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cat-searcher/leandojo-benchmark-4-random | test | 2,880 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨s, hs, rfl⟩ | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ ∀ ... | case refine_1.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆... | (:forall b (:fv _uniq.84775) (:forall _ ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) 0 ((:c Set.image) ((:c Set) (:fv _uniq.84775)) (:fv _uniq.84775) ((:c SupSet.sSup) (:fv _uniq.84775) ((:c CompleteLattice.toSupSet) (:fv _uniq.84775) (:fv _uniq.84778))... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:forall b :strict-implicit (:fv FV1) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rintro","sourceEnd":28270,"sourceStart":28264,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":28272,"sourceStart":28271,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":28272,"sourceStart":28271,"tag":"node"}],"kind":"Lean.Parser... | [{"role":"fresh_name","source":"s","source_end":28277,"source_start":28276,"syntax_kind":"ident"},{"role":"fresh_name","source":"hs","source_end":28281,"source_start":28279,"syntax_kind":"ident"}] | [{"source":"⟨s, hs, rfl⟩","source_end":28289,"source_start":28273,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 19 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffee3ccf8367e1aa0698269e52b26879cd3cade0f742617f6b40f477bf0e449e | 3bb45706f81c3892065aa2e1eb3eb94c86cd146a403f3d23754e15b197186170 | 62507042a7f5756538010dc2f9b99d437c1e978cba0c23751884a342ae7a0f6f | e22a28368f0d1326b5cb9b21314faeb43eac199b830d51ed871ac2dca0fa34dc |
cat-searcher/leandojo-benchmark-4-random | test | 2,881 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hc1 hs).2.1 | case refine_1.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":28301,"sourceStart":28296,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":28303,"sourceStart":28302,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hc1","sourceEnd":28306,"sourceStart":28303,"tag":"identifier"},{"ch... | [] | [{"source":"(hc1 hs).2.1","source_end":28314,"source_start":28302,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 20 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c9ca58c448fc3a25ea8c805d1eb9158a7dee2451c15652396c593b3b010738ad | e22a28368f0d1326b5cb9b21314faeb43eac199b830d51ed871ac2dca0fa34dc | 0782a76f24b592788b65a0b1eb7aab7f3d5103d32c8b103c06c11b770f82ffb2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,882 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>directedOn_image</a>] | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ Di... | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ Di... | ((:c DirectedOn) (:fv _uniq.84775) (:lambda _ (:fv _uniq.84775) (:lambda _ (:fv _uniq.84775) ((:c LE.le) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c DirectedOn) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda _ :explicit (:fv FV1) (:lambda _ :explicit (:fv FV1) (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 1) (:arg :explicit 3 0))))) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":28324,"sourceStart":28322,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28326,"sourceStart":28325,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"directedOn_image... | [] | [{"source":"directedOn_image","source_end":28342,"source_start":28326,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 25 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 75d3ff1f1dfe4a3b7529f5b5af51873c283915b5b187de8d83b009d35940be14 | 242347adc84d4765d0bc8e3e3431b695e8a2b2596dea1d3cb02a8511226ff301 | d816c6be4cfb4b3ee2b8dfc3ea71bb36951af3ea57f657e4ca881c17234767df | 3d9b9425118b0c16252e2d280660750a89538ac030518e95dedde7b2bb3c2ef3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,883 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hc2.directedOn.mono @fun s t => <a>sSup_le_sSup</a> | case refine_1
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
c : Set (Set α)
hc1 : c ⊆ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}
hc2 : IsChain (fun x x_1 => x ⊆ x_1) c
⊢ Di... | ((:c DirectedOn) ((:c Set) (:fv _uniq.84775)) ((:c Order.Preimage) ((:c Set) (:fv _uniq.84775)) (:fv _uniq.84775) ((:c SupSet.sSup) (:fv _uniq.84775) ((:c CompleteLattice.toSupSet) (:fv _uniq.84775) (:fv _uniq.84778))) (:lambda _ (:fv _uniq.84775) (:lambda _ (:fv _uniq.84775) ((:c LE.le) (:fv _uniq.84775) ((:c Preorder... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c DirectedOn) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c Order.Preimage) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c SupSet.sSup) (:arg :implicit-type 0 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":28355,"sourceStart":28350,"tag":"atom"},{"children":[{"source":"hc2.directedOn.mono","sourceEnd":28375,"sourceStart":28356,"tag":"identifier"},{"children":[{"children":[{"source":"@","sourceEnd":28377,"sourceStart":28376,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":2... | [] | [{"source":"hc2.directedOn.mono @fun s t => sSup_le_sSup","source_end":28400,"source_start":28356,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 28 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66abfa64512835e0d043a34c2f305088ca136119b8ee4e7a1330f6a8ceaa9414 | 3d9b9425118b0c16252e2d280660750a89538ac030518e95dedde7b2bb3c2ef3 | 1f43fc13ba800ed3456d035621e08044560839569091387eef9a81f081796f54 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,884 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.mem_union_right</a> _ (<a>Set.mem_singleton</a> _) | case refine_2.intro.intro.intro.intro
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind ... | ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) (:fv _uniq.86944) ((:c Union.union) ((:c Set) (:fv _uniq.84775)) ((:c Set.instUnion) (:fv _uniq.84775)) (:fv _uniq.86318) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.inst... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:fv FV14)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":29020,"sourceStart":29015,"tag":"atom"},{"children":[{"name":"Set.mem_union_right","semanticRole":"global","source":"Set.mem_union_right","sourceEnd":29040,"sourceStart":29021,"tag":"identifier"},{"children":[{"children":[{"source":"_","s... | [] | [{"source":"Set.mem_union_right _ (Set.mem_singleton _)","source_end":29064,"source_start":29021,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 56 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4839d94a137e465df12642ed1e8900040607061b4d4617300d972c624258d237 | 18b9c303a0efb1e6e010c4cf778ba922227c8cf375d826f11e3d16b7131789dc | ec42cadce7e1e08712ea5f990a4deffeba358d1c33883bb06780fa553b6d2c2b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,885 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | (:forall x (:fv _uniq.84775) (:forall hx ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) 0 ((:c Union.union) ((:c Set) (:fv _uniq.84775)) ((:c Set.instUnion) (:fv _uniq.84775)) (:fv _uniq.86318) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set) (:fv _u... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:forall x :explicit (:fv FV1) (:forall hx :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":29075,"sourceStart":29070,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":29077,"sourceStart":29076,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":29080,"sourceStart":29078,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":29077,"source_start":29076,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":29080,"source_start":29078,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 63 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07bf5945c70211cc01216d931600feda60ea53335ef03acfbda8914f8e2f7848 | 2820b66e3278cf5ffd42a042dd04dd55f5c17c4de190c667925305964a9db0f7 | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | 4029a3b9a182b446e7ecc952e7d55c9dfee7106a5f41f334b6688883e2f8625d |
cat-searcher/leandojo-benchmark-4-random | test | 2,886 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_union</a>, <a>Set.mem_singleton_iff</a>] at hx | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29087,"sourceStart":29085,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29089,"sourceStart":29088,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_union","... | [] | [{"source":"Set.mem_union","source_end":29102,"source_start":29089,"syntax_kind":"ident"},{"source":"hx","source_end":29132,"source_start":29130,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":29125,"source_start":29104,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 64 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 86ca99b48000320cff8505f00cbd5b42773b5e57955c6bcc7851257e61b72e87 | 4029a3b9a182b446e7ecc952e7d55c9dfee7106a5f41f334b6688883e2f8625d | 4b75a2e09bfbc16a664e0d91b6aded6c427e59eb72ad31af957c78ea931e77ee | cd69fcb0f6434795ecaf48e455cd7783f394c1ea568ac762bd3e8a15cfcdd235 |
cat-searcher/leandojo-benchmark-4-random | test | 2,887 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl | xa := <a>eq_or_ne</a> x a | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":29143,"sourceStart":29137,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":29147,"sourceStart":29144,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":29147,"sou... | [] | [{"source":"eq_or_ne x a","source_end":29168,"source_start":29156,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl | xa","source_end":29152,"source_start":29144,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 68 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3f641bb02dfc3e4a84f5fc755b76fb47327c31a963ad973137d902a786f894a8 | cd69fcb0f6434795ecaf48e455cd7783f394c1ea568ac762bd3e8a15cfcdd235 | fe3b4b4e239bd98ec69b21a5eea3592d1adbc62a4c0c4fc9ff6200ed1952ceb7 | 6fb53eca2515ffce326295b36f582b86d7221c17e531e69e857615f80328ea12 |
cat-searcher/leandojo-benchmark-4-random | test | 2,888 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_singleton</a>, <a>Set.insert_diff_of_mem</a>, <a>Set.union_singleton</a>] | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":29180,"sourceStart":29176,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":29185,"sourceStart":29181,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":291... | [] | [{"source":"Set.mem_singleton","source_end":29204,"source_start":29187,"syntax_kind":"ident"},{"source":"Set.insert_diff_of_mem","source_end":29228,"source_start":29206,"syntax_kind":"ident"},{"source":"Set.union_singleton","source_end":29249,"source_start":29230,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 73 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf4ca5a4b6298b5a3b83dc4a573b985b94931eb5134ec5cbf889cd29cc1e6df0 | da045addf46330fb94e82286ee8e14d6df36502239fa4ca7b97ff5f078917678 | d38e07ac3ce04392aaf938566fa1f7389dba3f9e0e29c73d40910edd1f8da670 | 370e2038f1f6df509bbf5ef43bd5272b061df7558245101c110518881c889fab |
cat-searcher/leandojo-benchmark-4-random | test | 2,889 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact con.mono_right ((<a>sSup_le_sSup</a> <a>Set.diff_subset</a>).<a>LE.le.trans</a> <a>le_sup_right</a>) | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":29262,"sourceStart":29257,"tag":"atom"},{"children":[{"source":"con.mono_right","sourceEnd":29277,"sourceStart":29263,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":29279,"sourceStart":29278,"tag":"atom"},{"children":[{"children":[{"children":[{"source... | [] | [{"source":"con.mono_right ((sSup_le_sSup Set.diff_subset).trans le_sup_right)","source_end":29329,"source_start":29263,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 74 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fddcd6ee0c3d8a1fc0cd7cfa82efae3e28bb66b61540ad24b14915b0da32259 | 370e2038f1f6df509bbf5ef43bd5272b061df7558245101c110518881c889fab | 4bd59ea366e0fa6339c2c1aac5b5eaa66a458519d7193537363b0c5adfdab351 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,890 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : (s ∪ {a}) \ {x} = s \ {x} ∪ {a} := by simp only [<a>Set.union_singleton</a>] rw [<a>Set.insert_diff_of_not_mem</a>] rw [<a>Set.mem_singleton_iff</a>] exact <a>Ne.symm</a> xa | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepen... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":29341,"sourceStart":29337,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":29343,"sourceStart":29342,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":29343,"sourceStart":29342,"tag":"node"... | [] | [{"source":"(s ∪ {a}) \\ {x} = s \\ {x} ∪ {a}","source_end":29381,"source_start":29346,"syntax_kind":"«term_=_»"},{"source":"Set.union_singleton","source_end":29426,"source_start":29407,"syntax_kind":"ident"},{"source":"Set.insert_diff_of_not_mem","source_end":29466,"source_start":29440,"syntax_kind":"ident"},{"source"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 79 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e4b49adbc297d76e696a8d1c1c264e98e35b230dd18c0a99635bb90ad3a0433 | c3fb531dfc1296e4b50423baa32a5782db186ab22c32128b81c360f52d433101 | d1a54b6434f8848ccba3670cc806cccff1fbc41270eccc58f865290debaeda0e | 62874af733166d7da29c32284197037909322197014a4a3c2aba7cc13f3d1f6d |
cat-searcher/leandojo-benchmark-4-random | test | 2,891 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h, <a>sSup_union</a>, <a>sSup_singleton</a>] | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepen... | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepen... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29536,"sourceStart":29534,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29538,"sourceStart":29537,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":21,"seman... | [] | [{"source":"h","source_end":29539,"source_start":29538,"syntax_kind":"ident"},{"source":"sSup_union","source_end":29551,"source_start":29541,"syntax_kind":"ident"},{"source":"sSup_singleton","source_end":29567,"source_start":29553,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 89 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6fe71844026386c0c1c65d83a2b21ae4deb9fbf66c57d79ca0a96ce01ab7205c | 62874af733166d7da29c32284197037909322197014a4a3c2aba7cc13f3d1f6d | 5e0effa998332ea2156f6bbfde37ba4d6ff38f42b5142ebd49822d6680f35b6d | 49a24377d033ae37891c8228ed131404c61ce747855d845ae702b8503b3adefb |
cat-searcher/leandojo-benchmark-4-random | test | 2,892 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (s_ind (hx.resolve_right xa)).<a>Disjoint.disjoint_sup_right_of_disjoint_sup_left</a> (a_dis_Sup_s.mono_right _).<a>Disjoint.symm</a> | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepen... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"apply","sourceEnd":29580,"sourceStart":29575,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":29590,"sourceStart":29589,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"s_ind","sourceEnd":29595,"sourceStart":29590,"tag":"identifier"},{"... | [] | [{"source":"(s_ind (hx.resolve_right xa)).disjoint_sup_right_of_disjoint_sup_left\n (a_dis_Sup_s.mono_right _).symm","source_end":29700,"source_start":29589,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 94 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e573d2ffad5dd48763a531e7c8073d5904e3927a20597fb7ec266e248c0a2742 | 49a24377d033ae37891c8228ed131404c61ce747855d845ae702b8503b3adefb | e55340c0014a7f3d21608741b5d9aca93ef699788ab33b7156c08a7512fb7c8a | 9d05ed9b5175075bb868f0d7e72cfbcd1cdc488e8159b6cf8d012c0aaa009219 |
