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value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
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cat-searcher/leandojo-benchmark-4-random | test | 3,900 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use <a>BoundedContinuousFunction.const</a> Y a | case intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
this : ... | case h
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
this : ∀ (x : X), f x... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"use","sourceEnd":19412,"sourceStart":19409,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"children":[{"name":"BoundedContinuousFunction.const","semanticRole":"global","source":"const","sourceEnd":19418,"... | [] | [{"source":"const Y a","source_end":19422,"source_start":19413,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 17 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7c6c2a7478f472ca2643543200b9a8554daa8193da9e4250023e0983dd9ded1 | 8b812ea6a1abe1e3f711fa3271a7386a8329f46fe2819becd57518e9a95563b9 | 9dfd838d6f8313ad4362b25af56d827cfaadbf08439ff876cabe7db454f4454f | 08de993d9af0a3582f15ca8c6c7b8d67e32b26ee20a3f6ac97c0c2b4a3fad795 |
cat-searcher/leandojo-benchmark-4-random | test | 3,901 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [this, <a>Function.funext_iff</a>] | case h
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
this : ∀ (x : X), f x... | ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.1440... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c And) (:arg :explicit 0 (:forall y :explicit (:fv FV1) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":19431,"sourceStart":19427,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19433,"sourceStart":19432,"tag":"a... | [] | [{"source":"this","source_end":19437,"source_start":19433,"syntax_kind":"ident"},{"source":"Function.funext_iff","source_end":19458,"source_start":19439,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 18 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5ee79a905a4b6df38a4da20c5eaaf2af5f7d3e1fbdc8f545674a9343b29f2224 | 08de993d9af0a3582f15ca8c6c7b8d67e32b26ee20a3f6ac97c0c2b4a3fad795 | 1eabcb4de8b5523385a48c51d6650078e0cb618616d67cf5036fb277dfefd22c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,902 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using hmem | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
hb : IsLUB (range ⇑f) a
hmem : ∀ (x : X), f x ∈ Icc a a
hle : a ≤ a
⊢ ∀ (x : X), f x = a | (:forall x (:fv _uniq.144068) ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144068) (:c Real) (:fv _uniq.144074) (:c Real.pseudoMetricSpace)) (:fv _uniq.144068) (:lambda _ (:fv _uniq.144068) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144068) (:c Real) (:fv _uniq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:forall x :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simpa","sourceEnd":19393,"sourceStart":19388,"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":"hmem","source_end":19404,"source_start":19400,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 16 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a29083a6ed7f51c98e3dc8d7922e089be5acfd9feb24787922e233cafe57b2b1 | fd247d17b512388215523ce9d5adb558fa50412c6f434796e75c6015be9ae70d | fa95beabeccd084b42b498864fa9e376a6c7d3c602327d315c816e9592f789bf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,903 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [c] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.151624) (:fv _uniq.145169)) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.145423) (:fv _uniq.151624))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (: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) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"field_simp","sourceEnd":19694,"sourceStart":19684,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":19696,"sourceSt... | [] | [{"source":"c","source_end":19697,"source_start":19696,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 24 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c9a27b36ca424a40a107e762d5bc4742f668e446329f89cf7f860f614b84a66 | 7e87b95e285d333f93ce3ad0da2de881298d678eeef5a2c432e5801eabdc6a13 | 4a8f324be1146f1de0159697713706c8f126928db48957caa1104387ef144ee8 | 93a6fa5e90e2eb57b757866ffa6c6e8720ca6393063c181780768a889db4008a |
cat-searcher/leandojo-benchmark-4-random | test | 3,904 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) ((:c Ring.toSub) (:c Real) ((:c DivisionRing.toRing) (:c Real) ((:c Field.toDivisionRing) (:c Real) (:c Real.field))))) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.145169) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (: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) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"ring","sourceEnd":19707,"sourceStart":19703,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring\n /- Due to `exists_extension_forall_mem_Icc_of_closedEmbedding`, there exists an extension `g`\n such that `g y ∈ [a, b]` for all `y`. However, if `a` and/or `b` do not belong to th... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 25 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e8d46055fe40f9bab804b79ac45de0887e12e22c7a5acb205cf83b190fd12c3 | 93a6fa5e90e2eb57b757866ffa6c6e8720ca6393063c181780768a889db4008a | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,905 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>BoundedContinuousFunction.exists_extension_forall_mem_Icc_of_closedEmbedding</a> f hmem hle he with ⟨g, hg_mem, hgf⟩ | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt :... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":20211,"sourceStart":20205,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"BoundedContinuousFunction.exists_extension_forall_mem_Icc_of_closedEmbedding","semanticRole":"global","source":"exists_extension_fora... | [] | [{"source":"exists_extension_forall_mem_Icc_of_closedEmbedding f hmem hle he","source_end":20276,"source_start":20212,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨g, hg_mem, hgf⟩\n -- If `a ∈ range f`, then we are done.","source_end":20302,"source_start":20282,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 31 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eb9e6faaedac9e569cca8e9432dc2ae8b330ac94c9110183bcb3621c94da6de6 | 456f453fa341352af8c57a692d792b0100f0315c0a6e4911269101b85a13b325 | 8333c9eafd30b2efd36baa45592ae717487531208dbdfdaad3e7401c8194039a | e8c29fa9639e1191f3b23f09c85137f44dc91e1a17559f29e1e446933dcab8ba |
cat-searcher/leandojo-benchmark-4-random | test | 3,906 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>em</a> (∃ x, f x = a) with (⟨x, rfl⟩ | ha') | case intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt :... | case intro.intro.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
x : X
ha : IsGLB (range ⇑f) (f x)
hmem :... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":20358,"sourceStart":20352,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"em","semanticRole":"global","source":"em","sourceEnd":20361,"sourceStart":20359,"tag":"identifier"},{"children":[{"children":[{"sourc... | [] | [{"source":"em (∃ x, f x = a)","source_end":20378,"source_start":20359,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(⟨x, rfl⟩ | ha')","source_end":20404,"source_start":20384,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 32 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b7ea632d02882abe2f795f811f0cdc9160c5c5ae98ba7bbbe3ddfc1b53079e83 | e8c29fa9639e1191f3b23f09c85137f44dc91e1a17559f29e1e446933dcab8ba | f4c372082233e0a892f96baaf1b57cdd3532e80fab2da8a92acc7063d5c35e90 | 6a9a4bc50de00ebf74305f1fa45645699d27ad3bd23d15c34a6a22155cb92cb0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,907 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>exists_bounded_mem_Icc_of_closed_of_le</a> (he.isClosed_range.union <| isClosed_Ici.preimage g.continuous) (isClosed_singleton.preimage g.continuous) hd (<a>sub_nonneg</a>.2 hac.le) with ⟨dg, dg0, dga, dgmem⟩ | case intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
h... | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":21082,"sourceStart":21076,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"exists_bounded_mem_Icc_of_closed_of_le","semanticRole":"global","source":"exists_bounded_mem_Icc_of_closed_of_le","sourceEnd":21121,"... | [] | [{"source":"exists_bounded_mem_Icc_of_closed_of_le\n (he.isClosed_range.union <| isClosed_Ici.preimage g.continuous)\n (isClosed_singleton.preimage g.continuous) hd (sub_nonneg.2 hac.le)","source_end":21269,"source_start":21083,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨dg, dg0, dga, dgmem⟩","sourc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 55 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32ed5f3cf22e92e51dc43d1a07f9016622fe601077f02743951960ed54196722 | e0527b88c155e81b0782b0009d65a01cac078bb58f1033a36af1e42db0d3497a | 1d068a2e733d36d78bfe5e121cbaa215a3dcbf024963b66d9b79d81a293d3231 | 19a2ee45518a9eb4fd3515945b17dbd4d03045fea6222ffc2c05a17d3d191fe3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,908 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace hgf : ∀ x, (g + dg) (e x) = f x := by intro x simp [dg0 (<a>Or.inl</a> <| <a>Set.mem_range_self</a> _), ← hgf] | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"replace","sourceEnd":21318,"sourceStart":21311,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hgf","sourceEnd":21322,"sourceStart":21319,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hgf","sourceEnd":21322,"sourceStart":21319,"tag"... | [] | [{"source":"∀ x, (g + dg) (e x) = f x","source_end":21352,"source_start":21325,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"dg0 (Or.inl <| mem_range_self _)","source_end":21417,"source_start":21385,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hgf","source_end":21426,"source_start":21423,"syntax_kind":"ident"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 56 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 602ff3d6f5b2e20349108e88a522613c223debebcb59a3faf315f7192333682a | 19a2ee45518a9eb4fd3515945b17dbd4d03045fea6222ffc2c05a17d3d191fe3 | 49aaa026c28721a8427fd71d728e236b78ba08cdf1a65ec60641341615b23a9e | 8b9bc8857f668b1cd8f2abacf0e60987d3f8d320dd69d1bfa19989c6fd3903a4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,909 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨g + dg, fun y => ?_, <a>funext</a> hgf⟩ | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":21438,"sourceStart":21432,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":21442,"sourceStart":21439,"tag":"atom"},{"children":[{"children":[{"contextIndex":22,"semanticRole":"local","source":"g","sourceEnd":21443,"sourceStart":21442,"tag":"identifier"},{"source":"+","sou... | [] | [{"source":"⟨g + dg, fun y => ?_, funext hgf⟩","source_end":21476,"source_start":21439,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 60 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 20803b2faf1aa0e486b50aaf086fb6607a1759c6677f14930292ebf005af0d1c | 8b9bc8857f668b1cd8f2abacf0e60987d3f8d320dd69d1bfa19989c6fd3903a4 | 1c93282b0bea7d1c39d76aacc0ab3edaa36e4f7eb4efa17232f31b6455558015 | 18089cc97c730dd6b8f35a97052db69367106a872cae68345318b0550e1ece4a |
cat-searcher/leandojo-benchmark-4-random | test | 3,910 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases ha.exists_between hay with ⟨_, ⟨x, rfl⟩, _, hxy⟩ | case intro.intro.inr.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc... | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hme... | ((:c Exists) (:fv _uniq.144068) (:lambda x (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":21775,"sourceStart":21769,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"ha.exists_between","sourceEnd":21793,"sourceStart":21776,"tag":"identifier"},{"children":[{"contextIndex":32,"semanticRole":"local"... | [] | [{"source":"ha.exists_between hay","source_end":21797,"source_start":21776,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨_, ⟨x, rfl⟩, _, hxy⟩","source_end":21832,"source_start":21803,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 75 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29b396ee37ca0c9b2e4d0e2089f7106b6a162fe7d0c6b9f5c52c7d84e53026cd | 309d17472e6a006d24e79c925e443277a5981cf90ebe01e593c5fdc1dbe88176 | 5d2b4732a0ed7466071affdb7fb326ebbbb5aef43671a4effe7ccca23751ce70 | bd3af559b988811d05b7aa7cb9d2d0a4bb658272a45bb824cfd38a75bf74a6a2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,911 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨x, hxy.le, ?_⟩ | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hme... | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hme... | ((:c Exists) (:fv _uniq.144068) (:lambda x (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":21843,"sourceStart":21837,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":21847,"sourceStart":21844,"tag":"atom"},{"children":[{"contextIndex":33,"semanticRole":"local","source":"x","sourceEnd":21848,"sourceStart":21847,"tag":"identifier"},{"source":",","sourceEnd":21849... | [] | [{"source":"⟨x, hxy.le, ?_⟩","source_end":21863,"source_start":21844,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 76 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8fc9d373154c83351e967d46dbeb5928449533f70a957e65f71c162210108029 | bd3af559b988811d05b7aa7cb9d2d0a4bb658272a45bb824cfd38a75bf74a6a2 | 3fadd98d7c7c300759dcdfb5ea91677ccbf8ec5bb459222dbe35def3f0f9e3e9 | df4c3e418690af07bbbfa78cb6c229d91ed218713fa1542914d401f4bef75522 |
cat-searcher/leandojo-benchmark-4-random | test | 3,912 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>le_total</a> c (g y) with hc | hc | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hme... | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":21874,"sourceStart":21868,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"le_total","semanticRole":"global","source":"le_total","sourceEnd":21883,"sourceStart":21875,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"le_total c (g y)","source_end":21891,"source_start":21875,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hc | hc","source_end":21904,"source_start":21897,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 77 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2433f94dba978fb40e10f390c3b9060182ee456f95066fde7afa373424f8a92 | df4c3e418690af07bbbfa78cb6c229d91ed218713fa1542914d401f4bef75522 | 7c73b33f2996cbbada5cfe18645c642b28bf84ff7bac749341623c95fd391975 | 7e6af92538ecc6ecd50fc471f22038d7eb9651096018998edae7a659ca371666 |
cat-searcher/leandojo-benchmark-4-random | test | 3,913 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨g, fun y => ⟨x, hg_mem _⟩, hgf⟩ | case intro.intro.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
x : X
ha : IsGLB (range ⇑f) (f x)
hmem :... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":20417,"sourceStart":20412,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":20421,"sourceStart":20418,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"g","sourceEnd":20422,"sourceStart":20421,"tag":"identi... | [] | [{"source":"⟨g, fun y => ⟨x, hg_mem _⟩, hgf⟩\n /- Otherwise, `g ⁻¹' {a}` is disjoint with `range e ∪ g ⁻¹' (Ici c)`, hence there exists a\n function `dg : Y → ℝ` such that `dg ∘ e = 0`, `dg y = 0` whenever `c ≤ g y`, `dg y = c - a`\n whenever `g y = a`, and `0 ≤ dg y ≤ c - a` for all `y`. -/","source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 35 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c67e284e759ea1df71024ffcefd45721430ea09a9672abf6da932533b1cb55e5 | ca4ea37e7b799aa46f39fb8645c4a5d59f3d049757157ef981489cb3c55329ba | 2eb7a9b7a819c3769de91709902127852def29f024f6dd0839f8c898d599efcf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,914 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Set.disjoint_union_left</a>.2 ⟨?_, <a>Disjoint.preimage</a> _ ?_⟩ | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:fv _uniq.144071)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c CompletelyDistribLattice.toCompleteLattice) ((:c Set) (:fv _uniq.144071)) ((:c CompleteAtomicBooleanAlgebra.toC... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":20827,"sourceStart":20821,"tag":"atom"},{"children":[{"children":[{"name":"Set.disjoint_union_left","semanticRole":"global","source":"disjoint_union_left","sourceEnd":20847,"sourceStart":20828,"tag":"identifier"},{"source":".","sourceEnd":20848,"sourceStart":20847,"tag":"atom... | [] | [{"source":"disjoint_union_left.2 ⟨?_, Disjoint.preimage _ ?_⟩","source_end":20882,"source_start":20828,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 40 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ecd21d2b72a685d08dd6060014759ed348848e7e7b6926ccebd14993d8209397 | 03a9dc9845e085c71ac592785ebdefb2ae62be1e1b5a517beb6b8717e3fd1d97 | c6e61241271ad2d97068196982287c108c921774af500da58df40c9418c6616e | 9debd2cec041deea09257a1d943450f8a3f594edb604904632497d515a111a2a |
