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) ((:c Sigma.mk) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) (:fv _uniq.402266) (:fv _uniq.402267)))) (:c Real) (:c Real.instCommMonoid) ((:c Finset.univ) ((:c Fin) ((:c Sigma... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"have","sourceEnd":20803,"sourceStart":20799,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"K","sourceEnd":20805,"sourceStart":20804,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"K","sourceEnd":20805,"sourceStart":20804,"tag":"node"... | [] | [{"source":"(compChangeOfVariables 2 (n + 1) n ⟨k, blocks_fun⟩ H).snd.length = k","source_end":20880,"source_start":20808,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 43 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6bb93732a365901ad37b10ceeb7335503ceee306c4d6aface10526df1324f8e | 2c8db29f35b8e0e4818bd0c5accb355176d7080762e39f1fb6e242952bb2e214 | 9823eb9c2d3216e1d52da1ba4c11961f70c805676fae4d168f0ef3ee6363ea89 | 446502798847aea94d103c61bd66b5e70d9833ba84888857db5e24170f8a22bd |
cat-searcher/leandojo-benchmark-4-random | test | 1,335 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr 2 <;> try rw [K] | case h.mk
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun⟩ ∈ co... | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | ((:c Eq) (:c Real) ((:c Finset.prod) ((:c Fin) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) ((:c Sigma.mk) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) (:fv _uniq.402266) (:fv _uniq.402267)))) (:c Real) (:c Real.instCommMonoid) ((:c Finset.univ) ((:c Fin) ((:c Sigma... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"source":"congr","sourceEnd":20903,"sourceStart":20898,"tag":"atom"},{"children":[{"children":[{"source":"2","sourceEnd":20905,"sourceStart":20904,"tag":"atom"}],"kind":"num","source":"2","sourceEnd":20905,"sourceStart":20904,"tag":"node"}],"kind":"null","source":"2","sourceEnd":20905,"source... | [] | [{"source":"K","source_end":20919,"source_start":20918,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 46 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d396f103c2cbf4bd04b828e595649ddff3a31c835bf870de0d72d3cd498d32ef | 446502798847aea94d103c61bd66b5e70d9833ba84888857db5e24170f8a22bd | 31c95a6612e6f253c387b8b6b64fdeb9ee527f06dcab15e29ba0fca6374eb2b1 | 74f4c038ff5eec922e12c49fc274564fbf7f1a35af5eb872784880d9029cc584 |
cat-searcher/leandojo-benchmark-4-random | test | 1,336 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Fin.heq_fun_iff</a> K.symm] | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | ((:c HEq) (:forall _ ((:c Fin) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) ((:c Sigma.mk) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) (:fv _uniq.402266) (:fv _uniq.402267)))) (:c Real)) (:lambda j ((:c Fin) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c HEq) (:arg :implicit-type 0 (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV16)) (:arg :explicit 3 (:fv FV17))))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":20929,"sourceStart":20927,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20931,"sourceStart":20930,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Fin... | [] | [{"source":"Fin.heq_fun_iff K.symm","source_end":20953,"source_start":20931,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 72 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26b130c4725a7791e14c681afdaa79b7b1bd16df710266be5171fd6eb1973453 | 74f4c038ff5eec922e12c49fc274564fbf7f1a35af5eb872784880d9029cc584 | 173750c247b02bcda4d65994b35c8e9c069a3d8ad3093bc340b134fbde4720a8 | d490e07d5672e2f1fde3fef69f282cfeeba3926224ca2e660e93fa574221bdb6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,337 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro j | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | (:forall i ((:c Fin) (:fv _uniq.402266)) ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.390711) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:forall i :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV16))) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"intro","sourceEnd":20966,"sourceStart":20961,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":20968,"sourceStart":20967,"tag":"identifier"}],"kind":"null","source":"j","sourceEnd":20968,"sourceStart":20967,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"j","source_end":20968,"source_start":20967,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 75 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4bbe062bce6a73b95660b4512ea248fde75fa2723dbfd04a344714a3797e1f07 | d490e07d5672e2f1fde3fef69f282cfeeba3926224ca2e660e93fa574221bdb6 | e5978ac39d65faffab38e22ab77f5f70254d2c1bc80e72cf58bbb06a2cf57747 | 9a87b93e75766b094f8bcc8b69262fc9420841cf88af0cbeae58aab85032ef27 |