cat-searcher/leandojo-benchmark-4-random | test | 2,893 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>sSup_insert</a>, <a>Set.insert_diff_singleton</a>, <a>Set.insert_eq_of_mem</a> (hx.resolve_right xa)] | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h✝ : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_... | ((:c LE.le) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))))) ((:c Sup.sup) (:fv _uniq.84775) ((:c SemilatticeSup.toS... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Sup.sup) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Sup) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV18)) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29709,"sourceStart":29707,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29711,"sourceStart":29710,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":29714,"sourceSt... | [] | [{"source":"sSup_insert","source_end":29726,"source_start":29715,"syntax_kind":"ident"},{"source":"Set.insert_diff_singleton","source_end":29753,"source_start":29728,"syntax_kind":"ident"},{"source":"Set.insert_eq_of_mem (hx.resolve_right xa)","source_end":29797,"source_start":29755,"syntax_kind":"Lean.Parser.Term.app"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 95 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b9648b9a22dbca927185096eff4510e426e1fa7c2aecef60151da07e1de1d3d5 | 9d05ed9b5175075bb868f0d7e72cfbcd1cdc488e8159b6cf8d012c0aaa009219 | 2b69b92c0ab4bcf665a787e12f717809b8001a5f854900e13debee1270f80421 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,894 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.union_singleton</a>] | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ((:c Eq) ((:c Set) (:fv _uniq.84775)) ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.84775)) ((:c Set.instSDiff) (:fv _uniq.84775)) ((:c Union.union) ((:c Set) (:fv _uniq.84775)) ((:c Set.instUnion) (:fv _uniq.84775)) (:fv _uniq.86318) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instSingle... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":29400,"sourceStart":29396,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":29405,"sourceStart":29401,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":294... | [] | [{"source":"Set.union_singleton","source_end":29426,"source_start":29407,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 81 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc6116a1de25ead67762803ef5b8c4aec6371fdf6ddf2b339327a72d22c1d3e7 | 3446215c5d7d5603a46fa925c76a152b08f2e6ab90a1cd586289eddd58716d98 | 6806b7603125bc9072faaa3be1020ee40e3a4abf645f07abaa23d773c87fae69 | f487760abd2b4d44cf562fd379aadf418e2a2cdafb7ed535b191169fbd85bcc1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,895 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.insert_diff_of_not_mem</a>] | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | case h
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependen... | ((:c Eq) ((:c Set) (:fv _uniq.84775)) ((:c SDiff.sdiff) ((:c Set) (:fv _uniq.84775)) ((:c Set.instSDiff) (:fv _uniq.84775)) ((:c Insert.insert) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instInsert) (:fv _uniq.84775)) (:fv _uniq.86944) (:fv _uniq.86318)) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :explicit 1 (:app (:c SDiff.sdiff) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c SDiff) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29438,"sourceStart":29436,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29440,"sourceStart":29439,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.insert_diff_... | [] | [{"source":"Set.insert_diff_of_not_mem","source_end":29466,"source_start":29440,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 82 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffad197600e160e05758eb76dd2fa77a457b839ad54d59dbddcd32adcc27baab | f487760abd2b4d44cf562fd379aadf418e2a2cdafb7ed535b191169fbd85bcc1 | 5f33e6ce22c083ac932bacf158580fb9ddc4f32f45fc42431f42a5d809a8ab26 | a4b981596635b0e7d6a2a29d5ab8a95a8abe0c4a3e9e94bfd6db5e22256c24fb |
cat-searcher/leandojo-benchmark-4-random | test | 2,896 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_singleton_iff</a>] | case h
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependen... | case h
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependen... | ((:c Not) ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) (:fv _uniq.86944) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instSingletonSet) (:fv _uniq.84775)) (:fv _uniq.88255)))) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29478,"sourceStart":29476,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29480,"sourceStart":29479,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_singleto... | [] | [{"source":"Set.mem_singleton_iff","source_end":29501,"source_start":29480,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 85 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3de3de507a33930dc0003a4924499331929e4c514ac3ae15caebb26543207a6d | a4b981596635b0e7d6a2a29d5ab8a95a8abe0c4a3e9e94bfd6db5e22256c24fb | bafd27727973ee87a1a0595f11d8d471eead0127639c9318d05c532da81b4897 | cf9ea5c44752b2927dd6c1f26973f32bb926b6aed9a2f048afb6d5ac150146c9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,897 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Ne.symm</a> xa | case h
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependen... | ((:c Not) ((:c Eq) (:fv _uniq.84775) (:fv _uniq.86944) (:fv _uniq.88255))) | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV14)) (:arg :explicit 2 (:fv FV18))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":29516,"sourceStart":29511,"tag":"atom"},{"children":[{"name":"Ne.symm","semanticRole":"global","source":"Ne.symm","sourceEnd":29524,"sourceStart":29517,"tag":"identifier"},{"children":[{"contextIndex":20,"semanticRole":"local","source":"xa","sourceEnd":29527,"sourceStart":2952... | [] | [{"source":"Ne.symm xa","source_end":29527,"source_start":29517,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 88 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a90739cc7d240c0f7a4158617f4d63a7f32b7d4efbbb5e8d288098c844fb436 | cf9ea5c44752b2927dd6c1f26973f32bb926b6aed9a2f048afb6d5ac150146c9 | 7c1c7ed2abfe6981ee4fbe931621972296a80c26e663bdb45aab96400499a4ec | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,898 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sSup_union</a>, <a>sSup_singleton</a>] | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29806,"sourceStart":29804,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29808,"sourceStart":29807,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sSup_union","sem... | [] | [{"source":"sSup_union","source_end":29818,"source_start":29808,"syntax_kind":"ident"},{"source":"sSup_singleton","source_end":29834,"source_start":29820,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 104 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48d39a013b7cad1a3b10f7560604b057271ba415131e0b868da455dd55992e51 | 441251e7af139cc407b20d860a3a88df6fd210d0da0de491ab5bfe0f9f1beb60 | b9a67287244babef23afeb182264c7696225269c34c88bba2efc7bc528a028b4 | 647c1c240d69ff9014931c66d01f0a131f0e1728f5ed7c447fb7a760ff18175c |
cat-searcher/leandojo-benchmark-4-random | test | 2,899 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact b_inf_Sup_s.disjoint_sup_right_of_disjoint_sup_left con.symm | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ((:c Disjoint) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c C... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":29845,"sourceStart":29840,"tag":"atom"},{"children":[{"source":"b_inf_Sup_s.disjoint_sup_right_of_disjoint_sup_left","sourceEnd":29897,"sourceStart":29846,"tag":"identifier"},{"children":[{"name":"Disjoint.symm","semanticRole":"global","source":"con.symm","sourceEnd":29906,"so... | [] | [{"source":"b_inf_Sup_s.disjoint_sup_right_of_disjoint_sup_left con.symm","source_end":29906,"source_start":29846,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 108 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2073c56f29313dff119c4726ed09d3b77ff2c13b9e13407872b3a50323ef85a0 | 647c1c240d69ff9014931c66d01f0a131f0e1728f5ed7c447fb7a760ff18175c | b944a93f20fe84aa4296da20f19011630f1273cb3b1a02667e827801ead6ab88 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,900 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | (:forall x (:fv _uniq.84775) (:forall hx ((:c Membership.mem) (:fv _uniq.84775) ((:c Set) (:fv _uniq.84775)) ((:c Set.instMembership) (:fv _uniq.84775)) 0 ((:c Union.union) ((:c Set) (:fv _uniq.84775)) ((:c Set.instUnion) (:fv _uniq.84775)) (:fv _uniq.86318) ((:c Singleton.singleton) (:fv _uniq.84775) ((:c Set) (:fv _u... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:forall x :explicit (:fv FV1) (:forall hx :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":29917,"sourceStart":29912,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":29919,"sourceStart":29918,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":29922,"sourceStart":29920,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":29919,"source_start":29918,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":29922,"source_start":29920,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 113 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0a2d6e7beaa8fa474628a0a0d18cd06853f6e052bce958684f0a26d0858999b | 4012cfc55a90041c04ee654a2930057542038849725cad1c5bfef82cb4e85e2e | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | 34c7aa95612e23343bdda84943b2e3f2a0ac17b5c1919ebae38fac21272f3a7e |
cat-searcher/leandojo-benchmark-4-random | test | 2,901 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_union</a>, <a>Set.mem_singleton_iff</a>] at hx | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | ((:c IsAtom) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778)))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c Pa... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c IsAtom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 3 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":29929,"sourceStart":29927,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29931,"sourceStart":29930,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_union","... | [] | [{"source":"Set.mem_union","source_end":29944,"source_start":29931,"syntax_kind":"ident"},{"source":"hx","source_end":29974,"source_start":29972,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":29967,"source_start":29946,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 114 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ec1134382da65dc2a94f900760a244f4f291b291c477408650c5f84f7953f1cc | 34c7aa95612e23343bdda84943b2e3f2a0ac17b5c1919ebae38fac21272f3a7e | 4b75a2e09bfbc16a664e0d91b6aded6c427e59eb72ad31af957c78ea931e77ee | f63c67173a0836cfa8f6978c51ddf1daf62a3d0bd9d023ddb78f3da80f4da919 |
cat-searcher/leandojo-benchmark-4-random | test | 2,902 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain hx | rfl := hx | ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndependent s
b_i... | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c IsAtom) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778)))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c Pa... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c IsAtom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 3 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":29985,"sourceStart":29979,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx","sourceEnd":29988,"sourceStart":29986,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"hx","sourceEnd":29988,"sourc... | [] | [{"source":"hx","source_end":30000,"source_start":29998,"syntax_kind":"ident"},{"source":"hx | rfl","source_end":29994,"source_start":29986,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 118 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60ec345d5d7989be38d6589f0e37a74a892a981c16fa7779cdd9cfd9a18b5f31 | f63c67173a0836cfa8f6978c51ddf1daf62a3d0bd9d023ddb78f3da80f4da919 | 966777cd24817981dc361319fbc68249c0d68bc7fafdf001a1f2f0b6fdf4302a | e22fb9fae553000f0cdfa5b17a5d417e6abe7874ed7fe77f09b7eeb5bc0f43a5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,903 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact s_atoms x hx | case inl
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c IsAtom) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778)))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c Pa... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c IsAtom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 3 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":30013,"sourceStart":30008,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"s_atoms","sourceEnd":30021,"sourceStart":30014,"tag":"identifier"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"x... | [] | [{"source":"s_atoms x hx","source_end":30026,"source_start":30014,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 121 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 383676641eff2b1f32f021e6e5a9dfc7c975599b4d9c6cdb09c0e9916b07ef01 | 3dfad225c2b36a84df70901bcd50f786392d82bb1cf5467f14443e4316328564 | 26b60efce80817017998da19296c068f19624614c00d6d5cf4df43d310e6a7c7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,904 | exists_setIndependent_isCompl_sSup_atoms | Mathlib/Order/CompactlyGenerated/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha | case inr
ι : Sort u_1
α : Type u_2
inst✝² : CompleteLattice α
f : ι → α
inst✝¹ : IsModularLattice α
inst✝ : IsCompactlyGenerated α
h : sSup {a | IsAtom a} = ⊤
b : α
s : Set α
s_max : ∀ a ∈ {s | CompleteLattice.SetIndependent s ∧ Disjoint b (sSup s) ∧ ∀ a ∈ s, IsAtom a}, s ⊆ a → a = s
s_ind : CompleteLattice.SetIndepend... | ((:c IsAtom) (:fv _uniq.84775) ((:c PartialOrder.toPreorder) (:fv _uniq.84775) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.84775) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.84775) (:fv _uniq.84778)))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.84775) ((:c Preorder.toLE) (:fv _uniq.84775) ((:c Pa... | [{"name":"ι","sexp":"(:sort u_1)"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c CompleteLattice) (:fv _uniq.84775))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.84772) (:fv _uniq.84775))"},{"name":"inst✝¹","sexp":"((:c IsModularLattice) (:fv _uniq.84775) ((:c ConditionallyCompleteLattice.toLatti... | (:app (:c IsAtom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV1)))))))) (:arg :explicit 3 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":30039,"sourceStart":30034,"tag":"atom"},{"contextIndex":15,"semanticRole":"local","source":"ha","sourceEnd":30042,"sourceStart":30040,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact ha","sourceEnd":30042,"sourceStar... | [] | [{"source":"ha","source_end":30042,"source_start":30040,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84772","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84775","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 102 | 126 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7557e02776f51cb7af59882f8d8f6b23102312153433a4dbf4dfefe76d76f58a | 3cc8107ac0c104926b0d85da8a125a452a9bd181c0b213246ed59a4692a35411 | ed7b20bfa58750585795fc60c8364f3d8cfaa54d8e6d316fdcf777f9aa77d07b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,905 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hab : a = b | k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : a = b
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c
case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
in... | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_cases","sourceEnd":4503,"sourceStart":4495,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hab","sourceEnd":4507,"sourceStart":4504,"tag":"identifier"},{"source":":","sourceEnd":4509,"sourceStart":4508,"tag":"atom"}],"kind":"null","source":"hab :","sourceEnd":4509,"sourceS... | [] | [{"source":"a = b","source_end":4515,"source_start":4510,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5558ce6035ab0552e680e9e0c6c8d05835ba4e9246fb9b095c6df700f46656ba | f35751b8b675e21e5a0f5148747329f0cb32e7352c8c6052d5ecb8faa40a5c25 | 255f36a399a64f52d4f0e0f20a4c80772c1f5fab1d232acde24583e55096c773 | 928281a4d33e7d921c7bf301b0c89bcdf5d8487491985177ba8655dbbabf2e1c |
cat-searcher/leandojo-benchmark-4-random | test | 2,906 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hbc : b = c | case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
hbc : b = c
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c
case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³... | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_cases","sourceEnd":4695,"sourceStart":4687,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hbc","sourceEnd":4699,"sourceStart":4696,"tag":"identifier"},{"source":":","sourceEnd":4701,"sourceStart":4700,"tag":"atom"}],"kind":"null","source":"hbc :","sourceEnd":4701,"sourceS... | [] | [{"source":"b = c","source_end":4707,"source_start":4702,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 30 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 10b65298e6b9cd3e869a9e688c02958cf8dda1b18d7920755bfac6001d9c6e6b | 7a535600981ffe84e0a9467ddab24b22d6316970188bf408431f9abe8b8c4e9c | 98cb636e7a574b5a26d9e31c3bd06a2f43317c4e35b802066d6f87f13ce29f76 | 63cf5c38c945c6843561c45688e232a9fcd78c50741e0eddc50f7c5361100b23 |