cat-searcher/leandojo-benchmark-4-random | test | 3,915 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.disjoint_left</a>] | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:fv _uniq.144071)) ((:c SemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c Lattice.toSemilatticeInf) ((:c Set) (:fv _uniq.144071)) ((:c GeneralizedCoheytingAlgebra.toLattice) ((:c Set) (:fv _uniq.144071)) ((:c CoheytingAlgebra.toGeneralizedCoheytingAlgebra) ((:c Set) (:fv _uniq.... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":20894,"sourceStart":20892,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20896,"sourceStart":20895,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.disjoint_lef... | [] | [{"source":"Set.disjoint_left","source_end":20913,"source_start":20896,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 45 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 898bba14d1b30cc19aa7d87c95ee3c777c0fc85d13cade0316320c502864f526 | e899f12b44227f83583a49c753e5217e6633ab0434594cf39b2728db805c3f45 | 102354865735a4e156ff7709985aad347580382fd83c431e111dd749533707e3 | 254735bfa528171e4e23866d6597f73e9ba18833712e893c7ca595da053bb5a5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,916 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨x, rfl⟩ (rfl : g (e x) = a) | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | case refine_1.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
x : X
ha : IsGLB (range ⇑f) (g (e x))
hmem : ∀ ... | (:forall a (:fv _uniq.144071) (:forall _ ((:c Membership.mem) (:fv _uniq.144071) ((:c Set) (:fv _uniq.144071)) ((:c Set.instMembership) (:fv _uniq.144071)) 0 ((:c Set.range) (:fv _uniq.144071) (:fv _uniq.144068) (:fv _uniq.144784))) ((:c Not) ((:c Membership.mem) (:fv _uniq.144071) ((:c Set) (:fv _uniq.144071)) ((:c Se... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:forall a :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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rintro","sourceEnd":20929,"sourceStart":20923,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":20931,"sourceStart":20930,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":20931,"sourceStart":20930,"tag":"node"}],"kind":"Lean.Parser... | [{"role":"fresh_name","source":"x","source_end":20936,"source_start":20935,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":20958,"source_start":20957,"syntax_kind":"ident"}] | [{"source":"⟨x, rfl⟩","source_end":20944,"source_start":20932,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"(rfl : g (e x) = a)","source_end":20964,"source_start":20945,"syntax_kind":"Lean.Parser.Tactic.rintroPat.binder"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 48 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b5c033676730e0d71ea0e5e65fdae4fec9b7d67e3a161e0aa24543e3f0b5e59f | 254735bfa528171e4e23866d6597f73e9ba18833712e893c7ca595da053bb5a5 | 6d83f5b2882fe45c4c845a5e68b97151c4ac8512834a2c0a9d74ca4af231dd04 | 6f401558e780413f23ad4edc05289c44d74df4d1f24b9c8b65218cc86bf4f981 |
cat-searcher/leandojo-benchmark-4-random | test | 3,917 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ha' ⟨x, (<a>congr_fun</a> hgf x).<a>Eq.symm</a>⟩ | case refine_1.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
x : X
ha : IsGLB (range ⇑f) (g (e x))
hmem : ∀ ... | (:c False) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":20978,"sourceStart":20973,"tag":"atom"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"ha'","sourceEnd":20982,"sourceStart":20979,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":20986,"sourceStart":20983,"tag":"atom"},{"children":[{"co... | [] | [{"source":"ha' ⟨x, (congr_fun hgf x).symm⟩","source_end":21014,"source_start":20979,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 49 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3bde166f6fdb9e6dba7ba77f0c28b8578d7c3f59c08671995123778c54f8375b | 6f401558e780413f23ad4edc05289c44d74df4d1f24b9c8b65218cc86bf4f981 | 3e95f7c6d02908cff7faba8f5cccd4d0325c1c58b6d6c572b4b8c1e864793710 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,918 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.disjoint_singleton_right</a>.2 hac.not_le | case refine_2
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:c Real)) ((:c SemilatticeInf.toPartialOrder) ((:c Set) (:c Real)) ((:c Lattice.toSemilatticeInf) ((:c Set) (:c Real)) ((:c GeneralizedCoheytingAlgebra.toLattice) ((:c Set) (:c Real)) ((:c CoheytingAlgebra.toGeneralizedCoheytingAlgebra) ((:c Set) (:c Real)) ((:c BiheytingAlgebra.toCoheytingAlg... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c R... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":21029,"sourceStart":21024,"tag":"atom"},{"children":[{"children":[{"name":"Set.disjoint_singleton_right","semanticRole":"global","source":"Set.disjoint_singleton_right","sourceEnd":21058,"sourceStart":21030,"tag":"identifier"},{"source":"... | [] | [{"source":"Set.disjoint_singleton_right.2 hac.not_le","source_end":21071,"source_start":21030,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 52 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7a4bd0902672937fe36febd729eea864f7e7699b65ed7d66ab1e04c2a89af27 | cd33b97a981c6b1be2ed5f32502ded1c878a083185bd31fd9e3002efedc1bd0d | e39eee57158d9547e7d73aae2a15282d95d6093cd5be901158dc30fd1330723f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,919 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | (:forall x (:fv _uniq.144068) ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:forall x :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"intro","sourceEnd":21370,"sourceStart":21365,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":21372,"sourceStart":21371,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":21372,"sourceStart":21371,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"x","source_end":21372,"source_start":21371,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 58 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71238b49e2ac85b35507dcfcbe4af0ecdb5cc8e5296a2e5cf5c0bea1b89c325f | 210e555d5619b9ea30a0f56c120fdf19ce85ab1894f15a3b72423375288c5811 | 727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d | 9c59b21f190d972cf35f2f364ef821e2d63839005c0cd87cd185179cdca8085c |
cat-searcher/leandojo-benchmark-4-random | test | 3,920 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [dg0 (<a>Or.inl</a> <| <a>Set.mem_range_self</a> _), ← hgf] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetric... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":21383,"sourceStart":21379,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":21385,"sourceStart":21384,"tag":"a... | [] | [{"source":"dg0 (Or.inl <| mem_range_self _)","source_end":21417,"source_start":21385,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hgf","source_end":21426,"source_start":21423,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 59 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 305a80097872e69f380404af9e1f2e04a854c3d2fd6c9d31644050440bcbfb9f | 9c59b21f190d972cf35f2f364ef821e2d63839005c0cd87cd185179cdca8085c | 0fb414815fcb7d4ad6ed707d1a0bb18792d006e20534cc8adb0914cca3579f95 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,921 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases (hg_mem y).1.<a>LE.le.eq_or_lt</a> with (rfl | hlt) | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g + dg) (e x) = f x
y : Y
ha : IsGLB (range ⇑f) (g y)
h... | ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.145169) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":21525,"sourceStart":21519,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":21527,"sourceStart":21526,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"lo... | [] | [{"source":"(hg_mem y).1.eq_or_lt","source_end":21547,"source_start":21526,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"(rfl | hlt)","source_end":21564,"source_start":21553,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 63 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e50a18d5a0bb2cc53dfc8010d5d9284c0db63c19261704bca80f2302c3e702bd | 0885d0e53d000a5453d075c9d87fae31850afa517d0ec9dc6a2ccf27603eca4a | a44b41b6bd3be3ac0906aacc285c7ea91ef7f1731d85e6431d3552a0c51d87c9 | b54cfb8f9962b636aad3dbf13f5ea480731a87a97113ad728f8bc1e9c47fd1ad |
cat-searcher/leandojo-benchmark-4-random | test | 3,922 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>lt_add_iff_pos_right</a> _).2 ?_ | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g + dg) (e x) = f x
y : Y
ha : IsGLB (range ⇑f) (g y)
h... | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g + dg) (e x) = f x
y : Y
ha : IsGLB (range ⇑f) (g y)
h... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":21580,"sourceStart":21574,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":21582,"sourceStart":21581,"tag":"atom"},{"children":[{"name":"lt_add_iff_pos_right","semanticRole":"global","source":"lt_add_iff_pos_right","sourceEnd":21602,"sourceStart"... | [] | [{"source":"(lt_add_iff_pos_right _).2 ?_","source_end":21610,"source_start":21581,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 68 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ffd4fb44ca986273c7d960b0f8904445283fc9049d0db7109732d49ed879854f | d8dfe9f65cdab1406bde95900ed5e37fd8a1d372c671c6c2d8a667098f356f33 | a79238453f93867a314d795685da9f2f71427a2f14285c3d566c45ddfddc0987 | 436b24b09ad771aba0157bb2faccdca7bd211be7355fb24fd63d9190b3c1bb9a |
cat-searcher/leandojo-benchmark-4-random | test | 3,923 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc 0 < c - g y := <a>sub_pos</a>.2 hac _ = dg y := (dga <a>rfl</a>).<a>Eq.symm</a> | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g + dg) (e x) = f x
y : Y
ha : IsGLB (range ⇑f) (g y)
h... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c AddZeroClass.toZero) (:c Real) ((:c AddMonoid.toAddZeroClass) (:c Real) (:c Real.instAddMonoid))))) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.p... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"calc","sourceEnd":21623,"sourceStart":21619,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"0","sourceEnd":21635,"sourceStart":21634,"tag":"atom"}],"kind":"num","source":"0","sourceEnd":21635,"sourceStart":21634,"tag":"node"},{"source":"<","sourceEnd":21637,"sourceSt... | [] | [{"source":"0 < c - g y","source_end":21645,"source_start":21634,"syntax_kind":"«term_<_»"},{"source":"sub_pos.2 hac","source_end":21662,"source_start":21649,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":21674,"source_start":21673,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"dg y","source_end":2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 69 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e602262cbb10846e0347187ca27ecf892caea0bd6a30b01c4b669189f9df029c | 436b24b09ad771aba0157bb2faccdca7bd211be7355fb24fd63d9190b3c1bb9a | 92c462d03328f529c958d64e922974cb540da0b2a939eeee210529ce2753ef7a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,924 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hlt.trans_le (<a>le_add_of_nonneg_right</a> (dgmem y).1) | case inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt✝ : a < b
... | ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.145169) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":21714,"sourceStart":21709,"tag":"atom"},{"children":[{"source":"hlt.trans_le","sourceEnd":21727,"sourceStart":21715,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":21729,"sourceStart":21728,"tag":"atom"},{"children... | [] | [{"source":"hlt.trans_le (le_add_of_nonneg_right (dgmem y).1)","source_end":21764,"source_start":21715,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 72 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1ad85e7e7ba78fe0790033807facba0adb1be5bfc24ef750773758946df65937 | 9aead8a44ddc429f62ac077b5f4f4172d47fefb296766b7b7ab73e01bf561ed7 | ce8ecabd4263484dc27561634d9d2d243110703a188ffb9883e7066c8abdb89a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,925 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [dg0 (<a>Or.inr</a> hc), (hg_mem y).2] | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":21916,"sourceStart":21912,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"dg0 (Or.inr hc)","source_end":21933,"source_start":21918,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(hg_mem y).2","source_end":21947,"source_start":21935,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 80 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b99dcc6e29c0f5bf4c4c2872501710158512f120ecae7ef32ebafec461bd70e2 | c5a872c9a5c5e8c0606b3a1efddc01d19d9c27b89130cdf1a537c626bc447ed3 | a71aaa19108894a8eacfdc51b41e0c9948e0d81239b394422fc2ea3cf5b28479 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,926 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc g y + dg y ≤ c + (c - a) := <a>add_le_add</a> hc (dgmem _).2 _ = b := by rw [hsub, <a>add_sub_cancel</a>] | case intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"calc","sourceEnd":21960,"sourceStart":21956,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"contextIndex":22,"semanticRole":"local","source":"g","sourceEnd":21970,"sourceStart":21969,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"g y + dg y ≤ c + (c - a)","source_end":21995,"source_start":21969,"syntax_kind":"«term_≤_»"},{"source":"add_le_add hc (dgmem _).2","source_end":22024,"source_start":21999,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":22034,"source_start":22033,"syntax_kind":"Lean.Parser.Term.hole"},{"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 85 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 068c6678c373f555b8fe1b2ea448c8070b160f56a5070d0d8461a3ec11c42ed2 | 5e82eacf115d0f062c1eef722fc7021dc75f1e2f59a9506f1c9fc1991f43d890 | 4d300c9619c98585a04a7f858fb2e3ed696fb1b8726334d87e7e17bbb9816c3f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,927 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hsub, <a>add_sub_cancel</a>] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.151624) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.151624) (:fv _uniq.145169))) (:fv _uniq.145423)) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HAdd.hAdd) (: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 HAdd) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":22047,"sourceStart":22045,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22049,"sourceStart":22048,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"hsub","source_end":22053,"source_start":22049,"syntax_kind":"ident"},{"source":"add_sub_cancel","source_end":22069,"source_start":22055,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 90 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 40f49810061993c976ae5183991c12ef7f3f2e1307aba1bcf9c07f4ac56e7978 | 9664aaf8194dc7138e09bb63a76e627baeeb1b82c5acb548bfa1ceb1e1a3af3c | ec26df0972f166b3f791178d2976833a1e0d65f08521220f94b769be6a8c7da3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,928 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨g, fun y => ⟨xl y, x, hxl y, hgb y⟩, hgf⟩ | case intro.intro.inr.intro.intro.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
xl : Y → X
hxl : ∀ (y : ... | ((:c Exists) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:lambda g ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) ((:c And) (:forall y (:fv _uniq.144071) ((:c Exists) (:fv _uniq.144068) (:lamb... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:c Real)))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":22335,"sourceStart":22330,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":22339,"sourceStart":22336,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"g","sourceEnd":22340,"sourceStart":22339,"tag":"identi... | [] | [{"source":"⟨g, fun y => ⟨xl y, x, hxl y, hgb y⟩, hgf⟩","source_end":22386,"source_start":22336,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 100 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd08377cd8f763501d3629b473b4ee59f51f8387348fedd4468b63985050858b | ef5da97d36a2969a526bccbe5bc62907f6cce539a4d3692aa954f36d753e53bd | d69f3982f92fa1117f05b3f153d0601ad3ea08ebab594131b2e5f36e5d0324c7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,929 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Set.disjoint_union_left</a>.2 ⟨?_, <a>Disjoint.preimage</a> _ ?_⟩ | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:fv _uniq.144071)) ((:c OmegaCompletePartialOrder.toPartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c CompleteLattice.instOmegaCompletePartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c CompletelyDistribLattice.toCompleteLattice) ((:c Set) (:fv _uniq.144071)) ((:c CompleteAtomicBooleanAlgebra.toC... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":22468,"sourceStart":22462,"tag":"atom"},{"children":[{"children":[{"name":"Set.disjoint_union_left","semanticRole":"global","source":"disjoint_union_left","sourceEnd":22488,"sourceStart":22469,"tag":"identifier"},{"source":".","sourceEnd":22489,"sourceStart":22488,"tag":"atom... | [] | [{"source":"disjoint_union_left.2 ⟨?_, Disjoint.preimage _ ?_⟩","source_end":22523,"source_start":22469,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 105 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 241dded67ef7ff57e4b99d5ad7431028492acb48d17458a46f20bde0aa31390b | 5badaaff0a187f8cb732ef550505593443e8e1b6c67fb47873a045927e69717e | c6e61241271ad2d97068196982287c108c921774af500da58df40c9418c6616e | fe8b2b378eebcb1ce5d1166c3ed62448e49c63d795294283172c7869ba97b7f4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,930 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.disjoint_left</a>] | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:fv _uniq.144071)) ((:c SemilatticeInf.toPartialOrder) ((:c Set) (:fv _uniq.144071)) ((:c Lattice.toSemilatticeInf) ((:c Set) (:fv _uniq.144071)) ((:c GeneralizedCoheytingAlgebra.toLattice) ((:c Set) (:fv _uniq.144071)) ((:c CoheytingAlgebra.toGeneralizedCoheytingAlgebra) ((:c Set) (:fv _uniq.... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":22533,"sourceStart":22531,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22535,"sourceStart":22534,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.disjoint_lef... | [] | [{"source":"Set.disjoint_left","source_end":22552,"source_start":22535,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 110 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab79e15e254cf7e3a552580f3b0ca9d4ffc1b8bcaf5014f23d8d22dd0241670a | 6fd35ac6ef3788efb26c4e4337f47f103e5944b9bfa26905cd84818d5811afee | 102354865735a4e156ff7709985aad347580382fd83c431e111dd749533707e3 | 88502da5105b643ba9335d9e107630ec439bad7a6e87acd4acdebbf0ee72c894 |