cat-searcher/leandojo-benchmark-4-random | test | 1,338 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>FormalMultilinearSeries.compChangeOfVariables_blocksFun</a>] | case h.mk.h.e_5
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.390711) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":20977,"sourceStart":20975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20979,"sourceStart":20978,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"FormalMultilinea... | [] | [{"source":"compChangeOfVariables_blocksFun","source_end":21010,"source_start":20979,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 76 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2958927c7492d3c0b4c70157a75afbd12cfd0f6b18a47ae4de7dfc96b8787edc | 9a87b93e75766b094f8bcc8b69262fc9420841cf88af0cbeae58aab85032ef27 | 8fe39c6940d8ae31cb4b20796201419a638a6a71bb91c87d717c76e5b824314c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,339 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks_fun⟩ ∈ compPartialS... | ((:c Eq) (:c Nat) ((:c Composition.length) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) ((:c Composition) 0)) ((:c FormalMultilinearSeries.compChangeOfVariables) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _un... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Composition.length) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Sigma.snd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c FormalMultilinearSeries.compChangeOfVariables) (:arg :explicit 0 (:app (:c OfNat.ofNat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":20891,"sourceStart":20887,"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.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 45 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f43193586a578e1584c250d3b7c007d988e156a17deba7b28434b2f9ce61d7e | 78a6e041660508359e56b2703b9e12b79fea23c9f2777028b6b6ce703a167e3d | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,340 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [K] | case h.mk.h.e_4.e_2
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
k : ℕ
blocks_fun : Fin k → ℕ
H : ⟨k, blocks... | ((:c HEq) ((:c Fintype) ((:c Fin) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) ((:c Sigma.mk) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat))) (:fv _uniq.402266) (:fv _uniq.402267))))) ((:c Fin.fintype) ((:c Sigma.fst) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c HEq) (:arg :implicit-type 0 (:app (:c Fintype) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Sigma.fst) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Sigma.mk) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV16)) (:arg :explicit 3 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":20916,"sourceStart":20914,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20918,"sourceStart":20917,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"K","source_end":20919,"source_start":20918,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 62 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8bf7eee7bc2c610c7c5cdadf9897b483c0c375625e30c5064e74885305583fa9 | 8f960f4bc9b29de0c97486a479d08481ac77b68f6d83ac205fdf479578ec2982 | 568f9546d445385abadbdf764d15119756743dc94a8031802e3c8f41f446a53c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,341 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>FormalMultilinearSeries.compPartialSumSource</a>, ← <a>Finset.sum_sigma'</a> (<a>Finset.Ico</a> 2 (n + 1)) (fun k : ℕ => (<a>Fintype.piFinset</a> fun _ : <a>Fin</a> k => <a>Finset.Ico</a> 1 n : <a>Finset</a> (<a>Fin</a> k → ℕ))) (fun n e => ∏ j : <a>Fin</a> n, r * (a ^ e j * p (e j)))] | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ e ∈ compPartialSumSource 2 (n + 1) n, ∏ j : Fin e.fst, r * ... | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ a_1 ∈ Ico 2 (n + 1), ∑ s ∈ Fintype.piFinset fun x => Ico 1 ... | ((:c Eq) (:c Real) ((:c Finset.sum) ((:c Sigma) (:c Nat) (:lambda n (:c Nat) (:forall _ ((:c Fin) 0) (:c Nat)))) (:c Real) (:c Real.instAddCommMonoid) ((:c FormalMultilinearSeries.compPartialSumSource) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2))) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c inst... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lambda n :explicit (:c Nat) (:forall _ :explicit (:app (:c Fin) (:arg :explicit 0 0)) (:c Nat)))))) (:arg :implicit-type 1 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"rw","sourceEnd":21104,"sourceStart":21102,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21106,"sourceStart":21105,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"FormalMultilinea... | [] | [{"source":"compPartialSumSource","source_end":21126,"source_start":21106,"syntax_kind":"ident"},{"source":"sum_sigma' (Ico 2 (n + 1))\n (fun k : ℕ => (Fintype.piFinset fun _ : Fin k => Ico 1 n : Finset (Fin k → ℕ)))\n (fun n e => ∏ j : Fin n, r * (a ^ e j * p (e j)))","source_end":21324,"source_start... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 83 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6b3c3a923daa42aa82ee285cbddfc9280811e628f48b48225314ac535af52d3 | 8121add1559ab0022da6295cd6d18ed9404b5c7773e3e65ea34771777e1ef5b8 | 671f02596c8d465c27941d73ab5157807f454eb1610f117d90038d80daa6c695 | 8cf8da65f00417bf47bfd0c85b0087ee3114b97cebf0bb9fff46a654ee3e5ae6 |
cat-searcher/leandojo-benchmark-4-random | test | 1,342 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr! with j | 𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
⊢ ∑ a_1 ∈ Ico 2 (n + 1), ∑ s ∈ Fintype.piFinset fun x => Ico 1 ... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ∑ s ∈ Fintype.piFinset fu... | ((:c Eq) (:c Real) ((:c Finset.sum) (:c Nat) (:c Real) (:c Real.instAddCommMonoid) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatN... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :explicit 3 (:app (:c Finset.Ico) (:arg :implicit-type 0 (:c Nat)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"congr!","sourceEnd":21338,"sourceStart":21332,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":21343,"sourceStart":21339,"tag":"atom"},{"children":[{"children":[{"children":[{"sem... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 87 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec751a844e005e337716e155979d1891a71a19aef0341cc8d332fb1f515b22a2 | 8cf8da65f00417bf47bfd0c85b0087ee3114b97cebf0bb9fff46a654ee3e5ae6 | 95b3624565ca31156be57f1e37c926c1877bd48d2b2f694a26057e61586930b5 | 2192052537d7907d745983e1fde9e268967d33eb3196ce04dbd455f4eb2540af |
cat-searcher/leandojo-benchmark-4-random | test | 1,343 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← @<a>MultilinearMap.mkPiAlgebra_apply</a> ℝ (<a>Fin</a> j) _ ℝ] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ∑ s ∈ Fintype.piFinset fu... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ (∑ x ∈ Fintype.piFinset f... | ((:c Eq) (:c Real) ((:c Finset.sum) (:forall a ((:c Fin) (:fv _uniq.406690)) (:c Nat)) (:c Real) (:c Real.instAddCommMonoid) ((:c Fintype.piFinset) ((:c Fin) (:fv _uniq.406690)) ((:c instDecidableEqFin) (:fv _uniq.406690)) ((:c Fin.fintype) (:fv _uniq.406690)) (:lambda _ ((:c Fin) (:fv _uniq.406690)) (:c Nat)) (:lambda... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:forall a :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV16))) (:c Nat))) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":21356,"sourceStart":21352,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":21361,"sourceStart":21357,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":213... | [] | [{"source":"@MultilinearMap.mkPiAlgebra_apply ℝ (Fin j) _ ℝ","source_end":21418,"source_start":21367,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 88 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 41fdfe67b03ab1a139aa2ce2b0c90f228101f5b92ddc4b2311ef2a9ef37182cf | 2192052537d7907d745983e1fde9e268967d33eb3196ce04dbd455f4eb2540af | 9a082daf6c8cf71ad15c5e75fb943dc191cda0a19283a7d6bfa9582ed3cb7f9d | c7cb3504a5eb0a968b3231dec93c3b7a90db98958773c63401b6c9ec8913d5b1 |