cat-searcher/leandojo-benchmark-4-random | test | 2,907 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_comm</a>] | case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
hbc : ¬b = c
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c | case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
hbc : ¬b = c
⊢ ((c - b) / (c - a)) • slope f b c + ((b - a) / (c - a)) • slope f a b = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":4767,"sourceStart":4765,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4769,"sourceStart":4768,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"add_comm","semanticR... | [] | [{"source":"add_comm","source_end":4777,"source_start":4769,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 38 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f7e9026b76e7de2cbf5206d044d47446cadd77d8b0d1d1bd14afbd44efcb89fc | 795255ec50f637fe1e1a01272fb6f23cde27977043bc80de59e06564e1ac8fe1 | 707f7395094bb37fad92bf71eb5cc4cfd5bf0547886ddb8474de13ffc18b39f4 | 84bd9b9c7a13796f7fdcf71294c1161585f5c3a20ff54d4d01afbfe2850fd5e9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,908 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>slope</a>, <a>div_eq_inv_mul</a>, <a>MulAction.mul_smul</a>, ← <a>smul_add</a>, <a>smul_inv_smul₀</a> (<a>sub_ne_zero</a>.2 <| <a>Ne.symm</a> hab), <a>smul_inv_smul₀</a> (<a>sub_ne_zero</a>.2 <| <a>Ne.symm</a> hbc), <a>vsub_add_vsub_cancel</a>] | case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
hbc : ¬b = c
⊢ ((c - b) / (c - a)) • slope f b c + ((b - a) / (c - a)) • slope f a b = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":4788,"sourceStart":4781,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4790,"sourceStart":4789,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"slope","semanti... | [] | [{"source":"slope","source_end":4795,"source_start":4790,"syntax_kind":"ident"},{"source":"div_eq_inv_mul","source_end":4811,"source_start":4797,"syntax_kind":"ident"},{"source":"mul_smul","source_end":4821,"source_start":4813,"syntax_kind":"ident"},{"source":"smul_add","source_end":4835,"source_start":4827,"syntax_kin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 41 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42a2255c6f9fdfe5454953fbd46eec0b5cb3c4d6cfc89adc6ea68d06e8e3fb95 | 84bd9b9c7a13796f7fdcf71294c1161585f5c3a20ff54d4d01afbfe2850fd5e9 | 86cb847e2b87a01441cb46079527cd76b7aed0875ffebaa48449edfe438ac248 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,909 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst hab | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : a = b
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
⊢ ((a - a) / (c - a)) • slope f a a + ((c - a) / (c - a)) • slope f a c = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"subst","sourceEnd":4526,"sourceStart":4521,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hab","sourceEnd":4530,"sourceStart":4527,"tag":"identifier"}],"kind":"null","source":"hab","sourceEnd":4530,"sourceStart":4527,"tag":"node"}],"kind":"Lean.Parser.Tactic.subst... | [] | [{"source":"hab","source_end":4530,"source_start":4527,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 9 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4abb0e0df0a82f8f53c3972defd22caded03ab12ac52f406d191a74d0f2e0e1a | 86688970a38d58b4249eacc7d91c54f43308e5c180f31172d50283abcfe16d5d | aa62d8c7ad336fe26434b37b9fb700e7e795261df017a67f37f5aa3ee7557b76 | 5d3c1b359d9753842d3363233f6883f100f7c78a8325fe841a0f4d19de03d288 |
cat-searcher/leandojo-benchmark-4-random | test | 2,910 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sub_self</a>, <a>zero_div</a>, <a>zero_smul</a>, <a>zero_add</a>] | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
⊢ ((a - a) / (c - a)) • slope f a a + ((c - a) / (c - a)) • slope f a c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
⊢ ((c - a) / (c - a)) • slope f a c = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":4537,"sourceStart":4535,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4539,"sourceStart":4538,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sub_self","semanticR... | [] | [{"source":"sub_self","source_end":4547,"source_start":4539,"syntax_kind":"ident"},{"source":"zero_div","source_end":4557,"source_start":4549,"syntax_kind":"ident"},{"source":"zero_smul","source_end":4568,"source_start":4559,"syntax_kind":"ident"},{"source":"zero_add","source_end":4578,"source_start":4570,"syntax_kind"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 10 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aacefcb4c29318972a92cc6d0f572d076db0050b87efca0757e7b06451f64311 | 5d3c1b359d9753842d3363233f6883f100f7c78a8325fe841a0f4d19de03d288 | c67342d85c9a158017db2a6eb8e88a108886b347d923543ff038cc793d4dbe8b | 0fd5fb610e9cf59fd33eac726350a44519234188ccbc7ba3df52f88e5ff77806 |
cat-searcher/leandojo-benchmark-4-random | test | 2,911 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hac : a = c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
⊢ ((c - a) / (c - a)) • slope f a c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
hac : a = c
⊢ ((c - a) / (c - a)) • slope f a c = slope f a c
case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module ... | ((:c Eq) (:fv _uniq.41224) ((:c HSMul.hSMul) (:fv _uniq.41221) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c SMulZeroClass.toSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c NegZeroClass.toZero) (:fv _uniq.41224) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.41224) ((:c S... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"by_cases","sourceEnd":4592,"sourceStart":4584,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hac","sourceEnd":4596,"sourceStart":4593,"tag":"identifier"},{"source":":","sourceEnd":4598,"sourceStart":4597,"tag":"atom"}],"kind":"null","source":"hac :","sourceEnd":4598,"sourceS... | [] | [{"source":"a = c","source_end":4604,"source_start":4599,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 16 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9803a3c05ddb07cf0c0b9f6a9f98ba87e5aea47e04cde5d6ee31aa1f0bae1ad7 | 0fd5fb610e9cf59fd33eac726350a44519234188ccbc7ba3df52f88e5ff77806 | 835ff8b0d960e3727165e1757c38e504bb2cc1416320097c294000b14e7df4aa | a66e0b00055af9640e4439cd151036eac9f5581a3e308e99c3256bbc54ebcd8e |
cat-searcher/leandojo-benchmark-4-random | test | 2,912 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [hac] | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
hac : a = c
⊢ ((c - a) / (c - a)) • slope f a c = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HSMul.hSMul) (:fv _uniq.41221) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c SMulZeroClass.toSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c NegZeroClass.toZero) (:fv _uniq.41224) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.41224) ((:c S... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4616,"sourceStart":4612,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"hac","source_end":4621,"source_start":4618,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 19 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b8c1b65d1b1add3c3cee1317e2602ebfd53756a8b50c921a62fbb65dca744290 | c9f8962b7510cb9d79dbb8d72adcc14e1424c6e60d6464e282f0b3e1beea9f63 | b6caedde32c634b9e792916087154aa7afd08595d11c5322f36035ea96f27d9f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,913 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>div_self</a> (<a>sub_ne_zero</a>.2 <| <a>Ne.symm</a> hac), <a>one_smul</a>] | case neg
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a c : k
hac : ¬a = c
⊢ ((c - a) / (c - a)) • slope f a c = slope f a c | ((:c Eq) (:fv _uniq.41224) ((:c HSMul.hSMul) (:fv _uniq.41221) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c SMulZeroClass.toSMul) (:fv _uniq.41221) (:fv _uniq.41224) ((:c NegZeroClass.toZero) (:fv _uniq.41224) ((:c SubNegZeroMonoid.toNegZeroClass) (:fv _uniq.41224) ((:c S... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4632,"sourceStart":4630,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4634,"sourceStart":4633,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"div_self (sub_ne_zero.2 <| Ne.symm hac)","source_end":4673,"source_start":4634,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_smul","source_end":4683,"source_start":4675,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 24 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f4b9574a11cf2bbfc4154b1b8a9b120ef95bc41b34032e0e63b2f133e8c97c7b | 9fec8bf7edead5ae36eb90754dd2ce6959ea2036de823fb6435cac59f04d61c2 | 4df196b72b0774d4653e3b0926ebaff7cbfd4103f0731bf92374c655020dd999 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,914 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | subst hbc | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b c : k
hab : ¬a = b
hbc : b = c
⊢ ((b - a) / (c - a)) • slope f a b + ((c - b) / (c - a)) • slope f b c = slope f a c | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b : k
hab : ¬a = b
⊢ ((b - a) / (b - a)) • slope f a b + ((b - b) / (b - a)) • slope f b b = slope f a b | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"subst","sourceEnd":4719,"sourceStart":4714,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"hbc","sourceEnd":4723,"sourceStart":4720,"tag":"identifier"}],"kind":"null","source":"hbc","sourceEnd":4723,"sourceStart":4720,"tag":"node"}],"kind":"Lean.Parser.Tactic.subst... | [] | [{"source":"hbc","source_end":4723,"source_start":4720,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 36 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb528f1e6600eb32d3a12201add251aa9e7f0c53b2f80b15dfdbb54f7d687a50 | c904cb1e2206888b608949a042323804608e6485379b7a5f878d4e74957b25ee | ae55a0cdfcc772877595b9c0d39ea77b664eb279440c160baa3187b0a9b61865 | 128d2c0c4dd683bf508184ae4945197da26b672ce811dbf0afac4877e4a77305 |
cat-searcher/leandojo-benchmark-4-random | test | 2,915 | sub_div_sub_smul_slope_add_sub_div_sub_smul_slope | Mathlib/LinearAlgebra/AffineSpace/Slope.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>sub_ne_zero</a>.2 (<a>Ne.symm</a> hab)] | case pos
k : Type u_1
E : Type u_2
PE : Type u_3
inst✝³ : Field k
inst✝² : AddCommGroup E
inst✝¹ : Module k E
inst✝ : AddTorsor E PE
f : k → PE
a b : k
hab : ¬a = b
⊢ ((b - a) / (b - a)) • slope f a b + ((b - b) / (b - a)) • slope f b b = slope f a b | ((:c Eq) (:fv _uniq.41224) ((:c HAdd.hAdd) (:fv _uniq.41224) (:fv _uniq.41224) (:fv _uniq.41224) ((:c instHAdd) (:fv _uniq.41224) ((:c AddCommMagma.toAdd) (:fv _uniq.41224) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.41224) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.41224) ((:c AddCommGroup.toAddCommMonoid)... | [{"name":"k","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"PE","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.41221))"},{"name":"inst✝²","sexp":"((:c AddCommGroup) (:fv _uniq.41224))"},{"name":"inst✝¹","sexp":"((:c Module) (:fv _uniq.41221) (:fv _uniq.41224) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"name":"k","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":4732,"sourceStart":4728,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4734,"sourceStart":4733,"tag":"atom"... | [] | [{"source":"sub_ne_zero.2 (Ne.symm hab)","source_end":4761,"source_start":4734,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41221","is_instance":false,"is_let":false,"user_name":"k"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.41224","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 34 | 37 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a6f509c457030d525136aa2fa72cbd7b46effab7df52784fb8ea691c6fb14f9 | 128d2c0c4dd683bf508184ae4945197da26b672ce811dbf0afac4877e4a77305 | 1a9912c467c0996616ca3aecca3f1da41c255a2d12bcaacb54b864b0a8490ff4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,916 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have ah : <a>Pairwise</a> fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j := by simpa only [<a>dist_eq_norm</a>] using a.h | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
⊢ 1 - δ ≤ ‖a.c i - a.c j‖ | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
⊢ 1 - δ ≤ ‖a.c i - a.... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16196,"sourceStart":16192,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ah","sourceEnd":16199,"sourceStart":16197,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"ah","sourceEnd":16199,"sourceStart":16197,"tag":"nod... | [] | [{"source":"Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨\n a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j","source_end":16349,"source_start":16208,"syntax_kind":"Lean.Parser.Term.app"},{"source":"dist_eq_norm","source_end":16384,"source_start":16372,"syntax_kind":"ident"},{"source":"a.h","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7ef31e3215f0f774a472b39612284201e4ca8ddc51a4ac5f59ea648787988fd1 | 33a9efc89074fed0032afc4197d9e1ee28244211dd02aaaa1442c7e242a30b70 | 612158c457772e914b330ab70221f35188b2dc89156849a24275bbbbbf2dad55 | 10b39b2849677ac1b22e4f135782ec16234bc03f2792e1f02f4b9ea1f307b262 |
cat-searcher/leandojo-benchmark-4-random | test | 2,917 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have δnonneg : 0 ≤ δ := by linarith only [hτ, hδ1] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
⊢ 1 - δ ≤ ‖a.c i - a.... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
⊢ 1 -... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16402,"sourceStart":16398,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"δnonneg","sourceEnd":16411,"sourceStart":16403,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"δnonneg","sourceEnd":16411,"sourceStart":16403,... | [] | [{"source":"0 ≤ δ","source_end":16422,"source_start":16414,"syntax_kind":"«term_≤_»"},{"source":"hτ","source_end":16447,"source_start":16444,"syntax_kind":"ident"},{"source":"hδ1","source_end":16453,"source_start":16449,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 7 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 874a0e41caf54c77d1bc13035ebd7d49da7439c7565a0d1830309c70f32e2fd7 | 10b39b2849677ac1b22e4f135782ec16234bc03f2792e1f02f4b9ea1f307b262 | 82646d03ff12cb86b2d87e6de911b395322dac6138a5239ae6203f4e836ca178 | 2dcfee1d55f58dd50cf9c13c30977f158f57250f475435f5fde827ffc31e5bdf |
cat-searcher/leandojo-benchmark-4-random | test | 2,918 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have D : 0 ≤ 1 - δ / 4 := by linarith only [hδ2] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
⊢ 1 -... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16461,"sourceStart":16457,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"D","sourceEnd":16463,"sourceStart":16462,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"D","sourceEnd":16463,"sourceStart":16462,"tag":"node"... | [] | [{"source":"0 ≤ 1 - δ / 4","source_end":16482,"source_start":16466,"syntax_kind":"«term_≤_»"},{"source":"hδ2","source_end":16508,"source_start":16504,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 10 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0bbc87ca3b8d6daa97333ae353edf329403cc39705967b3c2cb8519c104e597 | 2dcfee1d55f58dd50cf9c13c30977f158f57250f475435f5fde827ffc31e5bdf | ec1ab67504ba1d48c8cc0e419413144f723b15df50b8ba13c8236000f8e223a3 | 5619d83abaaaee67c5265717aec1ceb3625f246fefc1981662a960dfe4ff9b20 |
cat-searcher/leandojo-benchmark-4-random | test | 2,919 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have τpos : 0 < τ := _root_.zero_lt_one.trans_le hτ | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16516,"sourceStart":16512,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"τpos","sourceEnd":16522,"sourceStart":16517,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"τpos","sourceEnd":16522,"sourceStart":16517,"tag":... | [] | [{"source":"0 < τ","source_end":16531,"source_start":16525,"syntax_kind":"«term_<_»"},{"source":"_root_.zero_lt_one.trans_le hτ","source_end":16566,"source_start":16535,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 13 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5839b9bf3a6ab3aadb5ad3ba65633f6921958faaabaea8f14a52d057a869f6b2 | 5619d83abaaaee67c5265717aec1ceb3625f246fefc1981662a960dfe4ff9b20 | 9884e286696a5a82b392bbe02aa4088b6c12d419ed642b1c295267257f8ef322 | dd107850402c112a3564804d9652e5859cd8934005b5614e2430169d4a0b2f64 |