cat-searcher/leandojo-benchmark-4-random | test | 3,931 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro _ ⟨x, rfl⟩ (rfl : g (e x) = b) | case refine_1
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | case refine_1.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
x : ... | (:forall a (:fv _uniq.144071) (:forall _ ((:c Membership.mem) (:fv _uniq.144071) ((:c Set) (:fv _uniq.144071)) ((:c Set.instMembership) (:fv _uniq.144071)) 0 ((:c Set.range) (:fv _uniq.144071) (:fv _uniq.144068) (:fv _uniq.144784))) ((:c Not) ((:c Membership.mem) (:fv _uniq.144071) ((:c Set) (:fv _uniq.144071)) ((:c Se... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:forall a :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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rintro","sourceEnd":22566,"sourceStart":22560,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd":22568,"sourceStart":22567,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.ignore","source":"_","sourceEnd":22568,"sourceStart":22567,"tag":"node"}],"kind":"Lean.Parser... | [{"role":"fresh_name","source":"x","source_end":22573,"source_start":22572,"syntax_kind":"ident"},{"role":"fresh_name","source":"x","source_end":22595,"source_start":22594,"syntax_kind":"ident"}] | [{"source":"⟨x, rfl⟩","source_end":22581,"source_start":22569,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"},{"source":"(rfl : g (e x) = b)","source_end":22601,"source_start":22582,"syntax_kind":"Lean.Parser.Tactic.rintroPat.binder"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 113 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d849d62f3b537c322ecd0db48bf3528e11ad3981e857ee50715068b8fcd6be9 | 88502da5105b643ba9335d9e107630ec439bad7a6e87acd4acdebbf0ee72c894 | d8195c540928f7ff731806a304aba40a61c504514c1b7d45abb6f069767e8d25 | 6c1790133f851a633799f2b0146139ea33498e9b2914d9cf51cdab4a67796551 |
cat-searcher/leandojo-benchmark-4-random | test | 3,932 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hb' ⟨x, (<a>congr_fun</a> hgf x).<a>Eq.symm</a>⟩ | case refine_1.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
hgf : ⇑g ∘ e = ⇑f
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
x : ... | (:c False) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":22613,"sourceStart":22608,"tag":"atom"},{"children":[{"contextIndex":27,"semanticRole":"local","source":"hb'","sourceEnd":22617,"sourceStart":22614,"tag":"identifier"},{"children":[{"children":[{"source":"⟨","sourceEnd":22621,"sourceStart":22618,"tag":"atom"},{"children":[{"co... | [] | [{"source":"hb' ⟨x, (congr_fun hgf x).symm⟩","source_end":22649,"source_start":22614,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 114 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8f05567c644124e6fd2bff78869e23c4af79ac7277966fe06ce926486190d1e3 | 6c1790133f851a633799f2b0146139ea33498e9b2914d9cf51cdab4a67796551 | d3b337406fb08e196f4703dc2072cc7ca303b63d24e334811cc430f76136b021 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,933 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.disjoint_singleton_right</a>.2 hcb.not_le | case refine_2
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a ... | ((:c Disjoint) ((:c Set) (:c Real)) ((:c SemilatticeInf.toPartialOrder) ((:c Set) (:c Real)) ((:c Lattice.toSemilatticeInf) ((:c Set) (:c Real)) ((:c GeneralizedCoheytingAlgebra.toLattice) ((:c Set) (:c Real)) ((:c CoheytingAlgebra.toGeneralizedCoheytingAlgebra) ((:c Set) (:c Real)) ((:c BiheytingAlgebra.toCoheytingAlg... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Disjoint) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c R... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":22662,"sourceStart":22657,"tag":"atom"},{"children":[{"children":[{"name":"Set.disjoint_singleton_right","semanticRole":"global","source":"Set.disjoint_singleton_right","sourceEnd":22691,"sourceStart":22663,"tag":"identifier"},{"source":"... | [] | [{"source":"Set.disjoint_singleton_right.2 hcb.not_le","source_end":22704,"source_start":22663,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 117 | exact | true | 1 | 27 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97043d8335b8fe1f2096313892c6ba51101c8049c7bdb1d7bf42d7e378320bd1 | 01d948530faa1f38c75f055556c7bc2bd2c43d261bfb68068607c5f1bef16a67 | ba9bdddbbe01ff19f2aa08d646d972038471c68f33c4d0117818f4c982516baf | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,934 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | (:forall x (:fv _uniq.144068) ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:forall x :explicit (:fv FV0) (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"intro","sourceEnd":22991,"sourceStart":22986,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":22993,"sourceStart":22992,"tag":"identifier"}],"kind":"null","source":"x","sourceEnd":22993,"sourceStart":22992,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"x","source_end":22993,"source_start":22992,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 123 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f28c1b0d753c8d069ff0522b22d7b6c54ba8c4577963d93c40cca6a357be0ede | d4cfdfaa2cde1189c24252147b04a0b4f1be81471173d5dc6767cf2cd682917a | 727852cc0e84019aeee0e605b3833ee9bcd4d2abc203673e529dba747f5c5a0d | 768f8a6d94a0f26e0791956f60b14f87778c25ac33f9c97fce6877beeaa77be0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,935 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [dg0 (<a>Or.inl</a> <| <a>Set.mem_range_self</a> _), ← hgf] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetric... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":23002,"sourceStart":22998,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23004,"sourceStart":23003,"tag":"a... | [] | [{"source":"dg0 (Or.inl <| mem_range_self _)","source_end":23036,"source_start":23004,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hgf","source_end":23045,"source_start":23042,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 124 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd42afb60ad021920d5704f1d6403553798113afd7bfa30b40eae9ff978dec17 | 768f8a6d94a0f26e0791956f60b14f87778c25ac33f9c97fce6877beeaa77be0 | 0fb414815fcb7d4ad6ed707d1a0bb18792d006e20534cc8adb0914cca3579f95 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,936 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases (hgb y).<a>LE.le.eq_or_lt</a> with (rfl | hlt) | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g -... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":23138,"sourceStart":23132,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":23140,"sourceStart":23139,"tag":"atom"},{"children":[{"contextIndex":25,"semanticRole":"local","source"... | [] | [{"source":"(hgb y).eq_or_lt","source_end":23155,"source_start":23139,"syntax_kind":"Lean.Parser.Term.proj"},{"source":"(rfl | hlt)","source_end":23172,"source_start":23161,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 128 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6b5ff0be868dccb85f7b9f1c581023a6b1dd416ecbb227900fc3d607b5d22ed0 | eda95a1bd70c3586c8193162bf7097371fb3b78dcbfad05f5dd88ef2d4de62d2 | 5ff76d2d4a4199f023ddad9012a319aee676a72bcc186bd5e02aef4a45a3feef | f00f42e92c5d2859f39cfc7beca132df6810a23be0a56e3e64255654e23fc9e7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,937 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>sub_lt_self_iff</a> _).2 ?_ | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g -... | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g -... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":23186,"sourceStart":23180,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":23188,"sourceStart":23187,"tag":"atom"},{"children":[{"name":"sub_lt_self_iff","semanticRole":"global","source":"sub_lt_self_iff","sourceEnd":23203,"sourceStart":23188,"ta... | [] | [{"source":"(sub_lt_self_iff _).2 ?_","source_end":23211,"source_start":23187,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 133 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1cbb1708b7147f8708e1bcbb56484276532050b332638b7e9e3c9b5ee8c19d3e | 5bba5733f4b72d7cae03e3a4bfaaf4a0c7234b6b84e2eded20bef02eb1f79225 | 0682ce3d52689d1c5c821fbcba5aeed40dab148dd2b5e31a60a52a2c3e77fbc1 | 89ec34e1e65f15b80b6836de45bef1f3b68553e2e19aa693d210713847de84cd |
cat-searcher/leandojo-benchmark-4-random | test | 3,938 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc 0 < g y - c := <a>sub_pos</a>.2 hcb _ = dg y := (dgb <a>rfl</a>).<a>Eq.symm</a> | case inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
g : Y →ᵇ ℝ
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
dg : Y →ᵇ ℝ
hgf : ∀ (x : X), (g -... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c NegZeroClass.toZero) (:c Real) ((:c SubNegZeroMonoid.toNegZeroClass) (:c Real) ((:c SubtractionMonoid.toSubNegZeroMonoid) (:c Real) ((:c AddGroup.toSubtractionMonoid) (:c Real) (:c Real.instAddGroup))))))) ((:... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (: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.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"calc","sourceEnd":23222,"sourceStart":23218,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"0","sourceEnd":23232,"sourceStart":23231,"tag":"atom"}],"kind":"num","source":"0","sourceEnd":23232,"sourceStart":23231,"tag":"node"},{"source":"<","sourceEnd":23234,"sourceSt... | [] | [{"source":"0 < g y - c","source_end":23242,"source_start":23231,"syntax_kind":"«term_<_»"},{"source":"sub_pos.2 hcb","source_end":23259,"source_start":23246,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":23269,"source_start":23268,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"dg y","source_end":2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 134 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62a0af9aba2cba7f02d7ab5db103c507ae29fc02d6d40c034cf456e951546b25 | 89ec34e1e65f15b80b6836de45bef1f3b68553e2e19aa693d210713847de84cd | 96aa78303a868a53c3be7b1bc193ecf0e0fd5109d07af85d5c9d19a4e25c51dd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,939 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ((<a>sub_le_self_iff</a> _).2 (dgmem _).1).<a>LE.le.trans_lt</a> hlt | case inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt✝ : a < b
... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":23307,"sourceStart":23302,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":23309,"sourceStart":23308,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":23310,"sourceStart":23309,"t... | [] | [{"source":"((sub_le_self_iff _).2 (dgmem _).1).trans_lt hlt","source_end":23356,"source_start":23308,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 137 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 199e589c988afba69985523a9eb684054330d2b4a5e1b28c68ad8da0cf83801a | 9fe8fb24c37d158c50c032010ce7b9e6c20236d67801af532253c5dff3ea3cd9 | e963a820b3ecb23a90eb281b6f4f91c9b10ff7a6cb025e2862fd7799f806a17e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,940 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>em</a> (a ∈ <a>Set.range</a> f) with (⟨x, rfl⟩ | _) | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : Is... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g :... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":23473,"sourceStart":23467,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"em","semanticRole":"global","source":"em","sourceEnd":23476,"sourceStart":23474,"tag":"identifier"},{"children":[{"children":[{"sourc... | [] | [{"source":"em (a ∈ range f)","source_end":23492,"source_start":23474,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(⟨x, rfl⟩ | _)","source_end":23516,"source_start":23498,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 146 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60642152c6c79cc7ef6665c3bdd401685137f26b9799d05919c14c0d5d51ff58 | 62d45edff0eefd628e20100483712a05245b970d0d6eb76bc0094c8c509c19c8 | 41a4929124b487e3156d1b1e34cb6f5da5cd2e67055670f00c7e9eb325624ae6 | 1e8facbbdf7a8263cd439b8f60626e0b93ac34a4e9c9b993062d53405efa3d4a |
cat-searcher/leandojo-benchmark-4-random | test | 3,941 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨x, xu, ?_, hyxu.le⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g :... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g :... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":23530,"sourceStart":23524,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":23534,"sourceStart":23531,"tag":"atom"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"x","sourceEnd":23535,"sourceStart":23534,"tag":"identifier"},{"source":",","sourceEnd":23536... | [] | [{"source":"⟨x, xu, ?_, hyxu.le⟩","source_end":23555,"source_start":23531,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 151 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ded9da1c6218bab18fbb351502d2faf5a98138c545c033db4aa8911816e2b77b | 821419f629b2cd573f3d0963c2cfde39de4092be2bf05589180cfd1e2b3e3434 | 7af2e9c94ff2a25d51ca9a53ddd50eed4c0b91e370b98ebed92273b390b567ce | f60d2ff3536c907ce96328f8ff0c596e481f0647b5b1c21e40432ee32b8be9e2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,942 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc f x = c - (b - c) := by rw [← hsub, <a>sub_sub_cancel</a>] _ ≤ g y - dg y := <a>sub_le_sub</a> hc.le (dgmem _).2 | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inl.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g :... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144068) (:c Real) (:fv _uniq.144074) (:c Real.pseudoMetricSpace)) (:fv _uniq.144068) (:lambda _ (:fv _uniq.144068) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"calc","sourceEnd":23566,"sourceStart":23562,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":7,"semanticRole":"local","source":"f","sourceEnd":23576,"sourceStart":23575,"tag":"identifier"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"x","sourc... | [] | [{"source":"f x = c - (b - c)","source_end":23592,"source_start":23575,"syntax_kind":"«term_=_»"},{"source":"hsub","source_end":23611,"source_start":23607,"syntax_kind":"ident"},{"source":"sub_sub_cancel","source_end":23627,"source_start":23613,"syntax_kind":"ident"},{"source":"_","source_end":23638,"source_start":2363... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 152 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c037cbbc8c290a71d7a229d4e347fd8fda7aff8f3c39e2cd1700aec7b86feda6 | f60d2ff3536c907ce96328f8ff0c596e481f0647b5b1c21e40432ee32b8be9e2 | 96d08b693a497f69f0c36bf12fcab837e373beef2b8d350ceddeea2d7e81dfb0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,943 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hsub, <a>sub_sub_cancel</a>] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
b : ℝ
hb : IsLUB (range ⇑f) b
g : Y →ᵇ ℝ
xl : Y → X
hxl : ∀ (y : Y), f (xl y) ≤ g y
hgb : ∀ (y : Y), g y ≤ b