cat-searcher/leandojo-benchmark-4-random | test | 1,344 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>MultilinearMap.map_sum_finset</a> (<a>MultilinearMap.mkPiAlgebra</a> ℝ (<a>Fin</a> j) ℝ) fun _ (m : ℕ) => r * (a ^ m * p m)] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ (∑ x ∈ Fintype.piFinset f... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ((MultilinearMap.mkPiAlge... | ((:c Eq) (:c Real) ((:c Finset.sum) (:forall a ((:c Fin) (:fv _uniq.406690)) (:c Nat)) (:c Real) (:c Real.instAddCommMonoid) ((:c Fintype.piFinset) ((:c Fin) (:fv _uniq.406690)) ((:c instDecidableEqFin) (:fv _uniq.406690)) ((:c Fin.fintype) (:fv _uniq.406690)) (:lambda _ ((:c Fin) (:fv _uniq.406690)) (:c Nat)) (:lambda... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:forall a :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV16))) (:c Nat))) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":21430,"sourceStart":21426,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":21435,"sourceStart":21431,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":214... | [] | [{"source":"MultilinearMap.map_sum_finset (MultilinearMap.mkPiAlgebra ℝ (Fin j) ℝ) fun _ (m : ℕ) =>\n r * (a ^ m * p m)","source_end":21570,"source_start":21449,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 89 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 081fe625b10430f4b92432a629c203152cafe9df8c7f6b00273c143afdd76981 | c7cb3504a5eb0a968b3231dec93c3b7a90db98958773c63401b6c9ec8913d5b1 | 060a9e7ea6d3dfdd2e205b95e41436fdbd1aa8e4cfcedfb6e377413694301861 | d0cf698e9b2bf9147f731d37ef2276f45c8a03fd3cfbb9e25525a7a318d9ab1d |
cat-searcher/leandojo-benchmark-4-random | test | 1,345 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>MultilinearMap.mkPiAlgebra_apply</a>] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ((MultilinearMap.mkPiAlge... | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ∏ i : Fin j, ∑ j ∈ Ico 1 ... | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c MultilinearMap) (:c Real) ((:c Fin) (:fv _uniq.406690)) (:lambda _ ((:c Fin) (:fv _uniq.406690)) (:c Real)) (:c Real) ((:c CommSemiring.toSemiring) (:c Real) (:c Real.instCommSemiring)) (:lambda i ((:c Fin) (:fv _uniq.406690)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MultilinearMap) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Fin) (:arg :explicit 0 (:fv FV16)))) (:arg :explicit 2 (:lambda _ :explicit (:app (:c Fin) (:arg :explicit 0 (:fv FV16)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":21582,"sourceStart":21578,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":21587,"sourceStart":21583,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":215... | [] | [{"source":"MultilinearMap.mkPiAlgebra_apply","source_end":21621,"source_start":21589,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 90 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf7ee4fbcf8b3b08a4d732dbc406defd6485833c582c7956bb9ada00c302584b | d0cf698e9b2bf9147f731d37ef2276f45c8a03fd3cfbb9e25525a7a318d9ab1d | 813918f902e0e00078e6f1305996a62e2f1ce9a44a8f4f33b717baea8e7412b3 | cc0a11e846f914ca7d7937a5450b2ceae3801b0a50fd5588a115518fffe46ad3 |
cat-searcher/leandojo-benchmark-4-random | test | 1,346 | FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1 | Mathlib/Analysis/Analytic/Inverse.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Finset.prod_const</a>, ← <a>Finset.mul_sum</a>, <a>mul_pow</a>] | case a
𝕜 : Type u_1
inst✝⁴ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace 𝕜 E
F : Type u_3
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
n : ℕ
p : ℕ → ℝ
hp : ∀ (k : ℕ), 0 ≤ p k
r a : ℝ
hr : 0 ≤ r
ha : 0 ≤ a
j : ℕ
a✝ : j ∈ Ico 2 (n + 1)
⊢ ∏ i : Fin j, ∑ j ∈ Ico 1 ... | ((:c Eq) (:c Real) ((:c Finset.prod) ((:c Fin) (:fv _uniq.406690)) (:c Real) ((:c CommSemiring.toCommMonoid) (:c Real) (:c Real.instCommSemiring)) ((:c Finset.univ) ((:c Fin) (:fv _uniq.406690)) ((:c Fin.fintype) (:fv _uniq.406690))) (:lambda i ((:c Fin) (:fv _uniq.406690)) ((:c Finset.sum) (:c Nat) (:c Real) ((:c NonU... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c NontriviallyNormedField) (:fv _uniq.388565))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c NormedAddCommGroup) (:fv _uniq.388571))"},{"name":"inst✝²","sexp":"((:c NormedSpace) (:fv _uniq.388565) (:fv _uniq.388571) ((:c Non... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Finset.prod) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:fv FV16)))) (:arg :implicit-type 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :explicit 3 (:app (:c Finset.univ) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c NontriviallyNormedFi... | {"children":[{"source":"simp","sourceEnd":21633,"sourceStart":21629,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21635,"sourceStart":21634,"tag":"a... | [] | [{"source":"prod_const","source_end":21645,"source_start":21635,"syntax_kind":"ident"},{"source":"mul_sum","source_end":21658,"source_start":21651,"syntax_kind":"ident"},{"source":"mul_pow","source_end":21667,"source_start":21660,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.388565","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.388568","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":implicit","context_index":2,"int... | 39 | 91 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8878adeaac19aa69d6ff1456af03c4e0a6b2e1af80894ee9e824d4b2b25a7f9a | cc0a11e846f914ca7d7937a5450b2ceae3801b0a50fd5588a115518fffe46ad3 | 6b4cda8fed6e92d5e4a06972b1f9942d6e6a8898729a7c537ef4caa50bba74e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,347 | Matrix.det_succ_row_zero | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.det_transpose</a> A, <a>Matrix.det_succ_column_zero</a>] | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
⊢ A.det = ∑ j : Fin n.succ, (-1) ^ ↑j * A 0 j * (A.submatrix Fin.succ j.succAbove).det | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
⊢ ∑ i : Fin n.succ, (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ).det =
∑ j : Fin n.succ, (-1) ^ ↑j * A 0 j * (A.subm... | ((:c Eq) (:fv _uniq.336827) ((:c Matrix.det) ((:c Fin) ((:c Nat.succ) (:fv _uniq.337951))) ((:c instDecidableEqFin) ((:c Nat.succ) (:fv _uniq.337951))) ((:c Fin.fintype) ((:c Nat.succ) (:fv _uniq.337951))) (:fv _uniq.336827) (:fv _uniq.336830) (:fv _uniq.337952)) ((:c Finset.sum) ((:c Fin) ((:c Nat.succ) (:fv _uniq.337... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.336801))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.336801))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.336798))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Matrix.det) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV9)))))) (:arg :instance 1 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.suc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":instance-im... | {"children":[{"source":"rw","sourceEnd":35444,"sourceStart":35442,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35446,"sourceStart":35445,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":35449,"sourceSt... | [] | [{"source":"det_transpose A","source_end":35465,"source_start":35450,"syntax_kind":"Lean.Parser.Term.app"},{"source":"det_succ_column_zero","source_end":35487,"source_start":35467,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":instance-implicit","context_index":2,"interna... | 151 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ccce9ebea7d59a779ef9c42a8b1ce8d7b2d3172996970466f9f134ca70ee96e1 | 217041c7fb6c2d58f16f040c364ffc81c232c7f5e0479b840ea7942be866fec4 | 6bde1788c8ff8643776dba0d87c266652f2480c6de3c77aea8ef79d5f232bd6b | 2547ba5cc672a5ed807101e7f441810b5262d2d00f77a5bedeed550dd33bdd5d |
cat-searcher/leandojo-benchmark-4-random | test | 1,348 | Matrix.det_succ_row_zero | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Finset.sum_congr</a> <a>rfl</a> fun i _ => ?_ | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
⊢ ∑ i : Fin n.succ, (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ).det =
∑ j : Fin n.succ, (-1) ^ ↑j * A 0 j * (A.subm... | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
i : Fin n.succ
x✝ : i ∈ univ
⊢ (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ).det =
(-1) ^ ↑i * A 0 i * (A.submatrix F... | ((:c Eq) (:fv _uniq.336827) ((:c Finset.sum) ((:c Fin) ((:c Nat.succ) (:fv _uniq.337951))) (:fv _uniq.336827) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.336827) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.336827) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiri... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.336801))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.336801))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.336798))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Finset.sum) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV9)))))) (:arg :implicit-type 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV6))))) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":instance-im... | {"children":[{"source":"refine","sourceEnd":35497,"sourceStart":35491,"tag":"atom"},{"children":[{"name":"Finset.sum_congr","semanticRole":"global","source":"Finset.sum_congr","sourceEnd":35514,"sourceStart":35498,"tag":"identifier"},{"children":[{"name":"rfl","semanticRole":"global","source":"rfl","sourceEnd":35518,"s... | [] | [{"source":"Finset.sum_congr rfl fun i _ => ?_","source_end":35532,"source_start":35498,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":instance-implicit","context_index":2,"interna... | 151 | 8 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 91ed5e00d226b95399d29e72ce1a3d94507173cc29bfe28d788b8a783a8b784e | 2547ba5cc672a5ed807101e7f441810b5262d2d00f77a5bedeed550dd33bdd5d | c1bb72d549b2d038b69f6cd9eb45d57fe4a89bb73855b3a20afcb3d137b5172f | bbffacbd1b41c5a0fa43652bda09b6c5045c334f6e026aa4f0e3c57e7f929882 |
cat-searcher/leandojo-benchmark-4-random | test | 1,349 | Matrix.det_succ_row_zero | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Matrix.det_transpose</a>] | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
i : Fin n.succ
x✝ : i ∈ univ
⊢ (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ).det =
(-1) ^ ↑i * A 0 i * (A.submatrix F... | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
i : Fin n.succ
x✝ : i ∈ univ
⊢ (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ)ᵀ.det =
(-1) ^ ↑i * A 0 i * (A.submatrix ... | ((:c Eq) (:fv _uniq.336827) ((:c HMul.hMul) (:fv _uniq.336827) (:fv _uniq.336827) (:fv _uniq.336827) ((:c instHMul) (:fv _uniq.336827) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.336827) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.336827) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:fv ... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.336801))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.336801))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.336798))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:fv FV6)) (:arg :implicit-type 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":instance-im... | {"children":[{"source":"rw","sourceEnd":35537,"sourceStart":35535,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35539,"sourceStart":35538,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":35542,"sourceSt... | [] | [{"source":"det_transpose","source_end":35556,"source_start":35543,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":instance-implicit","context_index":2,"interna... | 151 | 9 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c5a410cd721126bf0099edd431a46906f8b7a0949857b10bf457720e53e09fd | bbffacbd1b41c5a0fa43652bda09b6c5045c334f6e026aa4f0e3c57e7f929882 | 09017d9e5a620df9cd27120dfaa3309dac8fffefd0b2fd084882ca3800170179 | 7d0a53155e66aa5aa741762ee190e67c9af7786b7f85882b6ca97e85d5086e1e |
cat-searcher/leandojo-benchmark-4-random | test | 1,350 | Matrix.det_succ_row_zero | Mathlib/LinearAlgebra/Matrix/Determinant/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Matrix.transpose_apply</a>, <a>Matrix.transpose_submatrix</a>, <a>Matrix.transpose_transpose</a>] | m : Type u_1
n✝ : Type u_2
inst✝⁴ : DecidableEq n✝
inst✝³ : Fintype n✝
inst✝² : DecidableEq m
inst✝¹ : Fintype m
R : Type v
inst✝ : CommRing R
n : ℕ
A : Matrix (Fin n.succ) (Fin n.succ) R
i : Fin n.succ
x✝ : i ∈ univ
⊢ (-1) ^ ↑i * Aᵀ i 0 * (Aᵀ.submatrix i.succAbove Fin.succ)ᵀ.det =
(-1) ^ ↑i * A 0 i * (A.submatrix ... | ((:c Eq) (:fv _uniq.336827) ((:c HMul.hMul) (:fv _uniq.336827) (:fv _uniq.336827) (:fv _uniq.336827) ((:c instHMul) (:fv _uniq.336827) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.336827) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.336827) ((:c NonUnitalCommRing.toNonUnitalNonAssocCommRing) (:fv ... | [{"name":"m","sexp":"(:sort (+ u_1 1))"},{"name":"n✝","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c DecidableEq) (:fv _uniq.336801))"},{"name":"inst✝³","sexp":"((:c Fintype) (:fv _uniq.336801))"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.336798))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _un... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:fv FV6)) (:arg :implicit-type 2 (:fv FV6)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:fv FV6)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"name":"n✝","sexp":"(:sort Type)"},{"binder_role":":instance-im... | {"children":[{"source":"simp","sourceEnd":35564,"sourceStart":35560,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":35569,"sourceStart":35565,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":355... | [] | [{"source":"transpose_apply","source_end":35586,"source_start":35571,"syntax_kind":"ident"},{"source":"transpose_submatrix","source_end":35607,"source_start":35588,"syntax_kind":"ident"},{"source":"transpose_transpose","source_end":35628,"source_start":35609,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.336798","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.336801","is_instance":false,"is_let":false,"user_name":"n✝"},{"binder_role":":instance-implicit","context_index":2,"interna... | 151 | 12 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 331b4a78aceabf1c23d1d906d1f1929e89aacedf2b071ac815438d97887f7059 | 7d0a53155e66aa5aa741762ee190e67c9af7786b7f85882b6ca97e85d5086e1e | 398c43c4815bff095bfa52166d4275cd7fdc18be6123b4aea4bf6aedaa5b4aac | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 1,351 | Real.cos_sq_le_one | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.sin_sq_add_cos_sq</a> x] | x y : ℝ
⊢ cos x ^ 2 ≤ 1 | x y : ℝ
⊢ cos x ^ 2 ≤ sin x ^ 2 + cos x ^ 2 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c Real.cos) (:fv _uniq.166638)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One... | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}] | (: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 HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.166638","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.166640","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"}] | {"children":[{"source":"rw","sourceEnd":35332,"sourceStart":35330,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35334,"sourceStart":35333,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":35337,"sourceSt... | [] | [{"source":"sin_sq_add_cos_sq x","source_end":35357,"source_start":35338,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.166638","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.166640","is_instance":false,"is_let":false,"user_name":"y"}] | 361 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a038017b5cf1d729fa8103c2c8c49fc8d29bb1954cafa48033f998ccfb4fffdc | 767a44e0c16bd514079b294484247687b0af8597719f1c8d58a78ca61ea6ba77 | 6db5fe09f72c748960c627d590cb8bbadd011b99eac83416a59a58e4fc3fb182 | 4a71a7ca317bc4ed400bc9859001d172fbf604c9f7992f4efbae399f7f7d0745 |
cat-searcher/leandojo-benchmark-4-random | test | 1,352 | Real.cos_sq_le_one | Mathlib/Data/Complex/Exponential.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_add_of_nonneg_left</a> (<a>sq_nonneg</a> _) | x y : ℝ
⊢ cos x ^ 2 ≤ sin x ^ 2 + cos x ^ 2 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c Real.cos) (:fv _uniq.166638)) ((:c OfNat.ofNat) (:c Nat) (:lit 2) ((:c instOfNatNat) (:lit 2)))) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real)... | [{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}] | (: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 HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:a... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.166638","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.166640","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"}] | {"children":[{"source":"exact","sourceEnd":35365,"sourceStart":35360,"tag":"atom"},{"children":[{"name":"le_add_of_nonneg_left","semanticRole":"global","source":"le_add_of_nonneg_left","sourceEnd":35387,"sourceStart":35366,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":35389,"sourceStart":35388... | [] | [{"source":"le_add_of_nonneg_left (sq_nonneg _)","source_end":35401,"source_start":35366,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.166638","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.166640","is_instance":false,"is_let":false,"user_name":"y"}] | 361 | 8 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8905a4573d1a1d90b9ebbc63dd423bf5c3097a33acff29aca97dae5653087291 | 4a71a7ca317bc4ed400bc9859001d172fbf604c9f7992f4efbae399f7f7d0745 | c4a68e5a9e2988a693a522eda08b21f445aeff5de85679cf5fb245bde92acaa7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 |
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