cat-searcher/leandojo-benchmark-4-random | test | 2,920 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have I : (1 - δ / 4) * τ ≤ 1 := calc (1 - δ / 4) * τ ≤ (1 - δ / 4) * (1 + δ / 4) := by gcongr _ = (1 : ℝ) - δ ^ 2 / 16 := by ring _ ≤ 1 := by linarith only [<a>sq_nonneg</a> δ] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16573,"sourceStart":16569,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"I","sourceEnd":16575,"sourceStart":16574,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"I","sourceEnd":16575,"sourceStart":16574,"tag":"node"... | [] | [{"source":"(1 - δ / 4) * τ ≤ 1","source_end":16601,"source_start":16578,"syntax_kind":"«term_≤_»"},{"source":"calc\n (1 - δ / 4) * τ ≤ (1 - δ / 4) * (1 + δ / 4) := by gcongr\n _ = (1 : ℝ) - δ ^ 2 / 16 := by ring\n _ ≤ 1 := by linarith only [sq_nonneg δ]","source_end":16776,"source_start":16609,"syntax_k... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 14 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbfa5a56829c42539e3f15d1d67caf091ed9a1a72faa71af8df16e0c45ddb01c | dd107850402c112a3564804d9652e5859cd8934005b5614e2430169d4a0b2f64 | a0c89a9f6647c88f2496dbb2c3c0b48f333e34876f6c846fa1b8d6b7fd52f800 | ead906cee0f448c94e047296c6f94f7192bba8cc88b597757d3820c184314e1c |
cat-searcher/leandojo-benchmark-4-random | test | 2,921 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have J : 1 - δ ≤ 1 - δ / 4 := by linarith only [δnonneg] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16783,"sourceStart":16779,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"J","sourceEnd":16785,"sourceStart":16784,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"J","sourceEnd":16785,"sourceStart":16784,"tag":"node"... | [] | [{"source":"1 - δ ≤ 1 - δ / 4","source_end":16809,"source_start":16788,"syntax_kind":"«term_≤_»"},{"source":"δnonneg","source_end":16839,"source_start":16831,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 30 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c20b7473e0d065a7623d90ad2df8d56b11f04824843882de0f0cef7e97a5196b | ead906cee0f448c94e047296c6f94f7192bba8cc88b597757d3820c184314e1c | ea54ed282075f9b467f8a61703a74c73bcf86f6bc6a61b0e58a2a7dd7d1f1925 | 570c33999f36c56181e267c5f7ec1f79397bb76e418f1efabb9ec191ed89ce0d |
cat-searcher/leandojo-benchmark-4-random | test | 2,922 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have K : 1 - δ / 4 ≤ τ⁻¹ := by rw [<a>inv_eq_one_div</a>, <a>le_div_iff</a> τpos]; exact I | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":16847,"sourceStart":16843,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"K","sourceEnd":16849,"sourceStart":16848,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"K","sourceEnd":16849,"sourceStart":16848,"tag":"node"... | [] | [{"source":"1 - δ / 4 ≤ τ⁻¹","source_end":16874,"source_start":16852,"syntax_kind":"«term_≤_»"},{"source":"inv_eq_one_div","source_end":16899,"source_start":16885,"syntax_kind":"ident"},{"source":"le_div_iff τpos","source_end":16917,"source_start":16901,"syntax_kind":"Lean.Parser.Term.app"},{"source":"I","source_end":1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 33 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69043b633bd90953a4956fa847442c4f18368655dfa36bc4914cdde777f6cfa0 | 570c33999f36c56181e267c5f7ec1f79397bb76e418f1efabb9ec191ed89ce0d | 400bb207ba8592cd20ac7270856307d4ad69b3de7c591465055ccebf8a9170f3 | 829c42a957dca6b18c580dbcbd91a065ba264a0e347265169e67b959f9d7f78c |
cat-searcher/leandojo-benchmark-4-random | test | 2,923 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices L : τ⁻¹ ≤ ‖a.c i - a.c j‖ by linarith only [J, K, L] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"suffices","sourceEnd":16938,"sourceStart":16930,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"L","sourceEnd":16940,"sourceStart":16939,"tag":"identifier"},{"source":":","sourceEnd":16942,"sourceStart":16941,"tag":"atom"}],"kind":"group","source":"L :","sourceEn... | [] | [{"source":"τ⁻¹ ≤ ‖a.c i - a.c j‖","source_end":16974,"source_start":16943,"syntax_kind":"«term_≤_»"},{"source":"J","source_end":16994,"source_start":16993,"syntax_kind":"ident"},{"source":"K","source_end":16997,"source_start":16996,"syntax_kind":"ident"},{"source":"L","source_end":17000,"source_start":16999,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 41 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e35869e81df4687e9703f0630ba91449398d5ce5f966c24a4bb9e378bb865b23 | 829c42a957dca6b18c580dbcbd91a065ba264a0e347265169e67b959f9d7f78c | b293ca56d3a26bbe1cbbb2b75a7e8b799c21dacbe5289d7cf16bcd3a38ddc904 | 3884c6cd2f6480a7135a5724ba00fce2c3aae6d5ae46b3751d7a938f9064341b |
cat-searcher/leandojo-benchmark-4-random | test | 2,924 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hτ' : ∀ k, τ⁻¹ ≤ a.r k := by intro k rw [<a>inv_eq_one_div</a>, <a>div_le_iff</a> τpos, ← lastr, <a>mul_comm</a>] exact a.hlast' k hτ | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031) (:fv _uniq.100034)) ((:c HSub.hSub) (:fv _uniq.100031) (:fv _uniq.100031) (:fv _uniq.100031) ((:c instHSub) (:fv _uniq.100031) ((:c S... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"have","sourceEnd":17008,"sourceStart":17004,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hτ'","sourceEnd":17013,"sourceStart":17009,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hτ'","sourceEnd":17013,"sourceStart":17009,"tag":"n... | [] | [{"source":"∀ k, τ⁻¹ ≤ a.r k","source_end":17040,"source_start":17016,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"inv_eq_one_div","source_end":17081,"source_start":17067,"syntax_kind":"ident"},{"source":"div_le_iff τpos","source_end":17099,"source_start":17083,"syntax_kind":"Lean.Parser.Term.app"},{"source":"la... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 45 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8445bc8ad08a6f1b4c5069510b6cb3913838e52cd1642666ccbed88090c365d5 | 3884c6cd2f6480a7135a5724ba00fce2c3aae6d5ae46b3751d7a938f9064341b | 01bc062d8536d21b80135873f6cc7cd28ab164b95bba29ea8562350ec9b5d151 | f1724435825fecc08e4cad70e8675b104215a9168e4a2d53bb064af262a3b869 |
cat-searcher/leandojo-benchmark-4-random | test | 2,925 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases ah inej with (H | H) | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | case inl
E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031) (:fv _uniq.100034)) ((:c HSub.hSub) (:fv _uniq.100031) (:fv _uniq.100031) (:fv _uniq.100031) ((:c instHSub) (:fv _uniq.100031) ((:c S... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"rcases","sourceEnd":17155,"sourceStart":17149,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"ah","sourceEnd":17158,"sourceStart":17156,"tag":"identifier"},{"children":[{"contextIndex"... | [] | [{"source":"ah inej","source_end":17163,"source_start":17156,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(H | H)","source_end":17176,"source_start":17169,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 55 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cde94f3ad01d7e18e168a38e01de7be09c7823af6b37316c15e7fffbfa65a934 | f1724435825fecc08e4cad70e8675b104215a9168e4a2d53bb064af262a3b869 | d06d433384dbdb796d05e20162598d3b51f9888d068969944884083240d52e53 | 572c76cd05127552db6b0ff2f2be6f3dfd908bd978e703ccf89bc1efb2c2983c |
cat-searcher/leandojo-benchmark-4-random | test | 2,926 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>dist_eq_norm</a>] using a.h | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
⊢ Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j | ((:c Pairwise) ((:c Fin) ((:c Nat.succ) (:fv _uniq.101072))) (:lambda i ((:c Fin) ((:c Nat.succ) (:fv _uniq.101072))) (:lambda j ((:c Fin) ((:c Nat.succ) (:fv _uniq.101072))) ((:c Or) ((:c And) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Besicovitch.SatelliteConfig.r) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetric... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (:app (:c Pairwise) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV3)))))) (:arg :explicit 1 (:lambda i :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV3))))) (:lambda j :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"simpa","sourceEnd":16365,"sourceStart":16360,"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":"dist_eq_norm","source_end":16384,"source_start":16372,"syntax_kind":"ident"},{"source":"a.h","source_end":16395,"source_start":16392,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 6 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d65315d253fd3adb2964a4d3321d5a7671ca6ea22684951b3b536338fb07be86 | 09b26b3db158567a03d7fcb8e8c11ca38e4fbed637f22265b8d1a26547316b75 | 30fd5f5304059fd0afdbbd1cae1b3a87ccf04031b4b31b51973ccb371ab5a22a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,927 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [hτ, hδ1] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
⊢ 0 ≤ δ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.101077)) | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"linarith","sourceEnd":16437,"sourceStart":16429,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16442,"sourceStart":16438,"tag":"atom"}],"kind":"null","source":"only... | [] | [{"source":"hτ","source_end":16447,"source_start":16444,"syntax_kind":"ident"},{"source":"hδ1","source_end":16453,"source_start":16449,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 9 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0aa326af7639f43c9b3709d208a9e52b567fe727ea1a6176070b3b66117bdb39 | 192f41d8f62b25467c1e8c6035ca0f8f32bf4040fef37df05d0fafeb50b79ada | a152ab34affb95dd81e0cae368cd35b55ee2944afa20976f0c0db5317f976252 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,928 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [hδ2] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
⊢ 0 ≤... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HDiv.hDiv) (... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"linarith","sourceEnd":16497,"sourceStart":16489,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16502,"sourceStart":16498,"tag":"atom"}],"kind":"null","source":"only... | [] | [{"source":"hδ2","source_end":16508,"source_start":16504,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 12 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 80b3203f1b00d477251df6bc5eb5509a3a562894f9d224448e2fa03b45c80205 | 95ea85bbd2cbdf2bedd87ccc4564ae8dfc2994eff3c4e90bba8af799d1e0cd9a | 237ebedb60677735ee69bafc9bc07dded06f98b830d283db6864f11a70739965 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,929 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HDiv.hDiv)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"children":[{"children":[{"children":[{"source":"gcongr","sourceEnd":16682,"sourceStart":16676,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":1668... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 17 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f58d07238779982c9ee5709687b7799f0d8152579733d21e750b763056beaefe | c7055fab876d42220955b9cd28f7150671100f7a90340c8bea7a96478629c9ea | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,930 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HDiv.hDiv) (:c Real) (:c Real)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":16727,"sourceStart":16723,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":16727,"sourceStart":16723,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":16727,"sourceStart":16723,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 22 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7230227fc688e65c630c94c549674e032ff2d36a9bd8831d5969870cda8a51b | 3c0c905609a1a3e9f82b1ffa3a2aa16e69836e4487b161478571af48684e8ce3 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,931 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [<a>sq_nonneg</a> δ] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":16756,"sourceStart":16748,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16761,"sourceStart":16757,"tag... | [] | [{"source":"sq_nonneg δ","source_end":16775,"source_start":16763,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 27 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0209d9db84e782a0ba4ba2531f965730b4dad4e9cb626ad8c93b1142829a3003 | a7e6a168f5a2e928b3544a93fd6b7e83569287e7b40ffe0f30f380542c9bd2c2 | 8e82a304e24c7b5f9de61132dc8d57f143fa8aa16cac4c4d12037ab260654db8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,932 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [δnonneg] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instS... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"linarith","sourceEnd":16824,"sourceStart":16816,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16829,"sourceStart":16825,"tag":"atom"}],"kind":"null","source":"only... | [] | [{"source":"δnonneg","source_end":16839,"source_start":16831,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 32 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a413001286ab259aee12c1e9cddf25af930a6b547c9fbb47ce128461657edb5 | c738277dd6a5462afe1964a5e1e926d4ad65e89b9337d340cd0c9b3f1475cfc1 | 103dac5a6fb28f86b1c42410c9569cf0b9418483e4844d9379dbbbe054a502a0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,933 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>inv_eq_one_div</a>, <a>le_div_iff</a> τpos] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"rw","sourceEnd":16883,"sourceStart":16881,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16885,"sourceStart":16884,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"inv_eq_one_div",... | [] | [{"source":"inv_eq_one_div","source_end":16899,"source_start":16885,"syntax_kind":"ident"},{"source":"le_div_iff τpos","source_end":16917,"source_start":16901,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 35 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f575d35e7cdf2d0fb5a99573c31f1013a0fa9f710105816bb15d801745cd558c | b9bad9a7d2dfa53a9f957c53e9bda4fc0b511823251827fb54e6e49cdc40a861 | b74198da6e02de138d88ab9376127086136e82cb2c2cde436ad8c705c5ef6cdd | fd2652cb4b36350f5c1818d7425d7509443b26f215e70d1889c2a53c6cbb8674 |
cat-searcher/leandojo-benchmark-4-random | test | 2,934 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact I | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"exact","sourceEnd":16925,"sourceStart":16920,"tag":"atom"},{"contextIndex":18,"semanticRole":"local","source":"I","sourceEnd":16927,"sourceStart":16926,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact I","sourceEnd":16927,"sourceStart":16920,"tag":"node"} | [] | [{"source":"I","source_end":16927,"source_start":16926,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 40 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 24f96e227ef060ed3e61f0c868f9de606f16bdac22f288f98d2dabe0234c0adf | fd2652cb4b36350f5c1818d7425d7509443b26f215e70d1889c2a53c6cbb8674 | 75ce1783c04cacfa69c9929baee867befdb234d596e9df1c39e46056d1e1f4a7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,935 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith only [J, K, L] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.101077)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031)... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 HSub.hSub) (: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 HSub) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":16986,"sourceStart":16978,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":16991,"sourceStart":16987,"tag... | [] | [{"source":"J","source_end":16994,"source_start":16993,"syntax_kind":"ident"},{"source":"K","source_end":16997,"source_start":16996,"syntax_kind":"ident"},{"source":"L","source_end":17000,"source_start":16999,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 42 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b803d472e6d74852295dde51d301f4b2e2f52fa4792e7e774f40af37f6cc435 | 8fa0cda0267753f04a8f0ade68bcf749bda57326568d7f35e585cdb8b6d5afae | b42793bda88081e8742f2088745645200ee7e47359e7f5cbaaf93e0675d31056 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,936 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro k | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | (:forall k ((:c Fin) ((:c Nat.succ) (:fv _uniq.101072))) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Besicovitch.SatelliteConfig.r) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100034)) (:fv _uniq.101072) (:fv _uniq... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (:forall k :explicit (:app (:c Fin) (:arg :explicit 0 (:app (:c Nat.succ) (:arg :explicit 0 (:fv FV3))))) (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"intro","sourceEnd":17056,"sourceStart":17051,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"k","sourceEnd":17058,"sourceStart":17057,"tag":"identifier"}],"kind":"null","source":"k","sourceEnd":17058,"sourceStart":17057,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"k","source_end":17058,"source_start":17057,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 47 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 887e68a616295d9386293adba225a9c0daa65c04a507d3b6cef0ebd826fa2ca8 | 9ce411b9c0c68cf7e71ab3b64c1b9a5921557a36af33d09b8a0aebf6bb2360bb | 9653f6a058d9d95b07138d1e03547b9946da63395fe2b8fef5ee0be0289c2521 | 0db739aafd9b3dfe1d84477e047e4822848b0ad38dfc754a4cca586e8dc5c03a |