hb' : ¬∃ x, f x =... | ((:c Eq) (:c Real) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144068) (:c Real) (:fv _uniq.144074) (:c Real.pseudoMetricSpace)) (:fv _uniq.144068) (:lambda _ (:fv _uniq.144068) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144068) (:c Real) (:fv _uniq.144074) (:c Real.pseudoMetric... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":23601,"sourceStart":23599,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23603,"sourceStart":23602,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"hsub","source_end":23611,"source_start":23607,"syntax_kind":"ident"},{"source":"sub_sub_cancel","source_end":23627,"source_start":23613,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 155 | exact | true | 1 | 38 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26ea4899bf81db016de0f6fe28bc2bbbb645c702cda560af650f8adb6672533f | eaa8618d5788dd4d72c73a2eb8897eb74b9990e97edaa69816bc84ac80b4f285 | 6dc98abe93f9ac7f4045cd96e88b2b1f571b40b4426b32a58864522c33198d89 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,944 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hay : a < (g - dg) y := by calc a = c - (b - c) := by rw [← hsub, <a>sub_sub_cancel</a>] _ < g y - (b - c) := <a>sub_lt_sub_right</a> hc _ _ ≤ g y - dg y := <a>sub_le_sub_left</a> (dgmem _).2 _ | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb ... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb ... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":23697,"sourceStart":23693,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hay","sourceEnd":23701,"sourceStart":23698,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hay","sourceEnd":23701,"sourceStart":23698,"tag":"n... | [] | [{"source":"a < (g - dg) y","source_end":23718,"source_start":23704,"syntax_kind":"«term_<_»"},{"source":"a = c - (b - c)","source_end":23763,"source_start":23748,"syntax_kind":"«term_=_»"},{"source":"hsub","source_end":23782,"source_start":23778,"syntax_kind":"ident"},{"source":"sub_sub_cancel","source_end":23798,"sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 165 | exact | true | 1 | 39 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e31ff7a19fbd9807f4cd18405db895d3bd46e7cc156c139dd0eaf88e980ae2d6 | 4b603303c3b192f33d25bfbab2f1a6494e814128a24900ec191c0de31096455f | dee87d3e4ddcd9edfd9b12315114e61c6c740e7656c646753c6982380df41085 | 9a6e41789ffa17162a037d9d9c37f08b44e254602cccc894665ca3f2985884d3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,945 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases ha.exists_between hay with ⟨_, ⟨x, rfl⟩, _, hxy⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb ... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inr.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGL... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rcases","sourceEnd":23925,"sourceStart":23919,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"ha.exists_between","sourceEnd":23943,"sourceStart":23926,"tag":"identifier"},{"children":[{"contextIndex":40,"semanticRole":"local"... | [] | [{"source":"ha.exists_between hay","source_end":23947,"source_start":23926,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨_, ⟨x, rfl⟩, _, hxy⟩","source_end":23982,"source_start":23953,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 176 | exact | true | 1 | 40 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cbaa89762003e6e041971fb284f88dba891fdd5892179976aff151c7d7905278 | 9a6e41789ffa17162a037d9d9c37f08b44e254602cccc894665ca3f2985884d3 | 5d2b4732a0ed7466071affdb7fb326ebbbb5aef43671a4effe7ccca23751ce70 | 9cb49eb2818c087d3920c1009430e49bbb0ad79a41aa74441e161b9b40988754 |
cat-searcher/leandojo-benchmark-4-random | test | 3,946 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨x, xu, hxy.le, hyxu.le⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inl.inr.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGL... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":23994,"sourceStart":23989,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":23998,"sourceStart":23995,"tag":"atom"},{"children":[{"contextIndex":41,"semanticRole":"local","source":"x","sourceEnd":23999,"sourceStart":23998,"tag":"identifier"},{"source":",","sourceEnd":24000,... | [] | [{"source":"⟨x, xu, hxy.le, hyxu.le⟩","source_end":24023,"source_start":23995,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 177 | exact | true | 1 | 43 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a77b85102d9b2e39cf5e1c16c83132318fa9b24f9ff60db1d01da2a1d65eab6b | 9cb49eb2818c087d3920c1009430e49bbb0ad79a41aa74441e161b9b40988754 | 0fdf34be16ee7332d8b764a351e5b89e621c9900e83347de751d754398d3b122 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,947 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc a = c - (b - c) := by rw [← hsub, <a>sub_sub_cancel</a>] _ < g y - (b - c) := <a>sub_lt_sub_right</a> hc _ _ ≤ g y - dg y := <a>sub_le_sub_left</a> (dgmem _).2 _ | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.145169) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Real.pseudoMetricSpace)) (:fv _uniq.144071) (:lambda _ (:fv _uniq.144071) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.144071) (:c Real) (... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:c Real)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"calc","sourceEnd":23737,"sourceStart":23733,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":11,"semanticRole":"local","source":"a","sourceEnd":23749,"sourceStart":23748,"tag":"identifier"},{"source":"=","sourceEnd":23751,"sourceStart":23750,"tag":"atom"},{"children":[{"conte... | [] | [{"source":"a = c - (b - c)","source_end":23763,"source_start":23748,"syntax_kind":"«term_=_»"},{"source":"hsub","source_end":23782,"source_start":23778,"syntax_kind":"ident"},{"source":"sub_sub_cancel","source_end":23798,"source_start":23784,"syntax_kind":"ident"},{"source":"_","source_end":23811,"source_start":23810,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 167 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa7e94681088227939138a1de9bc6e714f774540c406ee22cbfacfcca9db5272 | 9c1a46b45c1c43139b8f4869a2c0038c674578b7bd862c8250bbe017a7f5676f | df6f9d527f2b332a4118f9837b24dd41877c27d96c3555babe75def8dfe562de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,948 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← hsub, <a>sub_sub_cancel</a>] | X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : IsLUB (range ⇑f) b
hmem : ∀ (x : X), f x ∈ Icc a b
hle : a ≤ b
hlt : a < b
c : ℝ := (... | ((:c Eq) (:c Real) (:fv _uniq.145169) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.151624) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.instSub)) (:fv _uniq.145423) (:fv _uniq.151624)))) | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:fv FV11)) (: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) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Re... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":23772,"sourceStart":23770,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":23774,"sourceStart":23773,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"hsub","source_end":23782,"source_start":23778,"syntax_kind":"ident"},{"source":"sub_sub_cancel","source_end":23798,"source_start":23784,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 170 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e6ddca5e44aef00fd1b90890a2ad1e91d0475189675c9d02fee878c19645515 | 75e7b4e294172f5ab8c7248edc06ebd64becee17cfcbf3af0da2dc7dcc3a8197 | 6dc98abe93f9ac7f4045cd96e88b2b1f571b40b4426b32a58864522c33198d89 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,949 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨xl y, xu, ?_, hyxu.le⟩ | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : Is... | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : Is... | ((:c Exists) (:fv _uniq.144068) (:lambda x₁ (:fv _uniq.144068) ((:c Exists) (:fv _uniq.144068) (:lambda x₂ (:fv _uniq.144068) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144071) (:c Real) (:fv _uniq.144077) (:c Rea... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₁ :explicit (:fv FV0) (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x₂ :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":24035,"sourceStart":24029,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":24039,"sourceStart":24036,"tag":"atom"},{"children":[{"children":[{"contextIndex":23,"semanticRole":"local","source":"xl","sourceEnd":24041,"sourceStart":24039,"tag":"identifier"},{"children":[{"co... | [] | [{"source":"⟨xl y, xu, ?_, hyxu.le⟩","source_end":24063,"source_start":24036,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 182 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d43f8ab81794f78c569448dd8fd9432a8808203c837caee6ec1a331afbacb9df | a3d2792b9be952f62ab573acb03125025237a20e26f3fdc5bdcfdb4c52c44ac5 | 81251c99c3bd5b21df8888a0087e3ec05bfb3841d222cf42e401b4916dc7ee3f | 64cbbf0035fb785f227a84d4b85959cce4f39b2cac197d4d989e020a50cd022f |
cat-searcher/leandojo-benchmark-4-random | test | 3,950 | BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_closedEmbedding | Mathlib/Topology/TietzeExtension.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [dg0 (<a>Or.inr</a> hc), hxl] | case intro.intro.inr.intro.intro.inr.intro.intro.intro.intro.intro.intro.intro.inr
X : Type u_1
Y : Type u_2
inst✝³ : TopologicalSpace X
inst✝² : TopologicalSpace Y
inst✝¹ : NormalSpace Y
inst✝ : Nonempty X
f : X →ᵇ ℝ
e : X → Y
he : ClosedEmbedding e
inhabited_h : Inhabited X
a : ℝ
ha : IsGLB (range ⇑f) a
b : ℝ
hb : Is... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c DFunLike.coe) ((:c BoundedContinuousFunction) (:fv _uniq.144068) (:c Real) (:fv _uniq.144074) (:c Real.pseudoMetricSpace)) (:fv _uniq.144068) (:lambda _ (:fv _uniq.144068) (:c Real)) ((:c BoundedContinuousFunction.instFunLike) (:fv _uniq.1... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c TopologicalSpace) (:fv _uniq.144068))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.144071))"},{"name":"inst✝¹","sexp":"((:c NormalSpace) (:fv _uniq.144071) (:fv _uniq.144077))"},{"name":"inst✝"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c BoundedContinuousFunction) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:c Real)) (:arg :instance 2 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":24072,"sourceStart":24068,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24074,"sourceStart":24073,"tag":"a... | [] | [{"source":"dg0 (Or.inr hc)","source_end":24089,"source_start":24074,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hxl","source_end":24094,"source_start":24091,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.144068","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.144071","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal... | 39 | 183 | exact | true | 1 | 38 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9506416ae82cca4b1c9e24db1b0b0bce60f0e87080db4a3e9301508e4e26e50d | 64cbbf0035fb785f227a84d4b85959cce4f39b2cac197d4d989e020a50cd022f | 97d7acfce81fda0a4f0cf928195263cc84b627402975d325a4d9bca735731c09 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,951 | intervalIntegral.integral_comp_neg | Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>zero_sub</a>] using <a>intervalIntegral.integral_comp_sub_left</a> f 0 | ι : Type u_1
𝕜 : Type u_2
E : Type u_3
F : Type u_4
A : Type u_5
inst✝² : NormedAddCommGroup E
inst✝¹ : CompleteSpace E
inst✝ : NormedSpace ℝ E
a b c d : ℝ
f : ℝ → E
⊢ ∫ (x : ℝ) in a..b, f (-x) = ∫ (x : ℝ) in -b..-a, f x | ((:c Eq) (:fv _uniq.375163) ((:c intervalIntegral) (:fv _uniq.375163) (:fv _uniq.375172) (:fv _uniq.375394) (:lambda x (:c Real) ((:fv _uniq.375406) ((:c Neg.neg) (:c Real) (:c Real.instNeg) 0))) (:fv _uniq.375396) (:fv _uniq.375398) ((:c MeasureTheory.MeasureSpace.volume) (:c Real) (:c Real.measureSpace))) ((:c interv... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"A","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝²","sexp":"((:c NormedAddCommGroup) (:fv _uniq.375163))"},{"name":"inst✝¹","sexp":"((:c CompleteSpace) (... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c intervalIntegral) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 2 (:instance-of (:app (:c NormedSpace) (:arg :explicit 0 (:c Real)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.375157","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.375160","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":45510,"sourceStart":45505,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"zero_sub","source_end":45525,"source_start":45517,"syntax_kind":"ident"},{"source":"integral_comp_sub_left f 0","source_end":45559,"source_start":45533,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.375157","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.375160","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 284 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f15e54dee92655f901d9cb8b8b0865c483f350809b09a3fea080572472ae033 | 6a5b1e049c4f10f596c222b7932366d66eecf17a1bc35e90e517ab12bd8ce753 | 4727455ce44bb5d564f8e5f97895076e6b4b10f1002efed476eb3ada26882d7e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,952 | NNReal.summable_coe | Mathlib/Topology/Instances/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | constructor | α : Type u_1
f : α → ℝ≥0
⊢ (Summable fun a => ↑(f a)) ↔ Summable f | ((:c Iff) ((:c Summable) (:c Real) (:fv _uniq.21146) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:lambda a (:fv _uniq.21146) ((:c NNReal.toReal) ((:fv _uniq.21309) 0)))) ((:c Summable) (:c NNReal) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.21146) (:c NNReal))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Summable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:c NNReal))"}] | {"children":[{"children":[{"children":[{"children":[{"source":"constructor","sourceEnd":7836,"sourceStart":7825,"tag":"atom"}],"kind":"Lean.Parser.Tactic.constructor","source":"constructor","sourceEnd":7836,"sourceStart":7825,"tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":... | [] | [{"source":"fun ⟨a, ha⟩ => ⟨⟨a, ha.nonneg fun x => (f x).2⟩, hasSum_coe.1 ha⟩","source_end":7925,"source_start":7848,"syntax_kind":"Lean.Parser.Term.fun"},{"source":"fun ⟨a, ha⟩ => ⟨a.1, hasSum_coe.2 ha⟩","source_end":7982,"source_start":7937,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"user_name":"f"}] | 55 | 2 | branch_opener | false | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a13abbb0ee368397509ff968056363b0a00977f64f68652ef66f787bc6a0af9 | 0b474bd056193913132cf4cc4a5e524da70ea56dea304bcdd4c7f1275e7b7ab4 | e3c1703abf8a6b3df04dd30e184fe02bb6724f46830b544562ff083169371068 | 06a0f38c8d3579c5b68f6372578e2968fd2164f67788b1ab33d7980f4066ec23 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,953 | NNReal.summable_coe | Mathlib/Topology/Instances/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun ⟨a, ha⟩ => ⟨⟨a, ha.nonneg fun x => (f x).2⟩, <a>NNReal.hasSum_coe</a>.1 ha⟩ | case mp
α : Type u_1
f : α → ℝ≥0
⊢ (Summable fun a => ↑(f a)) → Summable f | (:forall _ ((:c Summable) (:c Real) (:fv _uniq.21146) (:c Real.instAddCommMonoid) ((:c UniformSpace.toTopologicalSpace) (:c Real) ((:c PseudoMetricSpace.toUniformSpace) (:c Real) (:c Real.pseudoMetricSpace))) (:lambda a (:fv _uniq.21146) ((:c NNReal.toReal) ((:fv _uniq.21309) 0)))) ((:c Summable) (:c NNReal) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.21146) (:c NNReal))"}] | (:forall _ :explicit (:app (:c Summable) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c Real))))) (:arg :explicit 4 (:lambda a :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:c NNReal))"}] | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7847,"sourceStart":7842,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":7851,"sourceStart":7848,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7855,"sourceStart":7852,"tag":"atom"},{"children":[{"sem... | [] | [{"source":"fun ⟨a, ha⟩ => ⟨⟨a, ha.nonneg fun x => (f x).2⟩, hasSum_coe.1 ha⟩","source_end":7925,"source_start":7848,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"user_name":"f"}] | 55 | 7 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26886b0a0c768565efbcf55acc4f9b441847eb37f3f1368a5d3c35060acd813a | ee1b7f9445abe8dde2e023dfe6e0527aa905fc22b96603e8c9c68fc6d79fe77c | 1383edc9e1d5549577e3a37d3d61d288f597aaa0560df7b43124b289b4815618 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,954 | NNReal.summable_coe | Mathlib/Topology/Instances/NNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun ⟨a, ha⟩ => ⟨a.1, <a>NNReal.hasSum_coe</a>.2 ha⟩ | case mpr
α : Type u_1
f : α → ℝ≥0
⊢ Summable f → Summable fun a => ↑(f a) | (:forall _ ((:c Summable) (:c NNReal) (:fv _uniq.21146) ((:c OrderedAddCommMonoid.toAddCommMonoid) (:c NNReal) ((:c OrderedSemiring.toOrderedAddCommMonoid) (:c NNReal) ((:c OrderedCommSemiring.toOrderedSemiring) (:c NNReal) (:c instNNRealOrderedCommSemiring)))) (:c NNReal.instTopologicalSpace) (:fv _uniq.21309)) ((:c S... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.21146) (:c NNReal))"}] | (:forall _ :explicit (:app (:c Summable) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:c NNReal))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:c NNReal))))) (:arg :explicit 4 (:fv F... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:fv FV0) (:c NNReal))"}] | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":7936,"sourceStart":7931,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":7940,"sourceStart":7937,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":7944,"sourceStart":7941,"tag":"atom"},{"children":[{"sem... | [] | [{"source":"fun ⟨a, ha⟩ => ⟨a.1, hasSum_coe.2 ha⟩","source_end":7982,"source_start":7937,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.21146","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.21309","is_instance":false,"is_let":false,"user_name":"f"}] | 55 | 12 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c35c9530d450dc6cfc744c904bf5908c96145b3c53b692e7d17638ac177e6668 | e821b58c75f4b0828d6ee236f609f2a11c0342859fb1f04b8993c45510985dc4 | f38109577f5a546902128454167e6914b2ed1a2a6b6af9ae077d463aedd851d9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,955 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