cat-searcher/leandojo-benchmark-4-random | test | 2,937 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>inv_eq_one_div</a>, <a>div_le_iff</a> τpos, ← lastr, <a>mul_comm</a>] | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Besicovitch.SatelliteConfig.r) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100034)) (:fv _uniq.101072) (:fv _uniq.101073) (:fv _uniq.101074) (:fv _uniq.112889))) | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"rw","sourceEnd":17065,"sourceStart":17063,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17067,"sourceStart":17066,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"inv_eq_one_div",... | [] | [{"source":"inv_eq_one_div","source_end":17081,"source_start":17067,"syntax_kind":"ident"},{"source":"div_le_iff τpos","source_end":17099,"source_start":17083,"syntax_kind":"Lean.Parser.Term.app"},{"source":"lastr","source_end":17110,"source_start":17105,"syntax_kind":"ident"},{"source":"mul_comm","source_end":17120,"s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 48 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cfcc0863f9f041c1c18c03614d02c82f3bb2ddb3f9e57800471510e0edca6865 | 0db739aafd9b3dfe1d84477e047e4822848b0ad38dfc754a4cca586e8dc5c03a | 6dd580d7233d4e616b5d26473d3069d6df928c6932250040915db8a76886f00f | 12a64bde2ccc9c0420d3faad6f9c964a8aec7e33471349cb46893e8cf26148ab |
cat-searcher/leandojo-benchmark-4-random | test | 2,938 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact a.hlast' k hτ | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Besicovitch.SatelliteConfig.r) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"exact","sourceEnd":17131,"sourceStart":17126,"tag":"atom"},{"children":[{"source":"a.hlast'","sourceEnd":17140,"sourceStart":17132,"tag":"identifier"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"k","sourceEnd":17142,"sourceStart":17141,"tag":"identifier"},{"contextIndex":7,"... | [] | [{"source":"a.hlast' k hτ","source_end":17146,"source_start":17132,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 54 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ff4dda20a5d82a4f52ead7792188db8b946e2b9722c203da270769866c63d45 | 12a64bde2ccc9c0420d3faad6f9c964a8aec7e33471349cb46893e8cf26148ab | 67c4d8f9aac5c896a939bc6e7cfdee255251e04a67eecc42da1ba09442517fb9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,939 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_trans</a> _ H.1 | case inl
E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031) (:fv _uniq.100034)) ((:c HSub.hSub) (:fv _uniq.100031) (:fv _uniq.100031) (:fv _uniq.100031) ((:c instHSub) (:fv _uniq.100031) ((:c S... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"apply","sourceEnd":17187,"sourceStart":17182,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":17196,"sourceStart":17188,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":17198,"sourceStart":17197,"tag":"atom"}],"kind":"Le... | [] | [{"source":"le_trans _ H.1","source_end":17202,"source_start":17188,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 60 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c1ab80db9e3d527a2470ba02d5ffdb9d2b0bf5bc6c78d4c407a4951d4df459f | 95a9f2fdbe12533c9a7387e13269819df934651356cba50dce6465fed7ed012e | 7ed4ab8d6ce8799786808b46623cd0be1a54081dc1f61b1c6688470ee82a0fa1 | 6577a773422020f6bedab4bfaf801bf12fef717e12441522c2bbeeeceb1e932b |
cat-searcher/leandojo-benchmark-4-random | test | 2,940 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hτ' i | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Besicovitch.SatelliteConfig.r) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100034)) (:fv _uniq.101072) (:fv _uniq.101073) (:fv _uniq.... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"exact","sourceEnd":17212,"sourceStart":17207,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"hτ'","sourceEnd":17217,"sourceStart":17213,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"i","sourceEnd":17219,"sourceStart":17218,"ta... | [] | [{"source":"hτ' i","source_end":17219,"source_start":17213,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 61 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bd5fa61ce3dd27336f3275f5ab671ef328ed4df893a55022bd8c3574159780c | 6577a773422020f6bedab4bfaf801bf12fef717e12441522c2bbeeeceb1e932b | f2b0da4d7bc7ead2b452a03c72bff70867711d7c25e1bba3953492928c0b984b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,941 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>norm_sub_rev</a>] | case inr
E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ... | case inr
E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Norm.norm) (:fv _uniq.100031) ((:c NormedAddCommGroup.toNorm) (:fv _uniq.100031) (:fv _uniq.100034)) ((:c HSub.hSub) (:fv _uniq.100031) (:fv _uniq.100031) (:fv _uniq.100031) ((:c instHSub) (:fv _uniq.100031) ((:c S... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"rw","sourceEnd":17227,"sourceStart":17225,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17229,"sourceStart":17228,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"norm_sub_rev","s... | [] | [{"source":"norm_sub_rev","source_end":17241,"source_start":17229,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 66 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d0edec9feeb4e20b6e13d1278c7171ffdc5faf5fd0bdc5335a88dcb6d40b70a7 | ff14510b62d78b078ce98f5c81b5a2bbbecc3fbcb74e17664d86f4dffc52d39b | 25bc654b21eceb269eb7395ec57466530c543c538ea66332013788581c1840c7 | 8265e16dcc20816b622a1967a7f3281e3235f6e64b92c871b9a76a32d22e178a |
cat-searcher/leandojo-benchmark-4-random | test | 2,942 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_trans</a> _ H.1 | case inr
E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ... | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Norm.norm) (:fv _uniq.100031) ((:c SeminormedAddGroup.toNorm) (:fv _uniq.100031) ((:c SeminormedAddCommGroup.toSeminormedAddGroup) (:fv _uniq.100031) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.100... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"apply","sourceEnd":17252,"sourceStart":17247,"tag":"atom"},{"children":[{"name":"le_trans","semanticRole":"global","source":"le_trans","sourceEnd":17261,"sourceStart":17253,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":17263,"sourceStart":17262,"tag":"atom"}],"kind":"Le... | [] | [{"source":"le_trans _ H.1","source_end":17267,"source_start":17253,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 69 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc50a382e7d853cf767f58896ece89a0517c96fb81977cdc2b169214ca0d7af7 | 8265e16dcc20816b622a1967a7f3281e3235f6e64b92c871b9a76a32d22e178a | 7ed4ab8d6ce8799786808b46623cd0be1a54081dc1f61b1c6688470ee82a0fa1 | cf8908a7e5a9400258954bbe7306cb3e0e539f8b7ac8aa4fddc0d202d059c0a2 |
cat-searcher/leandojo-benchmark-4-random | test | 2,943 | Besicovitch.SatelliteConfig.exists_normalized_aux1 | Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hτ' j | E : Type u_1
inst✝ : NormedAddCommGroup E
N : ℕ
τ : ℝ
a : SatelliteConfig E N τ
lastr : a.r (last N) = 1
hτ : 1 ≤ τ
δ : ℝ
hδ1 : τ ≤ 1 + δ / 4
hδ2 : δ ≤ 1
i j : Fin N.succ
inej : i ≠ j
ah : Pairwise fun i j => a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j
δnonneg : 0 ≤ δ
D : 0... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Inv.inv) (:c Real) (:c Real.instInv) (:fv _uniq.101073)) ((:c Besicovitch.SatelliteConfig.r) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100034)) (:fv _uniq.101072) (:fv _uniq.101073) (:fv _uniq.... | [{"name":"E","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c NormedAddCommGroup) (:fv _uniq.100031))"},{"name":"N","sexp":"(:c Nat)"},{"name":"τ","sexp":"(:c Real)"},{"name":"a","sexp":"((:c Besicovitch.SatelliteConfig) (:fv _uniq.100031) ((:c NormedAddCommGroup.toMetricSpace) (:fv _uniq.100031) (:fv _uniq.100... | (: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 Inv.inv) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Inv) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV4)))) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c NormedAddCommGroup) (:... | {"children":[{"source":"exact","sourceEnd":17277,"sourceStart":17272,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"hτ'","sourceEnd":17282,"sourceStart":17278,"tag":"identifier"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"j","sourceEnd":17284,"sourceStart":17283,"ta... | [] | [{"source":"hτ' j","source_end":17284,"source_start":17278,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.100031","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.100034","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"inter... | 47 | 70 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 758492e3347867ee30d69e1363f81ecbb37f00f39ecce4c6dbac7ee3a56f6621 | cf8908a7e5a9400258954bbe7306cb3e0e539f8b7ac8aa4fddc0d202d059c0a2 | d7f99e91ba54e027eef6d3e3620233bbc2649295f6d5700b37dd35b98a88e97b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,944 | rightCoset_mem_rightCoset | Mathlib/GroupTheory/Coset.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>mem_rightCoset_iff</a>, <a>mul_mem_cancel_right</a> (s.inv_mem ha)] | α : Type u_1
inst✝ : Group α
s : Subgroup α
a : α
ha : a ∈ s
b : α
⊢ b ∈ op a • ↑s ↔ b ∈ ↑s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.41468) ((:c Set) (:fv _uniq.41468)) ((:c Set.instMembership) (:fv _uniq.41468)) (:fv _uniq.42182) ((:c HSMul.hSMul) ((:c MulOpposite) (:fv _uniq.41468)) ((:c Set) (:fv _uniq.41468)) ((:c Set) (:fv _uniq.41468)) ((:c instHSMul) ((:c MulOpposite) (:fv _uniq.41468)) ((:c Set) (:fv... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c Group) (:fv _uniq.41468))"},{"name":"s","sexp":"((:c Subgroup) (:fv _uniq.41468) (:fv _uniq.41471))"},{"name":"a","sexp":"(:fv _uniq.41468)"},{"name":"ha","sexp":"((:c Membership.mem) (:fv _uniq.41468) ((:c Subgroup) (:fv _uniq.41468) (:fv _uniq.4147... | (: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.41468","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41471","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Group) (:arg :explicit 0... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7941,"sourceStart":7937,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"mem_rightCoset_iff","source_end":7961,"source_start":7943,"syntax_kind":"ident"},{"source":"mul_mem_cancel_right (s.inv_mem ha)","source_end":7998,"source_start":7963,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.41468","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.41471","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"interna... | 82 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9b2c2199539491e3a358a78e3e9ed65089bcccc09c951d23b64dec2f1027584 | 127f2ee29498247f03aa151250550ac2567f5b247a96550729e6381380322a9c | d1283914fe5f4081381053e881de96954947a664cd20690a25c3df62cccc1e42 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,945 | EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self | Mathlib/Geometry/Euclidean/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | V : Type u_1
P : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : InnerProductSpace ℝ V
inst✝³ : MetricSpace P
inst✝² : NormedAddTorsor V P
s : AffineSubspace ℝ P
inst✝¹ : Nonempty ↥s
inst✝ : HasOrthogonalProjection s.direction
p : ↥s
⊢ (orthogonalProjection s) ↑p = p | case a
V : Type u_1
P : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : InnerProductSpace ℝ V
inst✝³ : MetricSpace P
inst✝² : NormedAddTorsor V P
s : AffineSubspace ℝ P
inst✝¹ : Nonempty ↥s
inst✝ : HasOrthogonalProjection s.direction
p : ↥s
⊢ ↑((orthogonalProjection s) ↑p) = ↑p | ((:c Eq) ((:c Subtype) (:fv _uniq.141050) (:lambda x (:fv _uniq.141050) ((:c Membership.mem) (:fv _uniq.141050) ((:c AffineSubspace) (:c Real) (:fv _uniq.141047) (:fv _uniq.141050) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.141047) (:fv _uniq.141053)) ((:c NormedSpace.toModule) (:c Real) (:fv... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.141047))"},{"name":"inst✝⁴","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.141047) (:c Real.RCLike) (:fv _uniq.141053))"},{"name":"inst✝³","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :ex... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"ext","sourceEnd":19985,"sourceStart":19982,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":19985,"sourceStart":19982,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 54 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67094412bd16695733a485b6e729ada0e03490c2254d5cf5c2be07559f7aa977 | 123eb32d6386570fc6004f9db2a07bb0d1fe90b15907425348fbddcbaea2f745 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | b53126ad3596a14836abdce7bce07c170de39d5358f72e1533db2750f59be2c8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,946 | EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self | Mathlib/Geometry/Euclidean/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>EuclideanGeometry.orthogonalProjection_eq_self_iff</a>] | case a
V : Type u_1
P : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : InnerProductSpace ℝ V
inst✝³ : MetricSpace P
inst✝² : NormedAddTorsor V P
s : AffineSubspace ℝ P
inst✝¹ : Nonempty ↥s
inst✝ : HasOrthogonalProjection s.direction
p : ↥s
⊢ ↑((orthogonalProjection s) ↑p) = ↑p | case a
V : Type u_1
P : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : InnerProductSpace ℝ V
inst✝³ : MetricSpace P
inst✝² : NormedAddTorsor V P
s : AffineSubspace ℝ P
inst✝¹ : Nonempty ↥s
inst✝ : HasOrthogonalProjection s.direction
p : ↥s
⊢ ↑p ∈ s | ((:c Eq) (:fv _uniq.141050) ((:c Subtype.val) (:fv _uniq.141050) (:lambda x (:fv _uniq.141050) ((:c Membership.mem) (:fv _uniq.141050) ((:c AffineSubspace) (:c Real) (:fv _uniq.141047) (:fv _uniq.141050) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.141047) (:fv _uniq.141053)) ((:c NormedSpace.t... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.141047))"},{"name":"inst✝⁴","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.141047) (:c Real.RCLike) (:fv _uniq.141053))"},{"name":"inst✝³","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AffineMap) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":19990,"sourceStart":19988,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19992,"sourceStart":19991,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"EuclideanGeometr... | [] | [{"source":"orthogonalProjection_eq_self_iff","source_end":20024,"source_start":19992,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 54 | 5 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d8e242b563b248b98f4b2b52dc67d4a7c85b58c0b5424d881ffb7a3ecea88db | b53126ad3596a14836abdce7bce07c170de39d5358f72e1533db2750f59be2c8 | ad004f6ab4ffbc04ffa606856bd9bc12d836cced34414805435b5f381401a21e | 8d173e128c16c398925ebfd9732ab871954465c0befb0664fffa4225fd35910c |
cat-searcher/leandojo-benchmark-4-random | test | 2,947 | EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self | Mathlib/Geometry/Euclidean/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact p.2 | case a
V : Type u_1
P : Type u_2