⊢ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K} ⊆ D f K | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
⊢ x ∈ D f K | ((:c HasSubset.Subset) ((:c Set) (:c Real)) ((:c Set.instHasSubset) (:c Real)) ((:c setOf) (:c Real) (:lambda x (:c Real) ((:c And) ((:c DifferentiableWithinAt) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:c Real) (:c Real.normedAddCommGroup) ((:c NormedField.to... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"intro","sourceEnd":30928,"sourceStart":30923,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":30930,"sourceStart":30929,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":30933,"sourceStart":30931,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":30930,"source_start":30929,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":30933,"source_start":30931,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74d7494c936e1c9df8746614a5379458b48406de0be292665b4082cd73127d98 | cdb9c459e85c4c67571a310e5bea0631f2729b121848ece91f7c2110477b89e9 | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | f6b65d43d487523d4a274e48bfb0f043cbc49f003c91dc09ee288ed11ab21c26 |
cat-searcher/leandojo-benchmark-4-random | test | 3,956 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>RightDerivMeasurableAux.D</a>, <a>Set.mem_iInter</a>] | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
⊢ x ∈ D f K | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
⊢ ∀ (i : ℕ), x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ i) | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c RightDerivMeasurableAux.D) (:fv _uniq.401312) (:fv _uniq.401315) (:fv _uniq.401419) (:fv _uniq.401423) (:fv _uniq.401426))) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"rw","sourceEnd":30938,"sourceStart":30936,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30940,"sourceStart":30939,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"RightDerivMeasur... | [] | [{"source":"D","source_end":30941,"source_start":30940,"syntax_kind":"ident"},{"source":"mem_iInter","source_end":30953,"source_start":30943,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 64052ae5d6c439b0f6ffa66cd6eb870348b3afdee454205426dc965fe3c0b8f6 | f6b65d43d487523d4a274e48bfb0f043cbc49f003c91dc09ee288ed11ab21c26 | 455077e3957043bb9bd9ec9367d17ed577fa6f101b16cd967b2386b69449aaed | c12ca4a75531cbf5e8f498269cfe0ee6c1efda15c25a82ff6fdd4984b60dec0b |
cat-searcher/leandojo-benchmark-4-random | test | 3,957 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro e | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
⊢ ∀ (i : ℕ), x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ i) | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
⊢ x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e) | (:forall i (:c Nat) ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c Set.iUnion) (:c Real) (:c Nat) (:lambda n (:c Nat) ((:c Set.iInter) (:c Real) (:c Nat) (:lambda p (:c Nat) ((:c Set.iInter) (:c Real) ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) (:lambda _ ((... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:forall i :explicit (:c Nat) (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"intro","sourceEnd":30962,"sourceStart":30957,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"e","sourceEnd":30964,"sourceStart":30963,"tag":"identifier"}],"kind":"null","source":"e","sourceEnd":30964,"sourceStart":30963,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"e","source_end":30964,"source_start":30963,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 9 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 006e4142d2944e7b2654082c066e0d2c619d1ddaa1551075f175a5f7f0db2b62 | c12ca4a75531cbf5e8f498269cfe0ee6c1efda15c25a82ff6fdd4984b60dec0b | d97190aa489499e2113eb2b7ebfaf49976e5a9774a652c63907edf69e5878ebb | c60820a8d9b40f63cd8ba0641c50645e887342be49d02bc6c8d544ec32442163 |
cat-searcher/leandojo-benchmark-4-random | test | 3,958 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : (0 : ℝ) < (1 / 2) ^ e := <a>pow_pos</a> (by norm_num) _ | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
⊢ x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e) | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
⊢ x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e) | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c Set.iUnion) (:c Real) (:c Nat) (:lambda n (:c Nat) ((:c Set.iInter) (:c Real) (:c Nat) (:lambda p (:c Nat) ((:c Set.iInter) (:c Real) ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) (:lambda _ ((:c GE.ge) (:c Nat) (... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"have","sourceEnd":30971,"sourceStart":30967,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":30972,"sourceStart":30972,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":30972,"sourceStart":30972,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"(0 : ℝ) < (1 / 2) ^ e","source_end":30997,"source_start":30974,"syntax_kind":"«term_<_»"},{"source":"pow_pos (by norm_num) _","source_end":31024,"source_start":31001,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 10 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 68f768ec538e553ff52670be71bcea64db52371a0b3874a6f6fc8320eb8e5448 | c60820a8d9b40f63cd8ba0641c50645e887342be49d02bc6c8d544ec32442163 | cc1e1fe11e58e71c9aaf5311dd4a9f2ce8cf55fdc7b42c176b7a9d7548371139 | a080bc66afc67c3cc15bfd5db84c12857a115648d9143a12392d2c83d5ecffba |
cat-searcher/leandojo-benchmark-4-random | test | 3,959 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>RightDerivMeasurableAux.mem_A_of_differentiable</a> this hx.1 with ⟨R, R_pos, hR⟩ | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
⊢ x ∈ ⋃ n, ⋂ p, ⋂ (_ : p ≥ n), ⋂ q, ⋂ (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e) | case intro.intro
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
⊢ x ∈ ⋃ n... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c Set.iUnion) (:c Real) (:c Nat) (:lambda n (:c Nat) ((:c Set.iInter) (:c Real) (:c Nat) (:lambda p (:c Nat) ((:c Set.iInter) (:c Real) ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) (:lambda _ ((:c GE.ge) (:c Nat) (... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"rcases","sourceEnd":31033,"sourceStart":31027,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"RightDerivMeasurableAux.mem_A_of_differentiable","semanticRole":"global","source":"mem_A_of_differentiable","sourceEnd":31057,"source... | [] | [{"source":"mem_A_of_differentiable this hx.1","source_end":31067,"source_start":31034,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨R, R_pos, hR⟩","source_end":31091,"source_start":31073,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 16 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 282e06915e3aea3ee84da18a3210783c8939b2ca59bda2cbc4c1edb01ccc9596 | a080bc66afc67c3cc15bfd5db84c12857a115648d9143a12392d2c83d5ecffba | 0df9b0518122719c0cd9ee0f35721251fe7208a29e155e10d7b51b3974521af0 | a110aed874f404e80754d3349983986f3e1b20efdb8570a71bd3ad963d6a3813 |
cat-searcher/leandojo-benchmark-4-random | test | 3,960 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨n, hn⟩ : ∃ n : ℕ, (1 / 2) ^ n < R := <a>exists_pow_lt_of_lt_one</a> R_pos (by norm_num : (1 : ℝ) / 2 < 1) | case intro.intro
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
⊢ x ∈ ⋃ n... | case intro.intro.intro
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
n :... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c Set.iUnion) (:c Real) (:c Nat) (:lambda n (:c Nat) ((:c Set.iInter) (:c Real) (:c Nat) (:lambda p (:c Nat) ((:c Set.iInter) (:c Real) ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) (:lambda _ ((:c GE.ge) (:c Nat) (... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"obtain","sourceEnd":31100,"sourceStart":31094,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":31104,"sourceStart":31101,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n","sourceEn... | [] | [{"source":"∃ n : ℕ, (1 / 2) ^ n < R","source_end":31143,"source_start":31115,"syntax_kind":"«term∃_,_»"},{"source":"exists_pow_lt_of_lt_one R_pos (by norm_num : (1 : ℝ) / 2 < 1)","source_end":31214,"source_start":31151,"syntax_kind":"Lean.Parser.Term.app"},{"source":"obtain","source_end":31100,"source_start":31094,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 17 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43e3be78d28e884c605c758b23175129aeeae83a456b20d8232b18d2613d02d9 | a110aed874f404e80754d3349983986f3e1b20efdb8570a71bd3ad963d6a3813 | 9571702bc088514f6fa0e24ae0876be55964d7c86a9d21084d046cd0001f8cb9 | 34d993ecd1e8d576746088be5020ddfab32608f868f2401ce41c2d19d8418e7f |
cat-searcher/leandojo-benchmark-4-random | test | 3,961 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.mem_iUnion</a>, <a>Set.mem_iInter</a>, <a>RightDerivMeasurableAux.B</a>, <a>Set.mem_inter_iff</a>] | case intro.intro.intro
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
n :... | case intro.intro.intro
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
n :... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c Set.iUnion) (:c Real) (:c Nat) (:lambda n (:c Nat) ((:c Set.iInter) (:c Real) (:c Nat) (:lambda p (:c Nat) ((:c Set.iInter) (:c Real) ((:c GE.ge) (:c Nat) (:c instLENat) 0 1) (:lambda _ ((:c GE.ge) (:c Nat) (... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"simp","sourceEnd":31221,"sourceStart":31217,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":31226,"sourceStart":31222,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":312... | [] | [{"source":"mem_iUnion","source_end":31238,"source_start":31228,"syntax_kind":"ident"},{"source":"mem_iInter","source_end":31250,"source_start":31240,"syntax_kind":"ident"},{"source":"B","source_end":31253,"source_start":31252,"syntax_kind":"ident"},{"source":"mem_inter_iff","source_end":31268,"source_start":31255,"syn... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 23 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96e51d560d3739eae5a4647cf7c427bf75c106fe90341bf945433672bad167d7 | 34d993ecd1e8d576746088be5020ddfab32608f868f2401ce41c2d19d8418e7f | 8882242a0d5d3e4f6d735d2a1844e91218a856b623be3de8a2bc3f4873f89324 | df8ed823ff9f465577742f81aefba34289b2a818d6d1064e2cd71b48b6cdef09 |
cat-searcher/leandojo-benchmark-4-random | test | 3,962 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
⊢ 0 < 1 / 2 | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) (:c Real.strictOrderedSemiring)))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MonoidWithZero.toZero) (:c Real) ((:c Semiring.toMonoidWithZero) (:c... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (: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.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":31021,"sourceStart":31013,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 13 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f1ab59977e1b136e6c64948a51e33c857ee767c84ed68f3dcbc47e08857c69b | 2bc66088a6fcf53575c701543815b33fa3879390ecb0e4227f70bf12f3797263 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,963 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
⊢ 1 / 2 < 1 | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOf... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (: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 HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":31193,"sourceStart":31185,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 20 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c5cacbaa2ac2c23178ad760cc51f1a25923729eea3272cefcfbac9603a486a9 | a7a00717e3099d473a1ad2d66f1801c7694932db2dc95490529074263b57f649 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,964 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hR _ ⟨<a>pow_pos</a> (by norm_num) _, <a>lt_of_le_of_lt</a> ?_ hn⟩ | case intro.intro.intro.refine_2
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2)... | case intro.intro.intro.refine_2
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2)... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) (:fv _uniq.401854) ((:c RightDerivMeasurableAux.A) (:fv _uniq.401312) (:fv _uniq.401315) (:fv _uniq.401419) (:fv _uniq.401423) ((:c derivWithin) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.densely... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:fv FV6)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"refine","sourceEnd":31372,"sourceStart":31366,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hR","sourceEnd":31375,"sourceStart":31373,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":31377,"sourceStart":31376,"tag":"atom"}],"kind":"Lean.Par... | [] | [{"source":"hR _ ⟨pow_pos (by norm_num) _, lt_of_le_of_lt ?_ hn⟩","source_end":31429,"source_start":31373,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 57 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1c3325ffcd834ea3cb32f71a5ad8469cfeb21cd5a4703355a153ede196a8a0f2 | fb7adc2c050991a1e28b0830add41d4c6e9b70f18875bfae645803388365fd1a | 262c0861596670d90a6d8cd5d9bea2df229bd9949cce9ffb0c43ce468ff0a5b1 | 806a79031323c047acf1d410292b546eea4450d7de71ab5e7ade00d36bce0695 |
cat-searcher/leandojo-benchmark-4-random | test | 3,965 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>pow_le_pow_of_le_one</a> (by norm_num) (by norm_num) (by assumption) | case intro.intro.intro.refine_2
F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2)... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"source":"exact","sourceEnd":31441,"sourceStart":31436,"tag":"atom"},{"children":[{"name":"pow_le_pow_of_le_one","semanticRole":"global","source":"pow_le_pow_of_le_one","sourceEnd":31462,"sourceStart":31442,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":31464,"sourceStart":31463,"... | [] | [{"source":"pow_le_pow_of_le_one (by norm_num) (by norm_num) (by assumption)","source_end":31506,"source_start":31442,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 63 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 298cc31cd10ffc657813f486dfd13435574e8b8fc6bc4a20c24b1b251329f816 | 806a79031323c047acf1d410292b546eea4450d7de71ab5e7ade00d36bce0695 | e6f18ec0c14145ed01c364afe8c88f283c46a2e11a16bea8c74b66c3ff5a0ef5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,969 | RightDerivMeasurableAux.differentiable_set_subset_D | Mathlib/Analysis/Calculus/FDeriv/Measurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | F : Type u_1
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
f : ℝ → F
K : Set F
x : ℝ
hx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}
e : ℕ
this : 0 < (1 / 2) ^ e
R : ℝ
R_pos : R > 0
hR : ∀ r ∈ Ioo 0 R, x ∈ A f (derivWithin f (Ici x) x) r ((1 / 2) ^ e)
n : ℕ
hn : (1 / 2) ^ n < R... | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.403075) (:fv _uniq.404634)) | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.401312))"},{"name":"inst✝","sexp":"((:c NormedSpace) (:c Real) (:fv _uniq.401312) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.401312) (:fv _uniq.401315)))"},{"name":"f","sexp":"(:... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV13)) (:arg :explicit 3 (:fv FV17))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c NormedAddCommGroup) (... | {"children":[{"children":[{"children":[{"children":[{"source":"assumption","sourceEnd":31505,"sourceStart":31495,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":31505,"sourceStart":31495,"tag":"node"}],"kind":"null","source":"assumption","sourceEnd":31505,"sourceStart":31495,"tag... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.401312","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.401315","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 88 | 76 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 45f5bb34b791e80866f07002da5cdc609bdd1fae349e82f20b477ed18b06762c | b34b0b0606403f7aec04d09fd3fabb8fc16281564a0e3f16bebd909dc232359d | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,970 | constantCoeff_wittStructureRat_zero | Mathlib/RingTheory/WittVector/StructurePolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>wittStructureRat</a>, <a>MvPolynomial.bind₁</a>, <a>MvPolynomial.map_aeval</a>, <a>xInTermsOfW_zero</a>, <a>MvPolynomial.constantCoeff_rename</a>, <a>constantCoeff_wittPolynomial</a>, <a>MvPolynomial.aeval_X</a>, <a>MvPolynomial.constantCoeff_comp_algebraMap</a>, <a>MvPolynomial.eval₂Hom_zero'_apply</a>, ... | p : ℕ
R : Type u_1
idx : Type u_2
inst✝ : CommRing R
hp : Fact (Nat.Prime p)
Φ : MvPolynomial idx ℚ