inst✝⁵ : NormedAddCommGroup V
inst✝⁴ : InnerProductSpace ℝ V
inst✝³ : MetricSpace P
inst✝² : NormedAddTorsor V P
s : AffineSubspace ℝ P
inst✝¹ : Nonempty ↥s
inst✝ : HasOrthogonalProjection s.direction
p : ↥s
⊢ ↑p ∈ s | ((:c Membership.mem) (:fv _uniq.141050) ((:c AffineSubspace) (:c Real) (:fv _uniq.141047) (:fv _uniq.141050) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.141047) (:fv _uniq.141053)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.141047) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminorme... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.141047))"},{"name":"inst✝⁴","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.141047) (:c Real.RCLike) (:fv _uniq.141053))"},{"name":"inst✝³","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":20033,"sourceStart":20028,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"p","sourceEnd":20035,"sourceStart":20034,"tag":"identifier"},{"source":".","sourceEnd":20036,"sourceStart":20035,"tag":"atom"},{"children":[{"source":"2","sourceEnd":20037,... | [] | [{"source":"p.2","source_end":20037,"source_start":20034,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.141047","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.141050","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 54 | 8 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae42ed8c1cc02ba095c020d434456627499d5900a6eca8af945a26ecdf803d4e | 8d173e128c16c398925ebfd9732ab871954465c0befb0664fffa4225fd35910c | 705e0ce2d5752fc1ae274dcaca171d97ec7582c4a0433b42db4da6e39bd55bb4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,952 | Function.update_idem | Mathlib/Logic/Function/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | funext b | α✝ : Sort u
β✝ : α✝ → Sort v
α' : Sort w
inst✝² : DecidableEq α✝
inst✝¹ : DecidableEq α'
f✝ g : (a : α✝) → β✝ a
a✝ : α✝
b : β✝ a✝
α : Sort u_2
inst✝ : DecidableEq α
β : α → Sort u_1
a : α
v w : β a
f : (a : α) → β a
⊢ update (update f a v) a w = update f a w | case h
α✝ : Sort u
β✝ : α✝ → Sort v
α' : Sort w
inst✝² : DecidableEq α✝
inst✝¹ : DecidableEq α'
f✝ g : (a : α✝) → β✝ a
a✝ : α✝
b✝ : β✝ a✝
α : Sort u_2
inst✝ : DecidableEq α
β : α → Sort u_1
a : α
v w : β a
f : (a : α) → β a
b : α
⊢ update (update f a v) a w b = update f a w b | ((:c Eq) (:forall a (:fv _uniq.29096) ((:fv _uniq.29098) 0)) ((:c Function.update) (:fv _uniq.29096) (:fv _uniq.29098) (:fv _uniq.29097) ((:c Function.update) (:fv _uniq.29096) (:fv _uniq.29098) (:fv _uniq.29097) (:fv _uniq.29102) (:fv _uniq.29099) (:fv _uniq.29100)) (:fv _uniq.29099) (:fv _uniq.29101)) ((:c Function.u... | [{"name":"α✝","sexp":"(:sort u)"},{"name":"β✝","sexp":"(:forall _ (:fv _uniq.28920) (:sort v))"},{"name":"α'","sexp":"(:sort w)"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.28920))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.28926))"},{"name":"f✝","sexp":"(:forall a (:fv _uniq.28920) ((:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:forall a :explicit (:fv FV10) (:app (:fv FV12) (:arg :explicit 0 0)))) (:arg :explicit 1 (:app (:c Function.update) (:arg :implicit-type 0 (:fv FV10)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV10))))) (:arg :explicit 3 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28920","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28924","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"source":"funext","sourceEnd":32535,"sourceStart":32529,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":32537,"sourceStart":32536,"tag":"identifier"}],"kind":"null","source":"b","sourceEnd":32537,"sourceStart":32536,"tag":"node"}],"kind":"tacticFunext___","source":"funex... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28920","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28924","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 247 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9315ba244a301da93afb54396ff44ead7fbeb63f28313ac034a5059b7e576fab | 794de3bf8fa8ca6407a69abe4fbd54781607ec2358366c51b3f6937368448a8e | 2de0c9e5bd099011609e05a5ed1aa64b5091c76e1ddcbdf2efe52e3119141e67 | 5b86a97d721d53c0ea2c680928471c7aaf1152d68f40c00a5ba778a1a496d2a8 |
cat-searcher/leandojo-benchmark-4-random | test | 2,953 | Function.update_idem | Mathlib/Logic/Function/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : b = a <;> simp [<a>Function.update</a>, h] | case h
α✝ : Sort u
β✝ : α✝ → Sort v
α' : Sort w
inst✝² : DecidableEq α✝
inst✝¹ : DecidableEq α'
f✝ g : (a : α✝) → β✝ a
a✝ : α✝
b✝ : β✝ a✝
α : Sort u_2
inst✝ : DecidableEq α
β : α → Sort u_1
a : α
v w : β a
f : (a : α) → β a
b : α
⊢ update (update f a v) a w b = update f a w b | ((:c Eq) ((:fv _uniq.29098) (:fv _uniq.29125)) ((:c Function.update) (:fv _uniq.29096) (:fv _uniq.29098) (:fv _uniq.29097) ((:c Function.update) (:fv _uniq.29096) (:fv _uniq.29098) (:fv _uniq.29097) (:fv _uniq.29102) (:fv _uniq.29099) (:fv _uniq.29100)) (:fv _uniq.29099) (:fv _uniq.29101) (:fv _uniq.29125)) ((:c Functi... | [{"name":"α✝","sexp":"(:sort u)"},{"name":"β✝","sexp":"(:forall _ (:fv _uniq.28920) (:sort v))"},{"name":"α'","sexp":"(:sort w)"},{"name":"inst✝²","sexp":"((:c DecidableEq) (:fv _uniq.28920))"},{"name":"inst✝¹","sexp":"((:c DecidableEq) (:fv _uniq.28926))"},{"name":"f✝","sexp":"(:forall a (:fv _uniq.28920) ((:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:fv FV12) (:arg :explicit 0 (:fv FV17)))) (:arg :explicit 1 (:app (:c Function.update) (:arg :implicit-type 0 (:fv FV10)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:app (:c DecidableEq) (:arg :explicit 0 (:fv FV10))))) (:arg :explicit 3 (:app (:c Function.update) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28920","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28924","is_instance":false,"is_let":false,"name":"β✝","sexp":"(:forall _ :explicit (:fv FV0) (:sort Type))... | {"children":[{"children":[{"source":"by_cases","sourceEnd":32548,"sourceStart":32540,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":32550,"sourceStart":32549,"tag":"identifier"},{"source":":","sourceEnd":32552,"sourceStart":32551,"tag":"atom"}],"kind":"null","source":"h :","sourceEnd... | [] | [{"source":"b = a","source_end":32558,"source_start":32553,"syntax_kind":"«term_=_»"},{"source":"update","source_end":32575,"source_start":32569,"syntax_kind":"ident"},{"source":"h","source_end":32578,"source_start":32577,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28920","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28924","is_instance":false,"is_let":false,"user_name":"β✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 247 | 5 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd48d9ae5ac4c9adda09d6fcd6f1086982b7544fa430a4d40998538ccffd8055 | 5b86a97d721d53c0ea2c680928471c7aaf1152d68f40c00a5ba778a1a496d2a8 | a0b62b660b06e61925dd0345e51b2d34c11333b009bd9ba05f61c8651a2d4adf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,954 | Ordinal.one_lt_omega | Mathlib/SetTheory/Ordinal/Arithmetic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Nat.cast_one</a>] using <a>Ordinal.nat_lt_omega</a> 1 | ⊢ 1 < ω | ((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordinal.one))) (:c Ordinal.omega)) | [] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Ordinal)... | [] | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":107812,"sourceStart":107807,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [{"source":"Nat.cast_one","source_end":107831,"source_start":107819,"syntax_kind":"ident"},{"source":"nat_lt_omega 1","source_end":107853,"source_start":107839,"syntax_kind":"Lean.Parser.Term.app"}] | [] | 762 | 2 | exact | true | 1 | 0 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d4920bc33adee77a8fd6eae8a5ec8befb27816de39970074186be5fce2662d07 | 2023b9ed70da0a6867a321d133b981e1492322983fc1f8022b86e9559e31024f | d6e0716f8b17375aa5cedb7d08709184a1284284257e0ad183f2803ecc50e62f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,955 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let T : <a>Set</a> X.V := <a>MulAction.orbit</a> G x | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
⊢ ∃ g, g • x = y | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
⊢ ∃ g, g • x = y | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"let","sourceEnd":4742,"sourceStart":4739,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"T","sourceEnd":4744,"sourceStart":4743,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4746,"so... | [] | [{"source":"Set X.V","source_end":4754,"source_start":4747,"syntax_kind":"Lean.Parser.Term.app"},{"source":"MulAction.orbit G x","source_end":4777,"source_start":4758,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 58a17cc528db41bfd98c4fb6d7d451eaf5063308ca07765c13d2dd614b7932d6 | 4f5818137f70d5ab6feb975d38387ebee8d31d1b5922e8e0fdd9f88f252384c4 | ca21f92156c4178335f8f6c323e05aaf9abfb7a778e5671ec9d681aa1f7bd921 | 3f4245453a0b132f8c0931b9354abab19322360b9ffd18514bc9979d6ae60bab |
cat-searcher/leandojo-benchmark-4-random | test | 2,956 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>Fintype</a> T := <a>Fintype.ofFinite</a> T | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
⊢ ∃ g, g • x = y | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this : Fintype ↑T
⊢ ∃ g, g • x = y | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":4786,"sourceStart":4782,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4787,"sourceStart":4787,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4787,"sourceStart":4787,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"Fintype T","source_end":4798,"source_start":4789,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Fintype.ofFinite T","source_end":4820,"source_start":4802,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a7546739dc6a82f1ed3e01da1999acce77a07108aae5528c2ce967327cf644dd | 3f4245453a0b132f8c0931b9354abab19322360b9ffd18514bc9979d6ae60bab | e6ca0ad2d77840cd4af677175dc47d82544cc77ff8289a0cb5623575e7c67848 | 7451b80b472b7f824afed950652bc4b3f8f445c0d1a5e3ded234df8aecacb789 |
cat-searcher/leandojo-benchmark-4-random | test | 2,957 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI : <a>MulAction</a> G (<a>FintypeCat.of</a> T) := <a>inferInstanceAs</a> <| <a>MulAction</a> G ↑(<a>MulAction.orbit</a> G x) | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this : Fintype ↑T
⊢ ∃ g, g • x = y | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
⊢ ∃ g, g • x = y | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"letI","sourceEnd":4829,"sourceStart":4825,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4830,"sourceStart":4830,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4830,"sourceStart":4830,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"MulAction G (FintypeCat.of T)","source_end":4861,"source_start":4832,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inferInstanceAs <| MulAction G ↑(MulAction.orbit G x)","source_end":4920,"source_start":4865,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 6 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2000bf45a734d7093fbd2bd5daa44c46085754ee80a5e5081ed5596b697ce658 | 7451b80b472b7f824afed950652bc4b3f8f445c0d1a5e3ded234df8aecacb789 | 16b9baf7bab14c088b310cf42c0f3a2e36a24884946286e765635cfc059bb582 | 48613d85b848a57c02ed8e5dba81b139427d1806fc46bac94340b139b3eac190 |
cat-searcher/leandojo-benchmark-4-random | test | 2,958 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let T' : <a>Action</a> <a>FintypeCat</a> (<a>MonCat.of</a> G) := <a>Action.FintypeCat.ofMulAction</a> G (<a>FintypeCat.of</a> T) | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
⊢ ∃ g, g • x = y | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G (... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"let","sourceEnd":4928,"sourceStart":4925,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"T'","sourceEnd":4931,"sourceStart":4929,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4933,"s... | [] | [{"source":"Action FintypeCat (MonCat.of G)","source_end":4965,"source_start":4934,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Action.FintypeCat.ofMulAction G (FintypeCat.of T)","source_end":5018,"source_start":4969,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c6ce34e5ef4f7f1001775ff52c296c165b81802c2493924e098d9bfce3c728be | 48613d85b848a57c02ed8e5dba81b139427d1806fc46bac94340b139b3eac190 | 12401df9dc3111f051c963cd653f71c122b53f274656686ea24cc4dd57140d7b | b76e3a082da6b910f7b17e2ba5d57b303d1b2a37e5dfd4f5be957d39fed1de08 |
cat-searcher/leandojo-benchmark-4-random | test | 2,959 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let i : T' ⟶ X := ⟨<a>Subtype.val</a>, fun _ ↦ <a>rfl</a>⟩ | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G (... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G (... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"let","sourceEnd":5026,"sourceStart":5023,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":5028,"sourceStart":5027,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":5030,"so... | [] | [{"source":"T' ⟶ X","source_end":5039,"source_start":5031,"syntax_kind":"«term_⟶_»"},{"source":"⟨Subtype.val, fun _ ↦ rfl⟩","source_end":5075,"source_start":5043,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 8 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8515bfa57bdda9516d62779778cac619aaaebb9fa5747a0170f402b4659f19af | b76e3a082da6b910f7b17e2ba5d57b303d1b2a37e5dfd4f5be957d39fed1de08 | 49a67680b2b82253779b6f28bba0fac7f5b251ec1473946691ea9b28d4707aee | 1ef7b9c81ed65b5222303fee0c882d28497204a5c0c7773aaf1dc6816703e8df |
cat-searcher/leandojo-benchmark-4-random | test | 2,960 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>CategoryTheory.Mono</a> i := <a>CategoryTheory.ConcreteCategory.mono_of_injective</a> _ (<a>Subtype.val_injective</a>) | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝ : Fintype ↑T
this : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G (... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":5084,"sourceStart":5080,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5085,"sourceStart":5085,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5085,"sourceStart":5085,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"Mono i","source_end":5093,"source_start":5087,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ConcreteCategory.mono_of_injective _ (Subtype.val_injective)","source_end":5157,"source_start":5097,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 9 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a90e1e869705751a28f4e5513174c7ed7d154d14c89d067023fd422b32923e67 | 1ef7b9c81ed65b5222303fee0c882d28497204a5c0c7773aaf1dc6816703e8df | 5d6892bcf517dbb9548bbbf1738028fceef036de0e2e96dc38b646c30fb38ca9 | c6e33f2a8a00e97e785b1c5491f4c5fe8eac1498dfdaaa9af4156a14d185a17d |
cat-searcher/leandojo-benchmark-4-random | test | 2,961 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : <a>CategoryTheory.IsIso</a> i := by apply <a>CategoryTheory.PreGaloisCategory.IsConnected.noTrivialComponent</a> T' i apply (<a>CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty</a> (<a>Action.forget</a> _ _) T').<a>Iff.mpr</a> exact <a>Set.Nonempty.coe_sort</a> (<a>MulAction.orbit_nonempty</a> x) | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":5166,"sourceStart":5162,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":5167,"sourceStart":5167,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":5167,"sourceStart":5167,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"IsIso i","source_end":5176,"source_start":5169,"syntax_kind":"Lean.Parser.Term.app"},{"source":"IsConnected.noTrivialComponent T' i","source_end":5230,"source_start":5195,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(not_initial_iff_fiber_nonempty (Action.forget _ _) T').mpr","source_end":5302,"source_s... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 10 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c74434ab71c25bf2d4f57b01bb2090b24e2ae1f4d37579727784f1f3419f3162 | c6e33f2a8a00e97e785b1c5491f4c5fe8eac1498dfdaaa9af4156a14d185a17d | 3ff4b8a11e13910dd3b1c942183f2d35193f5d4bc489f9a438fec89b5146243d | c62880e5e793b9c41fc66f16a26e235fd2cc2fa00ad1a965879c64195cbc8927 |