⊢ constantCoeff (wittStructureRat p Φ 0) = constantCoeff Φ | ((:c Eq) (:c Rat) ((:c DFunLike.coe) ((:c RingHom) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.84031) (:c Nat)) (:c Rat) (:c Rat.commSemiring)) (:c Rat) ((:c Semiring.toNonAssocSemiring) ((:c MvPolynomial) ((:c Prod) (:fv _uniq.84031) (:c Nat)) (:c Rat) (:c Rat.commSemiring)) ((:c CommSemiring.toSemiring) ((:c MvPolynomia... | [{"name":"p","sexp":"(:c Nat)"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"idx","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.84028))"},{"name":"hp","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.84025)))"},{"name":"Φ","sexp":"((:c MvPolynomial) (:fv _uniq.84031) (:c Rat) (:c Rat.co... | (:app (:c Eq) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:app (:c MvPolynomial) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:c Nat)))) (:arg :explicit 1 (:c Rat)) (:arg :instance 2 (:instan... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.84025","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84028","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":17125,"sourceStart":17121,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17130,"sourceStart":17126,"tag":"atom"}],"kind"... | [] | [{"source":"wittStructureRat","source_end":17148,"source_start":17132,"syntax_kind":"ident"},{"source":"bind₁","source_end":17157,"source_start":17150,"syntax_kind":"ident"},{"source":"map_aeval","source_end":17168,"source_start":17159,"syntax_kind":"ident"},{"source":"xInTermsOfW_zero","source_end":17186,"source_start... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.84025","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84028","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 43 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f3c88f26274cc1049314a7ed9541ab7004ac4e56f4da2a3fe89ae7633ad2a01 | 7fae7f0ea358afd718e77e1c9a0091c6381070918beba483c3f0650672506c97 | c9600cd8a3609b80358acb145d0949a2b49cc87a1e4a53857c117191d95a573c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,971 | cfc_add | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases ha : p a | R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha : autoPa... | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha... | ((:c Eq) (:fv _uniq.237095) ((:c cfc) (:fv _uniq.237092) (:fv _uniq.237095) (:fv _uniq.237099) (:fv _uniq.237102) (:fv _uniq.237465) (:fv _uniq.237468) (:fv _uniq.237889) (:fv _uniq.238559) (:fv _uniq.238562) (:fv _uniq.238565) (:fv _uniq.238702) (:fv _uniq.238939) (:fv _uniq.239015) (:lambda x (:fv _uniq.237092) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.237095) (:sort 0))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.237092))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.237092) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c StarRing) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":22379,"sourceStart":22371,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"ha","sourceEnd":22382,"sourceStart":22380,"tag":"identifier"},{"source":":","sourceEnd":22384,"sourceStart":22383,"tag":"atom"}],"kind":"null","source":"ha :","sourceEnd":22384,"so... | [] | [{"source":"p a","source_end":22388,"source_start":22385,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 50 | 4 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce8a644b35f583ced9edeaebe0524ce04eed55424f993b14d6a871173a64f04a | 3644b3784a4075258d1c51b9415c63100f7cbbb06915386c05dcb6d62b85a012 | e0f6ae35a9ecbea121a97db4e5ccb674f04bae09eba61a66434917da158e2045 | a88c74281481900f1998107c47754389ba087b30aebf36426831194084705c27 |
cat-searcher/leandojo-benchmark-4-random | test | 3,972 | cfc_add | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>cfc_apply</a> f a, <a>cfc_apply</a> g a, ← <a>map_add</a>, <a>cfc_apply</a> _ a] | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha... | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha... | ((:c Eq) (:fv _uniq.237095) ((:c cfc) (:fv _uniq.237092) (:fv _uniq.237095) (:fv _uniq.237099) (:fv _uniq.237102) (:fv _uniq.237465) (:fv _uniq.237468) (:fv _uniq.237889) (:fv _uniq.238559) (:fv _uniq.238562) (:fv _uniq.238565) (:fv _uniq.238702) (:fv _uniq.238939) (:fv _uniq.239015) (:lambda x (:fv _uniq.237092) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.237095) (:sort 0))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.237092))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.237092) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c StarRing) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":22396,"sourceStart":22394,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":22398,"sourceStart":22397,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"cfc... | [] | [{"source":"cfc_apply f a","source_end":22411,"source_start":22398,"syntax_kind":"Lean.Parser.Term.app"},{"source":"cfc_apply g a","source_end":22426,"source_start":22413,"syntax_kind":"Lean.Parser.Term.app"},{"source":"map_add","source_end":22439,"source_start":22432,"syntax_kind":"ident"},{"source":"cfc_apply _ a","s... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 50 | 9 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 853a89b1d90ac83a90bc757d1e536d5c42e6da9333d8171aa7cd845f2f351d64 | a99a5acb2c3b53dc6c59a8bc3463b007a5aa3920ead553bc1cd43413b415b285 | 668316abe596185d7a7799aa8fc86c95ff8ef3f31850ed6c00c8dc6412e893b1 | 13b753d4d666d2a4c6b0bda285e12050c022b7dd9afc6ef08aeb9d85711d7f05 |
cat-searcher/leandojo-benchmark-4-random | test | 3,973 | cfc_add | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case pos
R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha... | ((:c Eq) (:fv _uniq.237095) ((:c DFunLike.coe) ((:c StarAlgHom) (:fv _uniq.237092) ((:c ContinuousMap) ((:c Set.Elem) (:fv _uniq.237092) ((:c spectrum) (:fv _uniq.237092) (:fv _uniq.237095) (:fv _uniq.237102) (:fv _uniq.238565) (:fv _uniq.238939) (:fv _uniq.239025))) (:fv _uniq.237092) ((:c instTopologicalSpaceSubtype)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.237095) (:sort 0))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.237092))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.237092) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c StarAlgHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c ContinuousMap) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c spectrum) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"congr","sourceEnd":22465,"sourceStart":22460,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":22465,"sourceStart":22460,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 50 | 15 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5b093c62ff54d1c6bbde94e18aae3ddbd76401b480cdb383e7f4f561c65539d | 13b753d4d666d2a4c6b0bda285e12050c022b7dd9afc6ef08aeb9d85711d7f05 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,974 | cfc_add | Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>cfc_apply_of_not_predicate</a> a ha] | case neg
R : Type u_1
A : Type u_2
p : A → Prop
inst✝⁹ : CommSemiring R
inst✝⁸ : StarRing R
inst✝⁷ : MetricSpace R
inst✝⁶ : TopologicalSemiring R
inst✝⁵ : ContinuousStar R
inst✝⁴ : TopologicalSpace A
inst✝³ : Ring A
inst✝² : StarRing A
inst✝¹ : Algebra R A
inst✝ : ContinuousFunctionalCalculus R p
f✝ g✝ : R → R
a : A
ha... | ((:c Eq) (:fv _uniq.237095) ((:c cfc) (:fv _uniq.237092) (:fv _uniq.237095) (:fv _uniq.237099) (:fv _uniq.237102) (:fv _uniq.237465) (:fv _uniq.237468) (:fv _uniq.237889) (:fv _uniq.238559) (:fv _uniq.238562) (:fv _uniq.238565) (:fv _uniq.238702) (:fv _uniq.238939) (:fv _uniq.239015) (:lambda x (:fv _uniq.237092) ((:c ... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"A","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.237095) (:sort 0))"},{"name":"inst✝⁹","sexp":"((:c CommSemiring) (:fv _uniq.237092))"},{"name":"inst✝⁸","sexp":"((:c StarRing) (:fv _uniq.237092) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c cfc) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit 2) (:arg :instance 3 (:instance-of (:app (:c CommSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 4 (:instance-of (:app (:c StarRing) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"name":"A","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":22475,"sourceStart":22471,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"cfc_apply_of_not_predicate a ha","source_end":22508,"source_start":22477,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.237092","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.237095","is_instance":false,"is_let":false,"user_name":"A"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 50 | 18 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 04098052d77f59ffe618ba1250e625f981a45db6c0d404fb180a9c2f8ead7dc4 | b884b60f6fcfe174bbca74dc4a053c801f1a3536e528a24b6e628c939d758452 | d6c921fd64b68ad63faa178e79f38326e7faa69e4b822a72b0675d40539b4e4f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,975 | PadicSeq.equiv_zero_of_val_eq_of_equiv_zero | Mathlib/NumberTheory/Padics/PadicNumbers.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [h] using hi _ hj | p : ℕ
inst✝ : Fact (Nat.Prime p)
f g : PadicSeq p
h : ∀ (k : ℕ), padicNorm p (↑f k) = padicNorm p (↑g k)
hf : f ≈ 0
ε : ℚ
hε : ε > 0
i : ℕ
hi : ∀ j ≥ i, padicNorm p (↑(f - 0) j) < ε
j : ℕ
hj : j ≥ i
⊢ padicNorm p (↑(g - 0) j) < ε | ((:c LT.lt) (:c Rat) ((:c Preorder.toLT) (:c Rat) ((:c PartialOrder.toPreorder) (:c Rat) ((:c StrictOrderedRing.toPartialOrder) (:c Rat) ((:c LinearOrderedRing.toStrictOrderedRing) (:c Rat) ((:c LinearOrderedCommRing.toLinearOrderedRing) (:c Rat) ((:c LinearOrderedField.toLinearOrderedCommRing) (:c Rat) (:c Rat.instLin... | [{"name":"p","sexp":"(:c Nat)"},{"name":"inst✝","sexp":"((:c Fact) ((:c Nat.Prime) (:fv _uniq.7266)))"},{"name":"f","sexp":"((:c PadicSeq) (:fv _uniq.7266))"},{"name":"g","sexp":"((:c PadicSeq) (:fv _uniq.7266))"},{"name":"h","sexp":"(:forall k (:c Nat) ((:c Eq) (:c Rat) ((:c padicNorm) (:fv _uniq.7266) ((:c Subtype.va... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c padicNorm) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:forall _ :explicit (:c Nat) (:c Rat))) (:arg :implicit 1) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7269","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Fact) (:arg :explicit 0 (:app ... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":5444,"sourceStart":5439,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"h","source_end":5447,"source_start":5446,"syntax_kind":"ident"},{"source":"hi _ hj","source_end":5462,"source_start":5455,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.7266","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.7269","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 24 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 890a37845317d89020e3ed483a1818b2cba3386577bd8260e940adf8ccd3abb0 | 0e28dcd5acd9d7692d33995ae57bfa425b070a4801490e0e034c1d24e3749de1 | 9927d658e1d311edfaf3d448e53a4e549e6a01919be546b9c67a4f0953b1d54e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,976 | EReal.coe_ennreal_pos | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>EReal.coe_ennreal_zero</a>, <a>EReal.coe_ennreal_lt_coe_ennreal_iff</a>] | x : ℝ≥0∞
⊢ 0 < ↑x ↔ 0 < x | ((:c Iff) ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c ENNReal.toEReal) (:fv _uniq.50013))) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNRe... | [{"name":"x","sexp":"(:c ENNReal)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:a... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50013","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":24735,"sourceStart":24733,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":24737,"sourceStart":24736,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"coe_ennreal_zero","source_end":24757,"source_start":24741,"syntax_kind":"ident"},{"source":"coe_ennreal_lt_coe_ennreal_iff","source_end":24789,"source_start":24759,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.50013","is_instance":false,"is_let":false,"user_name":"x"}] | 200 | 2 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 989cc35c896623e50f39513d46a20f35189bf104263569a09d89121268be2186 | f49ba98e865a733842279c26f3c3cec70cab94e56f14d1ef07ef946cc9ffdbbf | 80ff19e7830e48d0c730f6b76e7e2dadda94f4eef464162ec717bbad30ec948b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,977 | MeasureTheory.VectorMeasure.subset_le_of_restrict_le_restrict | Mathlib/MeasureTheory/Measure/VectorMeasure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hj₁ : <a>MeasurableSet</a> j | α : Type u_1
β : Type u_2
m : MeasurableSpace α
M : Type u_3
inst✝² : TopologicalSpace M
inst✝¹ : AddCommMonoid M
inst✝ : PartialOrder M
v w : VectorMeasure α M
i : Set α
hi : MeasurableSet i
hi₂ : v.restrict i ≤ w.restrict i
j : Set α
hj : j ⊆ i
⊢ ↑v j ≤ ↑w j | case pos
α : Type u_1
β : Type u_2
m : MeasurableSpace α
M : Type u_3
inst✝² : TopologicalSpace M
inst✝¹ : AddCommMonoid M
inst✝ : PartialOrder M
v w : VectorMeasure α M
i : Set α
hi : MeasurableSet i
hi₂ : v.restrict i ≤ w.restrict i
j : Set α
hj : j ⊆ i
hj₁ : MeasurableSet j
⊢ ↑v j ≤ ↑w j
case neg
α : Type u_1
β : Ty... | ((:c LE.le) (:fv _uniq.225062) ((:c Preorder.toLE) (:fv _uniq.225062) ((:c PartialOrder.toPreorder) (:fv _uniq.225062) (:fv _uniq.225071))) ((:c MeasureTheory.VectorMeasure.measureOf') (:fv _uniq.225053) (:fv _uniq.225059) (:fv _uniq.225062) (:fv _uniq.225068) (:fv _uniq.225065) (:fv _uniq.225095) (:fv _uniq.225375)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.225053))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.225062))"},{"name":"inst✝¹","sexp":"((:c AddCommMonoid) (:fv _uniq.225062))"... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c MeasureTheory.VectorMeasure.measureOf') (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"by_cases","sourceEnd":37055,"sourceStart":37047,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hj₁","sourceEnd":37061,"sourceStart":37056,"tag":"identifier"},{"source":":","sourceEnd":37063,"sourceStart":37062,"tag":"atom"}],"kind":"null","source":"hj₁ :","sourceEnd":37063,"... | [] | [{"source":"MeasurableSet j","source_end":37079,"source_start":37064,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 269 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1a38e082f8cce0bcbaaf314a72501a47f11962308c5ede2d187805572d6cf87a | 491601a123981c7e08dd34d19db5daadc810fc43085270b0e0de65319a94e50d | bba86345c344c014248638f0f3a34af0d42e34f3e4c5c510210754bee3a54db5 | 8443a7c08442d057de5f360bfe3dc24badce03ea1ffafddebe91e3d6c8f16d19 |
cat-searcher/leandojo-benchmark-4-random | test | 3,978 | MeasureTheory.VectorMeasure.subset_le_of_restrict_le_restrict | Mathlib/MeasureTheory/Measure/VectorMeasure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>MeasureTheory.VectorMeasure.restrict_le_restrict_iff</a> _ _ hi).1 hi₂ hj₁ hj | case pos
α : Type u_1
β : Type u_2
m : MeasurableSpace α
M : Type u_3
inst✝² : TopologicalSpace M
inst✝¹ : AddCommMonoid M
inst✝ : PartialOrder M
v w : VectorMeasure α M
i : Set α
hi : MeasurableSet i
hi₂ : v.restrict i ≤ w.restrict i
j : Set α
hj : j ⊆ i
hj₁ : MeasurableSet j
⊢ ↑v j ≤ ↑w j | ((:c LE.le) (:fv _uniq.225062) ((:c Preorder.toLE) (:fv _uniq.225062) ((:c PartialOrder.toPreorder) (:fv _uniq.225062) (:fv _uniq.225071))) ((:c MeasureTheory.VectorMeasure.measureOf') (:fv _uniq.225053) (:fv _uniq.225059) (:fv _uniq.225062) (:fv _uniq.225068) (:fv _uniq.225065) (:fv _uniq.225095) (:fv _uniq.225375)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.225053))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.225062))"},{"name":"inst✝¹","sexp":"((:c AddCommMonoid) (:fv _uniq.225062))"... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c MeasureTheory.VectorMeasure.measureOf') (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":37090,"sourceStart":37085,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":37092,"sourceStart":37091,"tag":"atom"},{"children":[{"name":"MeasureTheory.VectorMeasure.restrict_le_restrict_iff","semanticRole":"g... | [] | [{"source":"(restrict_le_restrict_iff _ _ hi).1 hi₂ hj₁ hj","source_end":37141,"source_start":37091,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 269 | 7 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c350b92f495f3b0629d2805992518d7c8280764408d0838b6f2c1aec449e9d8 | f90b409c095b7b7b45f32aa5ba6fbacace7bb92595b1bed2bb9c7e74e8efa1e6 | cef512ee8a0b1db32e2780b05445431d9dddf04184df79de221ba1b261b2ad77 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,979 | MeasureTheory.VectorMeasure.subset_le_of_restrict_le_restrict | Mathlib/MeasureTheory/Measure/VectorMeasure.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [v.not_measurable hj₁, w.not_measurable hj₁] | case neg
α : Type u_1
β : Type u_2
m : MeasurableSpace α
M : Type u_3
inst✝² : TopologicalSpace M
inst✝¹ : AddCommMonoid M
inst✝ : PartialOrder M
v w : VectorMeasure α M
i : Set α
hi : MeasurableSet i
hi₂ : v.restrict i ≤ w.restrict i
j : Set α
hj : j ⊆ i
hj₁ : ¬MeasurableSet j
⊢ ↑v j ≤ ↑w j | ((:c LE.le) (:fv _uniq.225062) ((:c Preorder.toLE) (:fv _uniq.225062) ((:c PartialOrder.toPreorder) (:fv _uniq.225062) (:fv _uniq.225071))) ((:c MeasureTheory.VectorMeasure.measureOf') (:fv _uniq.225053) (:fv _uniq.225059) (:fv _uniq.225062) (:fv _uniq.225068) (:fv _uniq.225065) (:fv _uniq.225095) (:fv _uniq.225375)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"m","sexp":"((:c MeasurableSpace) (:fv _uniq.225053))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.225062))"},{"name":"inst✝¹","sexp":"((:c AddCommMonoid) (:fv _uniq.225062))"... | (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c MeasureTheory.VectorMeasure.measureOf') (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":37149,"sourceStart":37147,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37151,"sourceStart":37150,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"v.not_measurable hj₁","source_end":37173,"source_start":37151,"syntax_kind":"Lean.Parser.Term.app"},{"source":"w.not_measurable hj₁","source_end":37197,"source_start":37175,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.225053","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.225056","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 269 | 12 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | afc69e6a96b9cc9e65ec7c5b268c1f7367dc6f2fab45eb96e7f57edc970e2b42 | da48b48b3715bd8145dc0d6296602827617a884f6c3a6a3671301b225b276a91 | c8fd1443546b91f80a155f5cbf690f421e867bdd8365cf7af93e7ac7670f63a7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,980 | CategoryTheory.MonoidalCategory.inv_hom_id_tensor | Mathlib/CategoryTheory/Monoidal/Category.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.MonoidalCategory.tensor_comp</a>, f.inv_hom_id] | C✝ : Type u
𝒞 : Category.{v, u} C✝
inst✝² : MonoidalCategory C✝
C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : MonoidalCategory C
U V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C
f : V ≅ W
g : X ⟶ Y
h : Y ⟶ Z
⊢ (f.inv ⊗ g) ≫ (f.hom ⊗ h) = (𝟙 W ⊗ g) ≫ (𝟙 W ⊗ h) | C✝ : Type u
𝒞 : Category.{v, u} C✝
inst✝² : MonoidalCategory C✝
C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : MonoidalCategory C
U V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C
f : V ≅ W
g : X ⟶ Y
h : Y ⟶ Z
⊢ 𝟙 W ⊗ g ≫ h = (𝟙 W ⊗ g) ≫ (𝟙 W ⊗ h) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.162953) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.162953) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.162953) (:fv _uniq.162956))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.162953) (:fv _uniq.162956) ((:c CategoryTheory.MonoidalCate... | [{"name":"C✝","sexp":"(:sort (+ u 1))"},{"name":"𝒞","sexp":"((:c CategoryTheory.Category) (:fv _uniq.162939))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.162939) (:fv _uniq.162942))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.162939","is_instance":false,"is_let":false,"name":"C✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.162942","is_instance":true,"is_let":false,"name":"𝒞","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"rw","sourceEnd":30651,"sourceStart":30649,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30653,"sourceStart":30652,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":30656,"sourceSt... | [] | [{"source":"tensor_comp","source_end":30668,"source_start":30657,"syntax_kind":"ident"},{"source":"f.inv_hom_id","source_end":30682,"source_start":30670,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.162939","is_instance":false,"is_let":false,"user_name":"C✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.162942","is_instance":true,"is_let":false,"user_name":"𝒞"},{"binder_role":":instance-implicit","context_index":2... | 152 | 4 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62983eccf6b0b290d1ec893191d2a90a74087e61c35adcd38996d869aa76476a | 7ced1597c465c3e8aa8784c8662d3a6b751f361fe5befc03aae79de33088e5fb | 94b7b3db37bbdad7ce52da7ed6944740ce43e21a97911b6d21fb93fffa81eb0b | d733f7b4d994bebcc7b06aecc882f1619da3cd1f9316b55790fb2fe8016e357b |
cat-searcher/leandojo-benchmark-4-random | test | 3,981 | CategoryTheory.MonoidalCategory.inv_hom_id_tensor | Mathlib/CategoryTheory/Monoidal/Category.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>CategoryTheory.MonoidalCategory.id_tensorHom</a>] | C✝ : Type u
𝒞 : Category.{v, u} C✝
inst✝² : MonoidalCategory C✝
C : Type u
inst✝¹ : Category.{v, u} C
inst✝ : MonoidalCategory C
U V✝ W✝ X✝ Y✝ Z✝ V W X Y Z : C
f : V ≅ W
g : X ⟶ Y
h : Y ⟶ Z
⊢ 𝟙 W ⊗ g ≫ h = (𝟙 W ⊗ g) ≫ (𝟙 W ⊗ h) | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.162953) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.162953) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.162953) (:fv _uniq.162956))) ((:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:fv _uniq.162953) (:fv _uniq.162956) ((:c CategoryTheory.MonoidalCate... | [{"name":"C✝","sexp":"(:sort (+ u 1))"},{"name":"𝒞","sexp":"((:c CategoryTheory.Category) (:fv _uniq.162939))"},{"name":"inst✝²","sexp":"((:c CategoryTheory.MonoidalCategory) (:fv _uniq.162939) (:fv _uniq.162942))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CategoryTheory.Category) (:fv _uniq... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV3))))) (:arg :explicit 2 (:app (:c CategoryTheory.MonoidalCategoryStruct.tensorObj) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.162939","is_instance":false,"is_let":false,"name":"C✝","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.162942","is_instance":true,"is_let":false,"name":"𝒞","sexp":"(:app (:c CategoryTheory.Category)... | {"children":[{"source":"simp","sourceEnd":30689,"sourceStart":30685,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":30691,"sourceStart":30690,"tag":"a... | [] | [{"source":"id_tensorHom","source_end":30703,"source_start":30691,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.162939","is_instance":false,"is_let":false,"user_name":"C✝"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.162942","is_instance":true,"is_let":false,"user_name":"𝒞"},{"binder_role":":instance-implicit","context_index":2... | 152 | 9 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 446798935232d933de3d923f6893b4e5f1c41d4efe848492eeae9e6b6d80ff6b | d733f7b4d994bebcc7b06aecc882f1619da3cd1f9316b55790fb2fe8016e357b | ccbc4f1495ca2677db2deb7c5d4dce46aa61ca42225789199dea8db4e001f544 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,982 | Set.Ico_eq_Ico_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.Subset.antisymm_iff</a>] at e | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h : a₁ < b₁ ∨ a₂ < b₂
e : Ico a₁ b₁ = Ico a₂ b₂
⊢ a₁ = a₂ ∧ b₁ = b₂ | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h : a₁ < b₁ ∨ a₂ < b₂
e : Ico a₁ b₁ ⊆ Ico a₂ b₂ ∧ Ico a₂ b₂ ⊆ Ico a₁ b₁
⊢ a₁ = a₂ ∧ b₁ = b₂ | ((:c And) ((:c Eq) (:fv _uniq.66290) (:fv _uniq.66300) (:fv _uniq.66302)) ((:c Eq) (:fv _uniq.66290) (:fv _uniq.66306) (:fv _uniq.66308))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.66290))"},{"name":"a","sexp":"(:fv _uniq.66290)"},{"name":"a₁","sexp":"(:fv _uniq.66290)"},{"name":"a₂","sexp":"(:fv _uniq.66290)"},{"name":"b","sexp":"(:fv _uniq.66290)"},{"name":"b₁","... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV8))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":42873,"sourceStart":42869,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":42878,"sourceStart":42874,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":428... | [] | [{"source":"Subset.antisymm_iff","source_end":42899,"source_start":42880,"syntax_kind":"ident"},{"source":"e","source_end":42905,"source_start":42904,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 503 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb0141a6be12ca680f3281eae83f712174f11de6192f967ec1b353d20bd33753 | 9e58d6676ddbe41792ea4fa1b02384ab848da56adbddb6fa7f68fdfdab33ccfe | 441cb7c9358a7b8f3b9a7b0e302918b3687da229ae55a311e7ea48bb7d289c4d | 9f45144a0b75733f7d8b6b01492e2413a0de0f0c443671d3e66f316af473bba9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,983 | Set.Ico_eq_Ico_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>le_antisymm_iff</a>] | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h : a₁ < b₁ ∨ a₂ < b₂
e : Ico a₁ b₁ ⊆ Ico a₂ b₂ ∧ Ico a₂ b₂ ⊆ Ico a₁ b₁
⊢ a₁ = a₂ ∧ b₁ = b₂ | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h : a₁ < b₁ ∨ a₂ < b₂
e : Ico a₁ b₁ ⊆ Ico a₂ b₂ ∧ Ico a₂ b₂ ⊆ Ico a₁ b₁
⊢ (a₁ ≤ a₂ ∧ a₂ ≤ a₁) ∧ b₁ ≤ b₂ ∧ b₂ ≤ b₁ | ((:c And) ((:c Eq) (:fv _uniq.66290) (:fv _uniq.66300) (:fv _uniq.66302)) ((:c Eq) (:fv _uniq.66290) (:fv _uniq.66306) (:fv _uniq.66308))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.66290))"},{"name":"a","sexp":"(:fv _uniq.66290)"},{"name":"a₁","sexp":"(:fv _uniq.66290)"},{"name":"a₂","sexp":"(:fv _uniq.66290)"},{"name":"b","sexp":"(:fv _uniq.66290)"},{"name":"b₁","... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5)))) (:arg :explicit 1 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV8))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":42916,"sourceStart":42912,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":42921,"sourceStart":42917,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":429... | [] | [{"source":"le_antisymm_iff","source_end":42938,"source_start":42923,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 503 | 5 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95c5da2c960ca87e7d35fdb9cae1666b5e27b557e1350f97232d4fd7afeb78ff | 9f45144a0b75733f7d8b6b01492e2413a0de0f0c443671d3e66f316af473bba9 | a5f3f2e561f1f4ffa65c15c1f79ba9670e7af42fb0fe1137ad8df581da2679aa | f588a5d21d3a9211ea6efcd546aea0ca912111cc82d1b552d4dec20c27cdb671 |
cat-searcher/leandojo-benchmark-4-random | test | 3,985 | Set.Ico_eq_Ico_iff | Mathlib/Order/Interval/Set/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h₁, h₂] | α : Type u_1
β : Type u_2
inst✝ : LinearOrder α
a a₁ a₂ b b₁ b₂ c d : α
h : a₁ < b₁ ∨ a₂ < b₂
x✝ : a₁ = a₂ ∧ b₁ = b₂
h₁ : a₁ = a₂
h₂ : b₁ = b₂
⊢ Ico a₁ b₁ = Ico a₂ b₂ | ((:c Eq) ((:c Set) (:fv _uniq.66290)) ((:c Set.Ico) (:fv _uniq.66290) ((:c PartialOrder.toPreorder) (:fv _uniq.66290) ((:c SemilatticeInf.toPartialOrder) (:fv _uniq.66290) ((:c Lattice.toSemilatticeInf) (:fv _uniq.66290) ((:c DistribLattice.toLattice) (:fv _uniq.66290) ((:c instDistribLatticeOfLinearOrder) (:fv _uniq.6... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c LinearOrder) (:fv _uniq.66290))"},{"name":"a","sexp":"(:fv _uniq.66290)"},{"name":"a₁","sexp":"(:fv _uniq.66290)"},{"name":"a₂","sexp":"(:fv _uniq.66290)"},{"name":"b","sexp":"(:fv _uniq.66290)"},{"name":"b₁","... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.Ico) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV7)))) (:arg :explicit 2 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":43423,"sourceStart":43421,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":43425,"sourceStart":43424,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"h₁","source_end":43429,"source_start":43425,"syntax_kind":"ident"},{"source":"h₂","source_end":43435,"source_start":43431,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66290","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66293","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 503 | 23 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d400d7617e75ffd57f2af21816f8462344a16c7564b5410610ff62fa49a8084f | 6e278850da7d824019fba8a13af75ae55ce23316b2e0219ece51042bf9f34a44 | f675fd073cb442d5f282adb75e9a57326f15c6b3d78d4b19f6cfbad12e59a106 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,986 | IsCompact.measure_eq_iInf_isOpen | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_antisymm</a> | α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ μ K = ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U | case a
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ μ K ≤ ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U
case a
α : Type u_1
β : Type u_... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874)) ((:c Set) (:fv _uniq.120868)) (:lambda _ ((:c Set) (:fv _uniq.120868)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.120868) (:fv _uniq.120874)) (:fv _uniq.120885) (:fv _uniq.121396)) ((:c iInf... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.120868))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.120868))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874))"},{"name":"in... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :expl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"apply","sourceEnd":44929,"sourceStart":44924,"tag":"atom"},{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":44941,"sourceStart":44930,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_antisymm","sourceEnd":44941,"sourceStart":44924,"tag":"n... | [] | [{"source":"le_antisymm","source_end":44941,"source_start":44930,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 103 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27e80d2648ff0a16f39a7a190175ed6ef7a72c0da78be75638350db66511b404 | 053afdf0d084017b1052880624a09043a6b1e362a1d6f89cf079e50280cf9a03 | 0abfddcb77ef175f592e63086534058d51fe8d6b63ac2fff9f69f045bc0962dc | f3320264a5f0c89634848ba600218789809d4dabec5dcb26b29018490e8221d6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,987 | IsCompact.measure_eq_iInf_isOpen | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>le_iInf_iff</a>] | case a
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ μ K ≤ ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U | case a
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ ∀ (i : Set α), K ⊆ i → IsOpen i → μ K ≤ μ i | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.120868))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.120868))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874))"},{"name":"in... | (: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.Measure) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":44951,"sourceStart":44947,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":44956,"sourceStart":44952,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":449... | [] | [{"source":"le_iInf_iff","source_end":44969,"source_start":44958,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 103 | 9 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 554c170862910e1e384df2458412d44d4663a6c52c7dc4cb475b4b5981756815 | 8d08246d305822c76633ad915b0c96c587897fc82cdf8b6389456a7915156fe4 | 634c502c90b918e87a413e2c7cc89259668ceaa7a67fd519dd645c5cf0552ebc | 7165cb98bc565b719db3f18aaf7cae93d89a9accb613abdfefac811e762f620b |
cat-searcher/leandojo-benchmark-4-random | test | 3,988 | IsCompact.measure_eq_iInf_isOpen | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact fun U KU _ ↦ <a>MeasureTheory.measure_mono</a> KU | case a
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ ∀ (i : Set α), K ⊆ i → IsOpen i → μ K ≤ μ i | (:forall i ((:c Set) (:fv _uniq.120868)) (:forall i ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.120868)) ((:c Set.instHasSubset) (:fv _uniq.120868)) (:fv _uniq.121396) 0) (:forall i ((:c IsOpen) (:fv _uniq.120868) (:fv _uniq.120877) 1) ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreord... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.120868))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.120868))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874))"},{"name":"in... | (:forall i :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:forall i :explicit (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":44980,"sourceStart":44975,"tag":"atom"},{"children":[{"source":"fun","sourceEnd":44984,"sourceStart":44981,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"U","sourceEnd":44986,"sourceStart":44985,"tag":"identifier"},{"semanticRole":"scoped_loca... | [] | [{"source":"fun U KU _ ↦ measure_mono KU","source_end":45011,"source_start":44981,"syntax_kind":"Lean.Parser.Term.fun"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 103 | 10 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5825f0827361b78090c9d8aa381a50bbb0789bce072a577b8218df49f27ff4e9 | 7165cb98bc565b719db3f18aaf7cae93d89a9accb613abdfefac811e762f620b | 93ef4e97e7ade6322ea615c98e059e8bcb584ed9f6f0a94701c8bd20e2844485 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,989 | IsCompact.measure_eq_iInf_isOpen | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_of_forall_lt'</a> | case a
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U ≤ μ K | case a.H
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ ∀ (c : ℝ≥0∞), μ K < c → ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U < c | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.120868))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.120868))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874))"},{"name":"in... | (: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 iInf) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Inf... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"apply","sourceEnd":45022,"sourceStart":45017,"tag":"atom"},{"name":"le_of_forall_lt'","semanticRole":"global","source":"le_of_forall_lt'","sourceEnd":45039,"sourceStart":45023,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_of_forall_lt'","sourceEnd":45039,"sourceStart"... | [] | [{"source":"le_of_forall_lt'","source_end":45039,"source_start":45023,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 103 | 15 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32e2012ae56b00d64e833bc061354ec02218daf335cf9fdc55012db23f8f4589 | c5f7df421636b719634e918e16c95b8e244526a764a1c4ed7f9d8c32b9b6b323 | 7ac1eeb7a67a27bcd4241d06832630036de49ec8a489322c573dc2f3ebb0466a | 570282c7da7a9c09c1431012760d0e53171f0d39ef8a469a24b6dba23a1ec457 |