cat-searcher/leandojo-benchmark-4-random | test | 2,962 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hb : <a>Function.Bijective</a> i.hom := by apply (<a>CategoryTheory.ConcreteCategory.isIso_iff_bijective</a> i.hom).<a>Iff.mp</a> exact <a>CategoryTheory.Functor.map_isIso</a> (<a>CategoryTheory.forget₂</a> _ <a>FintypeCat</a>) i | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"have","sourceEnd":5374,"sourceStart":5370,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hb","sourceEnd":5377,"sourceStart":5375,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hb","sourceEnd":5377,"sourceStart":5375,"tag":"node"},{"... | [] | [{"source":"Function.Bijective i.hom","source_end":5404,"source_start":5380,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(ConcreteCategory.isIso_iff_bijective i.hom).mp","source_end":5470,"source_start":5423,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"map_isIso (forget₂ _ FintypeCat) i","source_end":5519,"sou... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 15 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b31ba28f4dd4d8363f5cca23104fed506ce7c014e393d18d7cdfbd006e92efc | c62880e5e793b9c41fc66f16a26e235fd2cc2fa00ad1a965879c64195cbc8927 | 32ed6101d0584d79df1d90e1be9ca182a251e161f6d2d7d3eb0b6a288fb41146 | 6868cd507ea77f106eaa9873021f160492f8e968ef919220ba56d0d02efd4a97 |
cat-searcher/leandojo-benchmark-4-random | test | 2,963 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨y', ⟨g, (hg : g • x = y')⟩⟩, (hy' : y' = y)⟩ := hb.surjective y | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | case intro.mk.intro
G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.Fin... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"obtain","sourceEnd":5530,"sourceStart":5524,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5534,"sourceStart":5531,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":5537,"sourceStart":5534,"tag":"... | [] | [{"source":"hb.surjective y","source_end":5610,"source_start":5595,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨⟨y', ⟨g, (hg : g • x = y')⟩⟩, (hy' : y' = y)⟩","source_end":5591,"source_start":5531,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 19 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a3b9def791b5930e809c939bbe602a2f35aaa0f3622d0a786db28c0c722391c | 6868cd507ea77f106eaa9873021f160492f8e968ef919220ba56d0d02efd4a97 | 2d18d9d72aa9ce4b6edc92812db58b15859b6b5da2319e3e69bacb7d63dc2c27 | 0ed005a04e1d351d26a1f4822f6241e1de9fd740aa53054a4e10735c24ccbb55 |
cat-searcher/leandojo-benchmark-4-random | test | 2,964 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use g | case intro.mk.intro
G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.Fin... | case h
G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMul... | ((:c Exists) (:fv _uniq.23356) (:lambda g (:fv _uniq.23356) ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda g :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c Categor... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"use","sourceEnd":5618,"sourceStart":5615,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":16,"semanticRole":"local","source":"g","sourceEnd":5620,"sourceStart":5619,"tag":"identifier"}],"kind... | [] | [{"source":"g","source_end":5620,"source_start":5619,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 20 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e1e367047cd2b8ec4320bb0a6b73231be3e5d852de9238c771e4744040c0f71 | 0ed005a04e1d351d26a1f4822f6241e1de9fd740aa53054a4e10735c24ccbb55 | 6c053a36d3a4ea6e58125ea10360a652ec17ba87ba500b5f7054381a22b87b4d | 1843af793092a2e588aca5ea1c04ffefdef12bf40172e06268472d90430cd74b |
cat-searcher/leandojo-benchmark-4-random | test | 2,965 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hg.trans hy' | case h
G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMul... | ((:c Eq) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (:fv _uniq.24929))) ((:c HSMul.hSMul) (:fv _uniq.23356) ((:c ... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:arg :implicit 2) (:arg :explicit 3 (:fv FV3... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":5630,"sourceStart":5625,"tag":"atom"},{"children":[{"source":"hg.trans","sourceEnd":5639,"sourceStart":5631,"tag":"identifier"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"hy'","sourceEnd":5643,"sourceStart":5640,"tag":"identifier"}],"kind":"null","source"... | [] | [{"source":"hg.trans hy'","source_end":5643,"source_start":5631,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 21 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1b3a477e07cce2266e90974696d77577ac625a871f730f063fe0985bd52e015c | 1843af793092a2e588aca5ea1c04ffefdef12bf40172e06268472d90430cd74b | e11fd07e65c4265adb7692f82ade728bb539a112ca61b94d16078b3a31409625 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,966 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>CategoryTheory.PreGaloisCategory.IsConnected.noTrivialComponent</a> T' i | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | ((:c CategoryTheory.IsIso) ((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))) ((:c Action.instCategory) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:app (:c Action) (:arg :explicit 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:arg :explicit 2 (:app (:c MonCat.of) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":5194,"sourceStart":5189,"tag":"atom"},{"children":[{"name":"CategoryTheory.PreGaloisCategory.IsConnected.noTrivialComponent","semanticRole":"global","source":"IsConnected.noTrivialComponent","sourceEnd":5225,"sourceStart":5195,"tag":"identifier"},{"children":[{"contextIndex":1... | [] | [{"source":"IsConnected.noTrivialComponent T' i","source_end":5230,"source_start":5195,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 12 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50d24a5a6a736964cb1e563f85919bef1d1340ffcbaa3a16d96ab85a126e9205 | 04ddb4e3ef2ed7a8eeac81594bf3bea6d3524f2c81dda44c47409d83fecc2f0c | 86d2dbf60622f997cde96e476bb98d633898d104aea206eb357c3971a3c95aba | 26b4bf0fc89af0114b050f76ab8c39918a2ab893669a2868d1035162f219ce34 |
cat-searcher/leandojo-benchmark-4-random | test | 2,967 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty</a> (<a>Action.forget</a> _ _) T').<a>Iff.mpr</a> | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | (:forall _ ((:c CategoryTheory.Limits.IsInitial) ((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))) ((:c Action.instCategory) (:c FintypeCat) (:c FintypeCat.instCateg... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:forall _ :explicit (:app (:c CategoryTheory.Limits.IsInitial) (:arg :implicit-type 0 (:app (:c Action) (:arg :explicit 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:arg :explicit 2 (:app (:c MonCat.of) (:arg :explicit 0 (:fv FV0)) (:arg :... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":5242,"sourceStart":5237,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":5244,"sourceStart":5243,"tag":"atom"},{"children":[{"name":"CategoryTheory.PreGaloisCategory.not_initial_iff_fiber_nonempty","semanticRole":"global","source":"not_initial_iff_fiber_nonemp... | [] | [{"source":"(not_initial_iff_fiber_nonempty (Action.forget _ _) T').mpr","source_end":5302,"source_start":5243,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 13 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8faaac88b81266d110f4070ab8fe47efb207994ca4d73b7a4e8b7c79e06e72fc | 26b4bf0fc89af0114b050f76ab8c39918a2ab893669a2868d1035162f219ce34 | 01e13fc0a5190a463943720c363fc972c7cadaabd0d6ceebaa4228c265a6daba | 62376d04647e1c35fc92a9ecfc799ae882803fdc6f96a3ba882d140e9712d09e |
cat-searcher/leandojo-benchmark-4-random | test | 2,968 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.Nonempty.coe_sort</a> (<a>MulAction.orbit_nonempty</a> x) | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝¹ : Fintype ↑T
this✝ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction G... | ((:c Nonempty) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Prefunctor.obj) ((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))) ((:c CategoryTheory.CategoryStruct.... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Nonempty) (:arg :explicit 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c Action) (:arg :explicit 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":5314,"sourceStart":5309,"tag":"atom"},{"children":[{"name":"Set.Nonempty.coe_sort","semanticRole":"global","source":"Set.Nonempty.coe_sort","sourceEnd":5336,"sourceStart":5315,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":5338,"sourceStart":5337,"tag"... | [] | [{"source":"Set.Nonempty.coe_sort (MulAction.orbit_nonempty x)","source_end":5365,"source_start":5315,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 14 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a73f60dede0c35963684801cfc42ed587b4339fc3d327d923dd712ce29162aba | 62376d04647e1c35fc92a9ecfc799ae882803fdc6f96a3ba882d140e9712d09e | c460b3ac106a0b5966f6655b1a84b6186cc1194415e466421ca1b31827937049 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,969 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (<a>CategoryTheory.ConcreteCategory.isIso_iff_bijective</a> i.hom).<a>Iff.mp</a> | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | ((:c Function.Bijective) ((:c CategoryTheory.Bundled.α) (:c Fintype) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (:fv _uniq.28316))) ((:c CategoryTheory.Bundl... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c Function.Bijective) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c Action.V) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:arg :implicit 2) (:arg :exp... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"apply","sourceEnd":5422,"sourceStart":5417,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":5424,"sourceStart":5423,"tag":"atom"},{"children":[{"name":"CategoryTheory.ConcreteCategory.isIso_iff_bijective","semanticRole":"global","source":"ConcreteCategory.isIso_iff_bijective","s... | [] | [{"source":"(ConcreteCategory.isIso_iff_bijective i.hom).mp","source_end":5470,"source_start":5423,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 17 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2d6eb5f7b42347658681495db20238115755f2b3056baf10ec4da9a1a9d0146c | cfed504afd77a9a2b7011e27f71603f59843cd3923a3307e0e4f8d5cbb901c63 | 03d9d3a20863ba94a4a3d67454ddef38502407ef8efa3fc6ed678a94c73efe1a | 0d0158d85e7c08703f4b9be8d0b75bb5d09dbad0bf128c712312539f60351d2c |
cat-searcher/leandojo-benchmark-4-random | test | 2,970 | CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected | Mathlib/CategoryTheory/Galois/Examples.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>CategoryTheory.Functor.map_isIso</a> (<a>CategoryTheory.forget₂</a> _ <a>FintypeCat</a>) i | G : Type u
inst✝¹ : Group G
X : Action FintypeCat (MonCat.of G)
inst✝ : IsConnected X
x y : ↑X.V
T : Set ↑X.V := MulAction.orbit G x
this✝² : Fintype ↑T
this✝¹ : MulAction G ↑(FintypeCat.of ↑T) := inferInstanceAs (MulAction G ↑(MulAction.orbit G x))
T' : Action FintypeCat (MonCat.of G) := Action.FintypeCat.ofMulAction ... | ((:c CategoryTheory.IsIso) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c Action.V) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359)))) (:fv _uniq.28316)) ((:c Action.V) (:c Fint... | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Group) (:fv _uniq.23356))"},{"name":"X","sexp":"((:c Action) (:c FintypeCat) (:c FintypeCat.instCategory) ((:c MonCat.of) (:fv _uniq.23356) ((:c DivInvMonoid.toMonoid) (:fv _uniq.23356) ((:c Group.toDivInvMonoid) (:fv _uniq.23356) (:fv _uniq.23359))))... | (:app (:c CategoryTheory.IsIso) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:c FintypeCat))))) (:arg :implicit 2) (:arg :implicit 3) (:arg :explicit 4 (:app (:c Action.Hom.hom) (:arg :implicit-type 0 (:c FintypeCat)) (:arg :instance 1 (:i... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Group) (:arg :explicit ... | {"children":[{"source":"exact","sourceEnd":5482,"sourceStart":5477,"tag":"atom"},{"children":[{"name":"CategoryTheory.Functor.map_isIso","semanticRole":"global","source":"map_isIso","sourceEnd":5492,"sourceStart":5483,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":5494,"sourceStart":5493,"tag":... | [] | [{"source":"map_isIso (forget₂ _ FintypeCat) i","source_end":5519,"source_start":5483,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.23356","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.23359","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":3,"intern... | 16 | 18 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e087dec953e3ce31dc2c3f73503a3ae4db27b9cd2034eaeeea41a7b6494c8d37 | 0d0158d85e7c08703f4b9be8d0b75bb5d09dbad0bf128c712312539f60351d2c | 7f8398315cf88c3bfd4df7ba6ebd97df35d9c655e370500c86b2494a169f03e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,971 | MeasureTheory.addContent_union_le | Mathlib/MeasureTheory/Measure/AddContent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.union_diff_self</a>, <a>MeasureTheory.addContent_union</a> hC hs (hC.diff_mem ht hs)] | α : Type u_1
C : Set (Set α)
s t : Set α
I : Finset (Set α)
m m' : AddContent C
hC : IsSetRing C
hs : s ∈ C
ht : t ∈ C
⊢ m (s ∪ t) ≤ m s + m t | α : Type u_1
C : Set (Set α)
s t : Set α
I : Finset (Set α)
m m' : AddContent C
hC : IsSetRing C
hs : s ∈ C
ht : t ∈ C
⊢ m s + m (t \ s) ≤ m s + m t
α : Type u_1
C : Set (Set α)
s t : Set α
I : Finset (Set α)
m m' : AddContent C
hC : IsSetRing C
hs : s ∈ C
ht : t ∈ C
⊢ Disjoint s (t \ s) | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompletelyDis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"((:c Set) ((:c Set) (:fv _uniq.16679)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"I","sexp":"((:c Finset) ((:c Set) (:fv _uniq.16679)))"},{"name":"m","sexp":"((:c MeasureTheory.AddContent)... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.AddContent) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)))) (:arg :implicit-typ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"name":"C","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (:c Set... | {"children":[{"source":"rw","sourceEnd":5694,"sourceStart":5692,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5696,"sourceStart":5695,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":5699,"sourceStart":... | [] | [{"source":"union_diff_self","source_end":5715,"source_start":5700,"syntax_kind":"ident"},{"source":"addContent_union hC hs (hC.diff_mem ht hs)","source_end":5759,"source_start":5717,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 21 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb619f20a5e68454fac885029a4804e4d07d6377b67171a8fc5be5b00a704a44 | 8746c27cd33ff47eb6e8faabe393f304d4988c3aee52fa85c9aa1bf73ef3635b | aa7fa229b049d7ca4d63ae6631216db4776750c50d93bc93e76f7eb9efa881b3 | efabba66bf47ba79f5b3f402740966dbed64430686c652772568a7a960fd7065 |
cat-searcher/leandojo-benchmark-4-random | test | 2,972 | MeasureTheory.addContent_union_le | Mathlib/MeasureTheory/Measure/AddContent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>add_le_add</a> <a>le_rfl</a> (<a>MeasureTheory.addContent_mono</a> hC.isSetSemiring (hC.diff_mem ht hs) ht <a>Set.diff_subset</a>) | α : Type u_1
C : Set (Set α)
s t : Set α
I : Finset (Set α)
m m' : AddContent C
hC : IsSetRing C
hs : s ∈ C
ht : t ∈ C
⊢ m s + m (t \ s) ≤ m s + m t | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c CompleteSemilatticeInf.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.toCompleteSemilatticeInf) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompletelyDis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"((:c Set) ((:c Set) (:fv _uniq.16679)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"I","sexp":"((:c Finset) ((:c Set) (:fv _uniq.16679)))"},{"name":"m","sexp":"((:c MeasureTheory.AddContent)... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c ENNReal)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"name":"C","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (:c Set... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":5771,"sourceStart":5766,"tag":"atom"},{"children":[{"name":"add_le_add","semanticRole":"global","source":"add_le_add","sourceEnd":5782,"sourceStart":5772,"tag":"identifier"},{"children":[{"name":"le_rfl","semanticRole":"global","source":"... | [] | [{"source":"add_le_add le_rfl\n (addContent_mono hC.isSetSemiring (hC.diff_mem ht hs) ht diff_subset)","source_end":5865,"source_start":5772,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 21 | 10 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c846ddb649fb9cbb8f965b2b7bdcdc2f07341068857016da136dad54556780ff | 97e5ab0676b28ccde59714ff7f77bcb93476ffa2550fbe0edf3aad024894db54 | 0d8c7f585f1cfc7e2ddd985cd175f94041e8a6f86e3e879987300e7710cece38 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,973 | MeasureTheory.addContent_union_le | Mathlib/MeasureTheory/Measure/AddContent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.disjoint_iff_inter_eq_empty</a>, <a>Set.inter_diff_self</a>] | α : Type u_1
C : Set (Set α)
s t : Set α
I : Finset (Set α)
m m' : AddContent C
hC : IsSetRing C
hs : s ∈ C
ht : t ∈ C
⊢ Disjoint s (t \ s) | ((:c Disjoint) ((:c Set) (:fv _uniq.16679)) ((:c CompleteSemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.16679)) ((:c CompleteLattice.toCompleteSemilatticeInf) ((:c Set) (:fv _uniq.16679)) ((:c CompletelyDistribLattice.toCompleteLattice) ((:c Set) (:fv _uniq.16679)) ((:c CompleteAtomicBooleanAlgebra.toCompletelyDis... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"C","sexp":"((:c Set) ((:c Set) (:fv _uniq.16679)))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"t","sexp":"((:c Set) (:fv _uniq.16679))"},{"name":"I","sexp":"((:c Finset) ((:c Set) (:fv _uniq.16679)))"},{"name":"m","sexp":"((:c MeasureTheory.AddContent)... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"name":"C","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (:c Set... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5873,"sourceStart":5871,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5875,"sourceStart":5874,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"Set.disjoint_iff_inter_eq_empty","source_end":5906,"source_start":5875,"syntax_kind":"ident"},{"source":"inter_diff_self","source_end":5923,"source_start":5908,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16679","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16683","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 21 | 15 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33612b398dfef2225b6f0b187ee392ba031cb8a948fa9ae9d5a8222dcd71074e | 24f2984560834fc702ec84f4eadaf516af91a2f1423f7a34ccbed9e33d117097 | fe688f323e9b05121b476b296e47b7556b7b59fafd787cd07936f17c52cfc2b4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,974 | Set.countable_pi | Mathlib/Data/Set/Countable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [← <a>Set.mem_univ_pi</a>] using <a>Set.countable_univ_pi</a> hs | α : Type u
β : Type v
γ : Type w
ι : Sort x
π : α → Type u_1
inst✝ : Finite α
s : (a : α) → Set (π a)
hs : ∀ (a : α), (s a).Countable
⊢ {f | ∀ (a : α), f a ∈ s a}.Countable | ((:c Set.Countable) (:forall a (:fv _uniq.11028) ((:fv _uniq.11125) 0)) ((:c setOf) (:forall a (:fv _uniq.11028) ((:fv _uniq.11125) 0)) (:lambda f (:forall a (:fv _uniq.11028) ((:fv _uniq.11125) 0)) (:forall a (:fv _uniq.11028) ((:c Membership.mem) ((:fv _uniq.11125) 0) ((:c Set) ((:fv _uniq.11125) 0)) ((:c Set.instMem... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"π","sexp":"(:forall _ (:fv _uniq.11028) (:sort (+ u_1 1)))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.11028))"},{"name":"s","sexp":"(:forall a (:fv _uniq.110... | (:app (:c Set.Countable) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:app (:fv FV5) (:arg :explicit 0 0)))) (:arg :explicit 1 (:app (:c setOf) (:arg :implicit-type 0 (:forall a :explicit (:fv FV0) (:app (:fv FV5) (:arg :explicit 0 0)))) (:arg :explicit 1 (:lambda f :explicit (:forall a :explicit (:fv FV0) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11028","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11030","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":13473,"sourceStart":13468,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"mem_univ_pi","source_end":13495,"source_start":13484,"syntax_kind":"ident"},{"source":"countable_univ_pi hs","source_end":13523,"source_start":13503,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11028","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11030","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 102 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4b4706dfa2da3434658592bef4f3b777a650f746cfacbd9f9b7959f20cf069c0 | 89e7a58f01a6c8c7e64797881229828f1d8be1cab148f8bff40fe024b91465f0 | b3b972800d077a9d72bdf8cca35beade572cd080f3e2d0fa3c8c3eb0e8caf5e5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,975 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro J | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
⊢ ∀ (I_1 : LieIdeal R ↥↑I), I_1 = ⊥ ∨ I_1 = ⊤ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
⊢ J = ⊥ ∨ J = ⊤ | (:forall I ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c Add... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:forall I :explicit (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":4420,"sourceStart":4415,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"J","sourceEnd":4422,"sourceStart":4421,"tag":"identifier"}],"kind":"null","source":"J\n -- We first show that `J` is also an ideal of the ambient Lie algebra `L`.","sourceEnd":4422,"... | [{"role":"fresh_name","source":"J\n -- We first show that `J` is also an ideal of the ambient Lie algebra `L`.","source_end":4422,"source_start":4421,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5cef2f87fb10d28333c8633c5ada9b159be7f84ea55b56fed948f0a9af3ac4ea | aeae743a11416f5809a5098d18c97a4390ccebe060a9fcb1abdefbde818ef4a2 | 663294dacd4424b454afeb475795d1b2cf52e82cba7c798589b8dcc0a80db69b | e03a0f333ce5f308258effdd2f2ea0a76ad7ab4655d9f9284700b743a394630c |
cat-searcher/leandojo-benchmark-4-random | test | 2,976 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Classical.or_iff_not_imp_right</a>] | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
⊢ J = ⊥ ∨ J = ⊤ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
⊢ ¬J = ⊤ → J = ⊥ | ((:c Or) ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) (... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Or) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":6516,"sourceStart":6514,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6518,"sourceStart":6517,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Classical.or_iff_not... | [] | [{"source":"or_iff_not_imp_right","source_end":6538,"source_start":6518,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 58 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb2422d78d448840151e263a2a0b39755c9f5f7afd08a1754ab47e02eeb12f14 | 678325b8c9a074312808d5d3ff836276b3128bb0de31618daa409266562a91be | 016c1f7c3c3331cd630691bf994fd78847a429bddec00d9523a7e999c6aa65f0 | 13020c6406acdc16f076cbeef75d822df8a9188656d7188ddb8424086e9a7a2a |
cat-searcher/leandojo-benchmark-4-random | test | 2,977 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro hJ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
⊢ ¬J = ⊤ → J = ⊥ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J = ⊥ | (:forall _ ((:c Not) ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:forall _ :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":6549,"sourceStart":6544,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hJ","sourceEnd":6552,"sourceStart":6550,"tag":"identifier"}],"kind":"null","source":"hJ","sourceEnd":6552,"sourceStart":6550,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source":"i... | [{"role":"fresh_name","source":"hJ","source_end":6552,"source_start":6550,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 61 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29a6acf26ed2aecbc570de046901101f8c6bdc400a825f5297da6dcc637256e2 | 13020c6406acdc16f076cbeef75d822df8a9188656d7188ddb8424086e9a7a2a | 0a8e8a9c768bf0d57c4e9e2ede6dcc8820c85f71be7bfffcd1bf68228ce3c7e0 | 224f197bab954e63152b2f46069fca34715caad3d6637d176d08fb535760fe78 |
cat-searcher/leandojo-benchmark-4-random | test | 2,978 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices J' = ⊥ by rw [<a>eq_bot_iff</a>] at this ⊢ intro x hx suffices x ∈ J → x = 0 from this hx simpa [J'] using @this x.1 | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J = ⊥ | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' = ⊥ | ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCo... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"suffices","sourceEnd":6565,"sourceStart":6557,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":6566,"sourceStart":6566,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":6566,"sourceStart":6566,"tag":"node"},{"children":[{"contextIndex":10,"semanticRole":"local","s... | [] | [{"source":"J' = ⊥","source_end":6574,"source_start":6566,"syntax_kind":"«term_=_»"},{"source":"eq_bot_iff","source_end":6598,"source_start":6588,"syntax_kind":"ident"},{"source":"this","source_end":6607,"source_start":6603,"syntax_kind":"ident"},{"source":"x ∈ J → x = 0","source_end":6661,"source_start":6644,"syntax_k... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 62 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9ee133e4f9b9a0fad71ee7a2b58b1900797a2b6f3f5b299008892373b58ee5a2 | 224f197bab954e63152b2f46069fca34715caad3d6637d176d08fb535760fe78 | b34c380ce25fb7b0525f498ef70b83cfff485bb19de8f93f550e3cf05267e2bf | 2bd144afb34f5085c2405479b3eae5897445916b7dc4eac1096c3f6991a06156 |
cat-searcher/leandojo-benchmark-4-random | test | 2,979 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply hI.2 | R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' = ⊥ | case a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' < I | ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) (:fv _uniq.16432) ((:c Bot.bot) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c LieSubmodule.instBot) (:fv _uniq.14419) (:fv _uniq.14422) (:fv... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"apply","sourceEnd":6854,"sourceStart":6849,"tag":"atom"},{"children":[{"contextIndex":8,"semanticRole":"local","source":"hI","sourceEnd":6857,"sourceStart":6855,"tag":"identifier"},{"source":".","sourceEnd":6858,"sourceStart":6857,"tag":"atom"},{"children":[{"source":"2","sourceEnd":6859,"source... | [] | [{"source":"hI.2","source_end":6859,"source_start":6855,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 71 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dfad5714c9c16f477361597209156d53641e30de6eace810604a2b19923c5640 | 2bd144afb34f5085c2405479b3eae5897445916b7dc4eac1096c3f6991a06156 | 8e9d2944f429486c97eecbe40584d43406ea2edba6a556cd4ef202241b761407 | 91b3f2d6a8ecae175d733b428d3ca40711d6837c250cee42a57b70c01d57eace |
cat-searcher/leandojo-benchmark-4-random | test | 2,980 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>lt_iff_le_and_ne</a>] | case a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' < I | case a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' ≤ I ∧ J' ≠ I | ((:c LT.lt) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c Preorder.toLT) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c PartialOrder.toPreorder) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":6866,"sourceStart":6864,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":6868,"sourceStart":6867,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"lt_iff_le_and_ne","s... | [] | [{"source":"lt_iff_le_and_ne","source_end":6884,"source_start":6868,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 72 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1486c9420fae7d5442d7ed1633470b42ea715245e18a6475ce04c30ecde3c9eb | 91b3f2d6a8ecae175d733b428d3ca40711d6837c250cee42a57b70c01d57eace | e1c86cb74a389fe36b2d1a1772d4b988a61460be86bca11c6aa9ec6c34b72556 | c29fd2fdcbab2c7857c57cd5dd4eca4a0850ab3c2fab586ddba17c25566551f9 |
cat-searcher/leandojo-benchmark-4-random | test | 2,981 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | case a
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' ≤ I ∧ J' ≠ I | case a.left
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' ≤ I
case a.rig... | ((:c And) ((:c LE.le) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c Preorder.toLE) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) ((:c PartialOrder.toPreorder) ((:c LieIdeal) (:fv _uniq.14419) (:f... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c And) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"constructor","sourceEnd":6901,"sourceStart":6890,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor\n -- We know that `J ≤ I` since `J` is an ideal of `I`.","sourceEnd":6901,"sourceStart":6890,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 75 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b930ca9928c3c8d6cf688c4b58fc8502ec20ae1af3eb4ab6a9af6f7a18dab2a9 | c29fd2fdcbab2c7857c57cd5dd4eca4a0850ab3c2fab586ddba17c25566551f9 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 29243e38f12cc35a5ea4018aa96dfa281efa33ee9cd691f386f481306000b028 |
cat-searcher/leandojo-benchmark-4-random | test | 2,982 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | contrapose! hJ | case a.right
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : ¬J = ⊤
⊢ J' ≠ I | case a.right
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
⊢ J = ⊤ | ((:c Ne) ((:c LieIdeal) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428) (:fv _uniq.14445)) (:fv _uniq.16432) (:fv _uniq.15078)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c LieRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"contrapose!","sourceEnd":7154,"sourceStart":7143,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"hJ","sourceEnd":7157,"sourceStart":7155,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"null","source":"hJ","sourceEnd":7157,"source... | [] | [{"source":"hJ","source_end":7157,"source_start":7155,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 82 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c584a3a51f296f362dd47c64310f9b46e721c044de03e55cb2d9e2891c09393 | 42dcd6a776392db56645bdccd8bb8448698fe082e19bc14835517cd52d65f929 | 061281695cfa79a4a4a1ceb37d5594c68445966acc8ff1d918681fc82c27877b | b5068a0ca511a881f298450954dc4a594f157eb9d76da96c1f11aee30fb235d3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,983 | LieAlgebra.IsSemisimple.isSimple_of_isAtom | Mathlib/Algebra/Lie/Semisimple/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_top_iff</a>] | case a.right
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
⊢ J = ⊤ | case a.right
R : Type u_1
L : Type u_2
inst✝³ : CommRing R
inst✝² : LieRing L
inst✝¹ : LieAlgebra R L
inst✝ : IsSemisimple R L
I : LieIdeal R L
hI : IsAtom I
J : LieIdeal R ↥↑I
J' : LieIdeal R L :=
let __spread.0 := Submodule.map ↑I.incl ↑J;
{ toSubmodule := __spread.0, lie_mem := ⋯ }
hJ : J' = I
⊢ ⊤ ≤ J | ((:c Eq) ((:c LieIdeal) (:fv _uniq.14419) ((:c Subtype) (:fv _uniq.14422) (:lambda x (:fv _uniq.14422) ((:c Membership.mem) (:fv _uniq.14422) ((:c Submodule) (:fv _uniq.14419) (:fv _uniq.14422) ((:c CommSemiring.toSemiring) (:fv _uniq.14419) ((:c CommRing.toCommSemiring) (:fv _uniq.14419) (:fv _uniq.14425))) ((:c AddCo... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"L","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c CommRing) (:fv _uniq.14419))"},{"name":"inst✝²","sexp":"((:c LieRing) (:fv _uniq.14422))"},{"name":"inst✝¹","sexp":"((:c LieAlgebra) (:fv _uniq.14419) (:fv _uniq.14422) (:fv _uniq.14425) (:fv _uniq.14428))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LieIdeal) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"name":"L","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":7164,"sourceStart":7162,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7166,"sourceStart":7165,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"eq_top_iff","semanti... | [] | [{"source":"eq_top_iff","source_end":7176,"source_start":7166,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14419","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14422","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 28 | 83 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 34988316be5bd4de8e7c7681d1082cbce12d7d4846b056c21875ea832f73026d | b5068a0ca511a881f298450954dc4a594f157eb9d76da96c1f11aee30fb235d3 | a95829e92a74024226a07ba797519ec117b87da558ce8e6b61789e398f6fae8f | 6fefbe006071259ff33f9f6ef25c94aa8f82e5ef8e03bc5802bb5b51b59d366a |
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