cat-searcher/leandojo-benchmark-4-random | test | 3,990 | IsCompact.measure_eq_iInf_isOpen | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>iInf_lt_iff</a>, <a>exists_prop</a>, <a>exists_and_left</a>] using hK.exists_isOpen_lt_of_lt | case a.H
α : Type u_1
β : Type u_2
inst✝⁵ : MeasurableSpace α
inst✝⁴ : TopologicalSpace α
μ : Measure α
inst✝³ : μ.InnerRegularCompactLTTop
inst✝² : IsLocallyFiniteMeasure μ
inst✝¹ : R1Space α
inst✝ : BorelSpace α
K : Set α
hK : IsCompact K
⊢ ∀ (c : ℝ≥0∞), μ K < c → ⨅ U, ⨅ (_ : K ⊆ U), ⨅ (_ : IsOpen U), μ U < c | (:forall c (:c ENNReal) (:forall _ ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c LinearOrder.toPartialOrder) (:c ENNReal) ((:c ConditionallyCompleteLinearOrder.toLinearOrder) (:c ENNReal) ((:c ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁵","sexp":"((:c MeasurableSpace) (:fv _uniq.120868))"},{"name":"inst✝⁴","sexp":"((:c TopologicalSpace) (:fv _uniq.120868))"},{"name":"μ","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.120868) (:fv _uniq.120874))"},{"name":"in... | (:forall c :explicit (:c ENNReal) (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV0)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simpa","sourceEnd":45049,"sourceStart":45044,"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":"iInf_lt_iff","source_end":45067,"source_start":45056,"syntax_kind":"ident"},{"source":"exists_prop","source_end":45080,"source_start":45069,"syntax_kind":"ident"},{"source":"exists_and_left","source_end":45097,"source_start":45082,"syntax_kind":"ident"},{"source":"hK.exists_isOpen_lt_of_lt","source_end":451... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.120868","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.120871","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal... | 103 | 16 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8d42b1f54903aaef4079b54221ead52718cec019ae0272d0e4e7f72dccb1f6f | 570282c7da7a9c09c1431012760d0e53171f0d39ef8a469a24b6dba23a1ec457 | 4e6dc538a227e1d129abc5c8b551b2942af1d7a84e48870256ac2f8b31868352 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,991 | one_sub_goldConj | Mathlib/Data/Real/GoldenRatio.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith [<a>gold_add_goldConj</a>] | ⊢ 1 - φ = ψ | ((:c Eq) (:c Real) ((: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 goldenRatio)) (:c goldenConj)) | [] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (: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) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [] | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":2342,"sourceStart":2334,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"sour... | [] | [{"source":"gold_add_goldConj","source_end":2361,"source_start":2344,"syntax_kind":"ident"}] | [] | 21 | 2 | exact | true | 1 | 0 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b83210486ac29341237b215145f62a34b6534c5542dde72feb9c26b2086be644 | 352d2ba0129a052b7e360c12339e08bc9c3fbc3ab7868ff4db848ae468272995 | f6b6adbcfc78a9ebdad09f6a1ecf9c0f7d463974839aefa6f1054a00db8c0921 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,992 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let G' := Φ.localizedFunctor L₁ L₂ | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"let","sourceEnd":2861,"sourceStart":2858,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"G'","sourceEnd":2864,"sourceStart":2862,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so... | [] | [{"source":"Φ.localizedFunctor L₁ L₂","source_end":2897,"source_start":2868,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 4 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb5e62ffd7dc438f503990aa4efc8aeca6341aba8b0f2d6fbe40752cb7d9bcc0 | 95e768f73e98b8f0cbec40ad52b7ae6925890bc614272e484b8e167eed15701f | 472a549aa7e50568608eccee0e7939849885057867c7e1d72a51241af960eb12 | e2fd763e72da0cfea1d46e5b2a490d650382966ac39066634eef66b60c5c990a |
cat-searcher/leandojo-benchmark-4-random | test | 3,993 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let e' := <a>CategoryTheory.CatCommSq.iso</a> Φ.functor L₁ L₂ G' | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"let","sourceEnd":2903,"sourceStart":2900,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"e'","sourceEnd":2906,"sourceStart":2904,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"so... | [] | [{"source":"CatCommSq.iso Φ.functor L₁ L₂ G'","source_end":2947,"source_start":2910,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 5 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5408521839364aef9020b06962c9ae38c5af46f391486321986b75013959b5d7 | e2fd763e72da0cfea1d46e5b2a490d650382966ac39066634eef66b60c5c990a | 4585e644efd2de2fd1c60922359d8d2bbd13e1381474f3a09e475b58c72aa39d | 57cce2681516e008685076b5da5605d43614bd72d6f063000b11289a37772343 |
cat-searcher/leandojo-benchmark-4-random | test | 3,994 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change e'.hom.app X ≫ G'.map f ≫ e'.inv.app Y = _ | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"change","sourceEnd":2956,"sourceStart":2950,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"e'.hom.app","sourceEnd":2967,"sourceStart":2957,"tag":"identifier"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"X","sourceEnd":2969,"sourceStart":2968,"tag":"identifie... | [] | [{"source":"e'.hom.app X ≫ G'.map f ≫ e'.inv.app Y = _","source_end":3003,"source_start":2957,"syntax_kind":"«term_=_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 6 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9a315d6d34bb38e786c4d188420b196ead0ebc8e6ee65ed79c9f0df2d2e718d4 | 57cce2681516e008685076b5da5605d43614bd72d6f063000b11289a37772343 | c64369d959ca480a25a46dd734fff7c72f1807127fe892215e047979fcff0cf0 | 7dc82b98014b93898c7c6733ea67b679a0843da0af788a98c7408434bc05a85e |
cat-searcher/leandojo-benchmark-4-random | test | 3,995 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | letI : <a>CategoryTheory.Localization.Lifting</a> L₁ W₁ (Φ.functor ⋙ L₂) G := ⟨e.symm⟩ | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15852) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15852) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"letI","sourceEnd":3010,"sourceStart":3006,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":3011,"sourceStart":3011,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":3011,"sourceStart":3011,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"Localization.Lifting L₁ W₁ (Φ.functor ⋙ L₂) G","source_end":3067,"source_start":3013,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨e.symm⟩","source_end":3083,"source_start":3071,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 7 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | baa1f2dd1a7c2ac4fa77f083e2880f45f4180db08805b2ee134b5f4d90b3c8da | 7dc82b98014b93898c7c6733ea67b679a0843da0af788a98c7408434bc05a85e | 30a5ef5faa4e10cac6f5bf2d101f72b3030627c5a3f9a8bd5daa44bf6e40dcb5 | ab7a612702bc55e5d5527b88a71bd8cabef9e8c789aa3fc379b0562d269ff92d |
cat-searcher/leandojo-benchmark-4-random | test | 3,996 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let α : G' ≅ G := <a>CategoryTheory.Localization.liftNatIso</a> L₁ W₁ (L₁ ⋙ G') (Φ.functor ⋙ L₂) _ _ e'.symm | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15852) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15852) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"let","sourceEnd":3089,"sourceStart":3086,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"α","sourceEnd":3092,"sourceStart":3090,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":3094,"so... | [] | [{"source":"G' ≅ G","source_end":3103,"source_start":3095,"syntax_kind":"CategoryTheory.«term_≅_»"},{"source":"Localization.liftNatIso L₁ W₁ (L₁ ⋙ G') (Φ.functor ⋙ L₂) _ _ e'.symm","source_end":3188,"source_start":3107,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 8 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef8c74724bfc47ef5f7c7783f4e61f4c563ec4ca07ab91a487ade02561024f27 | ab7a612702bc55e5d5527b88a71bd8cabef9e8c789aa3fc379b0562d269ff92d | 174f6612c975aed4358332883f757d37fe775401acd765b5eb99d92e56ad8ef8 | 1f9466466284ea23f3818afda2fe013ed53fad8e55cf43a2de1a33d314c1ecf9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,997 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : e = e' ≪≫ <a>CategoryTheory.isoWhiskerLeft</a> _ α := by ext X dsimp [α] rw [<a>CategoryTheory.Localization.liftNatTrans_app</a>] erw [<a>CategoryTheory.Category.id_comp</a>] rw [<a>CategoryTheory.Iso.hom_inv_id_app_assoc</a>] rfl | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15852) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15852) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"have","sourceEnd":3195,"sourceStart":3191,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":3196,"sourceStart":3196,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":3196,"sourceStart":3196,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"e = e' ≪≫ isoWhiskerLeft _ α","source_end":3231,"source_start":3198,"syntax_kind":"«term_=_»"},{"source":"α","source_end":3261,"source_start":3259,"syntax_kind":"ident"},{"source":"Localization.liftNatTrans_app","source_end":3300,"source_start":3271,"syntax_kind":"ident"},{"source":"id_comp","source_end":33... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 9 | exact | true | 1 | 35 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b4640eea2c64a1ab98fc0ae8d4bc44df64539a0fb66801ce092003a516f39e62 | 1f9466466284ea23f3818afda2fe013ed53fad8e55cf43a2de1a33d314c1ecf9 | 6c39caeea1952d2ffa43628d3bce198ac0042471fe2a0e7f0189a769f9288ea1 | c9b44dcaae9ebf9ceee6095146229c41021b426123611eb7a036134fdcad3e5c |
cat-searcher/leandojo-benchmark-4-random | test | 3,998 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [this] | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15852) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15852) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simp","sourceEnd":3368,"sourceStart":3364,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3370,"sourceStart":3369,"tag":"atom"... | [] | [{"source":"this","source_end":3374,"source_start":3370,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 23 | exact | true | 1 | 36 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0018fce7de49c806aed79ef047532694148ee534d319af9013315fc611d849c4 | c9b44dcaae9ebf9ceee6095146229c41021b426123611eb7a036134fdcad3e5c | 2739860bec7952c6457e85d62dcc82ff2a268ce0336906f3574a07be169573c0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,999 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext X | C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : Category.{?... | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c CategoryTheory.Iso) ((:c CategoryTheory.Functor) (:fv _uniq.15852) (:fv _uniq.15875) (:fv _uniq.15864) (:fv _uniq.15891)) ((:c CategoryTheory.Functor.category) (:fv _uniq.15852) (:fv _uniq.15875) (:fv _uniq.15864) (:fv _uniq.15891)) ((:c CategoryTheory.Functor.comp) (:fv _uniq.15852) (:fv _uniq.15875) (:f... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Iso) (:arg :implicit-type 0 (:app (:c CategoryTheory.Functor) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV5)) (:arg :instance 3 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"ext","sourceEnd":3245,"sourceStart":3242,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"X","sourceEnd":3247,"sourceStart":3246,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"X","sourceEnd":3247,"sourceStart":3246,"tag":"nod... | [{"role":"fresh_name","source":"X","source_end":3247,"source_start":3246,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 11 | exact | true | 1 | 35 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c7f2eb5ea15ca2236140c4a060f1768cf21247070f06a13f638b12ead0923d9 | 52a58ec5da72af58d19ee8ea0932a2b3a940c3946641869d5a793e195afd6754 | b9fd42f0337fc2601ad1a536450feb3363c42f98fd2367a477dfb38b60f321cd | febae5999930130ff0d40f854eb6c76150c133eeda4481ffb24358304528b210 |
cat-searcher/leandojo-benchmark-4-random | test | 4,000 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [α] | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15852) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15852) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"dsimp","sourceEnd":3257,"sourceStart":3252,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3259,"sourceStart":3258,"tag":"atom... | [] | [{"source":"α","source_end":3261,"source_start":3259,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 12 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 462f43eff81eb92802c39afc6555ea567d69e4dcce253816ad4de1a13d41c28a | febae5999930130ff0d40f854eb6c76150c133eeda4481ffb24358304528b210 | 6d6b228de8a0800be6bb8aee3f68931f8aef481f46d5ca0bfe5b5efd76d7a39e | cf624f273eddd0c2e179984ce3ed32c80660cec1c358afa234113c270bcc19fe |
cat-searcher/leandojo-benchmark-4-random | test | 4,001 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>CategoryTheory.Localization.liftNatTrans_app</a>] | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":3269,"sourceStart":3267,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3271,"sourceStart":3270,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Local... | [] | [{"source":"Localization.liftNatTrans_app","source_end":3300,"source_start":3271,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 13 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6832cdb3ae1166eea08f652659323247fbc7eb5191d587071f5337cca6cbd7d8 | cf624f273eddd0c2e179984ce3ed32c80660cec1c358afa234113c270bcc19fe | 6af89a73e24c0e6359398a3acafb1f1feb2af32dc39d96c0fcc003342400dae4 | 89786e52e7fde147f47962a8713da19bdfce306683af51732d3b8d0590398f5c |
cat-searcher/leandojo-benchmark-4-random | test | 4,002 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>CategoryTheory.Category.id_comp</a>] | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"erw","sourceEnd":3309,"sourceStart":3306,"tag":"atom"},{"children":[{"source":"[","sourceEnd":3311,"sourceStart":3310,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Category.id_comp","semanticRole":"global","source":"id_comp... | [] | [{"source":"id_comp","source_end":3318,"source_start":3311,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 16 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a64f9b2044877a78eac55dba582ad4a9e0b3d406cc215e3d213eca14c8a0d189 | 89786e52e7fde147f47962a8713da19bdfce306683af51732d3b8d0590398f5c | 3ac79922607e88a86deac098f7d7986d44e3c7c924bcdf9bbf4063e32ce6f836 | 28bb988034d58f75f38a09db81c0f6c00a0138375b4de2c72b952e968738b52f |
cat-searcher/leandojo-benchmark-4-random | test | 4,003 | CategoryTheory.LocalizerMorphism.homMap_apply | Mathlib/CategoryTheory/Localization/HomEquiv.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>CategoryTheory.Iso.hom_inv_id_app_assoc</a>] | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | case w.w.h
C : Type u_1
C₁ : Type u_2
C₂ : Type u_3
C₃ : Type u_4
D₁ : Type u_5
D₂ : Type u_6
D₃ : Type u_7
inst✝⁹ : Category.{?u.15870, u_1} C
inst✝⁸ : Category.{u_10, u_2} C₁
inst✝⁷ : Category.{u_11, u_3} C₂
inst✝⁶ : Category.{?u.15882, u_4} C₃
inst✝⁵ : Category.{u_8, u_5} D₁
inst✝⁴ : Category.{u_9, u_6} D₂
inst✝³ : ... | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.15864) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15864) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.15864) (:fv _uniq.15891))) ((:c Prefunctor.obj) (:fv _uniq.15855) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.15855) ((:c CategoryTheory.Catego... | [{"name":"C","sexp":"(:sort (+ u_1 1))"},{"name":"C₁","sexp":"(:sort (+ u_2 1))"},{"name":"C₂","sexp":"(:sort (+ u_3 1))"},{"name":"C₃","sexp":"(:sort (+ u_4 1))"},{"name":"D₁","sexp":"(:sort (+ u_5 1))"},{"name":"D₂","sexp":"(:sort (+ u_6 1))"},{"name":"D₃","sexp":"(:sort (+ u_7 1))"},{"name":"inst✝⁹","sexp":"((:c Cat... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV5))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"name":"C₁","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"rw","sourceEnd":3326,"sourceStart":3324,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3328,"sourceStart":3327,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"CategoryTheory.Iso.h... | [] | [{"source":"Iso.hom_inv_id_app_assoc","source_end":3352,"source_start":3328,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.15849","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.15852","is_instance":false,"is_let":false,"user_name":"C₁"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 10 | 19 | exact | true | 1 | 36 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5b4ac931a66ab51df05d32c7dc7d060261fd06076d48ec89f70c37006d1df15c | 28bb988034d58f75f38a09db81c0f6c00a0138375b4de2c72b952e968738b52f | a182844abe27ec18960055196598f68b4429837377809bf391e911f2f305fb26 | e33ea32b5599e2387ef474c8d9651cd1dac7ceb5ff2224ea70492a8cd1d309b0 |
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