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cat-searcher/leandojo-benchmark-4-random | test | 3,084 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>le_antisymm</a> | ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ map (↑(opLinearEquiv R)) (M * N) = map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ map (↑(opLinearEquiv R)) (M * N) ≤ map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M
case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semi... | ((:c Eq) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.112892) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiri... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"apply","sourceEnd":10369,"sourceStart":10364,"tag":"atom"},{"name":"le_antisymm","semanticRole":"global","source":"le_antisymm","sourceEnd":10381,"sourceStart":10370,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply le_antisymm","sourceEnd":10381,"sourceStart":10364,"tag":"n... | [] | [{"source":"le_antisymm","source_end":10381,"source_start":10370,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6fa0e1cc77f7269bb572bf2862c42c57351c3c9e833eb6d4e79a073ff399e1b | acaa31782c93a6855fb7fbee9de95e3738f7aac6a16d8f9d9591e1f1e2a34a0a | 0abfddcb77ef175f592e63086534058d51fe8d6b63ac2fff9f69f045bc0962dc | 242a60c15dc83a85fa81d2d2be980ad59045bc7a0f1beaa5ac4edde0b83638c2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,085 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Submodule.map_le_iff_le_comap</a>] | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ map (↑(opLinearEquiv R)) (M * N) ≤ map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ M * N ≤ comap (↑(opLinearEquiv R)) (map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M) | ((:c LE.le) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.112892) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSem... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":10394,"sourceStart":10387,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10396,"sourceStart":10395,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Submodule.m... | [] | [{"source":"map_le_iff_le_comap","source_end":10415,"source_start":10396,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 9 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93e57548300f477d8f81a92d9d84a93aa1ad7bfc9e8788a442a1535825985cb1 | 74f2d91f5b4753fe31ffa28212c7b0e5e9464a8f5c13c6e8321d48d745d4df04 | 783190adba1758a89b720ba07f8027b0b39f75968c9731e3f332e67e688f0f0f | 2937e7a2aa036ce21113dc578d82056cedc6e613aff9d36e55cb5a026d4d824c |
cat-searcher/leandojo-benchmark-4-random | test | 3,086 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Submodule.mul_le</a>.2 fun m hm n hn => ?_ | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ M * N ≤ comap (↑(opLinearEquiv R)) (map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M) | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ m * n ∈ comap (↑(opLinearEquiv R)) (map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M) | ((:c LE.le) ((:c Submodule) (:fv _uniq.112887) (:fv _uniq.112892) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.112892) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.112... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV3))))) (:arg :instance 4 (:instance... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":10427,"sourceStart":10421,"tag":"atom"},{"children":[{"children":[{"name":"Submodule.mul_le","semanticRole":"global","source":"mul_le","sourceEnd":10434,"sourceStart":10428,"tag":"identifier"},{"source":".","sourceEnd":10435,"sourceStart":10434,"tag":"atom"},{"children":[{"so... | [] | [{"source":"mul_le.2 fun m hm n hn => ?_","source_end":10456,"source_start":10428,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 12 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a47762e5def00eb9ff76ac50a80ad48eb3711d5f6f715f3c8e2045df340593a | 2937e7a2aa036ce21113dc578d82056cedc6e613aff9d36e55cb5a026d4d824c | a548758426f7eac57bbc790596dba1649b3587ed3d42c5341264d4697b3fddc3 | 20a713c06a70b97fd865e9dbf441ff84352eded2bce0c79660b78aa353452bd6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,087 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Submodule.mem_comap</a>, <a>Submodule.map_equiv_eq_comap_symm</a>, <a>Submodule.map_equiv_eq_comap_symm</a>] | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ m * n ∈ comap (↑(opLinearEquiv R)) (map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M) | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ ↑(opLinearEquiv R) (m * n) ∈ comap (↑(opLinearEquiv R).symm) N * comap (↑(opLinearEquiv R).symm) M | ((:c Membership.mem) (:fv _uniq.112892) ((:c Submodule) (:fv _uniq.112887) (:fv _uniq.112892) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.112892) ((:c Semiring.toNonA... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":10463,"sourceStart":10461,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10465,"sourceStart":10464,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Submodule.mem_co... | [] | [{"source":"mem_comap","source_end":10474,"source_start":10465,"syntax_kind":"ident"},{"source":"map_equiv_eq_comap_symm","source_end":10499,"source_start":10476,"syntax_kind":"ident"},{"source":"map_equiv_eq_comap_symm","source_end":10524,"source_start":10501,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 13 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ba0210cfb79660a36a435f9b36ccafdb364340f86d0e2c60bf7dfde1f257daaf | 20a713c06a70b97fd865e9dbf441ff84352eded2bce0c79660b78aa353452bd6 | 2bf766a77cec61212129c47ad9de077aef60e88583d7caa3e92707b6adf2c81f | 8c071d71bbab16519af2e39c9e06098475550b9b51b2636da8bb2a9bff74f07e |
cat-searcher/leandojo-benchmark-4-random | test | 3,088 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | show <a>MulOpposite.op</a> n * <a>MulOpposite.op</a> m ∈ _ | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ ↑(opLinearEquiv R) (m * n) ∈ comap (↑(opLinearEquiv R).symm) N * comap (↑(opLinearEquiv R).symm) M | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ op n * op m ∈ comap (↑(opLinearEquiv R).symm) N * comap (↑(opLinearEquiv R).symm) M | ((:c Membership.mem) ((:c MulOpposite) (:fv _uniq.112892)) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.112892) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.11289... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"show","sourceEnd":10534,"sourceStart":10530,"tag":"atom"},{"children":[{"children":[{"children":[{"name":"MulOpposite.op","semanticRole":"global","source":"op","sourceEnd":10537,"sourceStart":10535,"tag":"identifier"},{"children":[{"contextIndex":17,"semanticRole":"local","source":"n","sourceEnd... | [] | [{"source":"op n * op m ∈ _","source_end":10552,"source_start":10535,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 18 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c63dd789c40879ed83022d34c08bb208e7e55dc07cf44288fba0887c8a3e4a9d | 8c071d71bbab16519af2e39c9e06098475550b9b51b2636da8bb2a9bff74f07e | 57c0d700a865d826f8eece4cb98aa7a83cadf23e08a4cc98f8706425224a24b6 | b266b41a27ec4cc0bb551ecd25467dcadcad12059e5b5d52ca0950bdd4c72198 |
cat-searcher/leandojo-benchmark-4-random | test | 3,089 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Submodule.mul_mem_mul</a> hn hm | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : m ∈ M
n : A
hn : n ∈ N
⊢ op n * op m ∈ comap (↑(opLinearEquiv R).symm) N * comap (↑(opLinearEquiv R).symm) M | ((:c Membership.mem) ((:c MulOpposite) (:fv _uniq.112892)) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.112892) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.11289... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":10562,"sourceStart":10557,"tag":"atom"},{"children":[{"name":"Submodule.mul_mem_mul","semanticRole":"global","source":"mul_mem_mul","sourceEnd":10574,"sourceStart":10563,"tag":"identifier"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"hn","sourceEnd":10577,... | [] | [{"source":"mul_mem_mul hn hm","source_end":10580,"source_start":10563,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 19 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b9df5a0f2d03bb069f37f0cf373fb0139530e2e881e9e3a9eb984441f044785c | b266b41a27ec4cc0bb551ecd25467dcadcad12059e5b5d52ca0950bdd4c72198 | f8cf6786e72cf33e4fe84903ad1bd89ad463580770ab25dc36d0ae7aa38647d0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,090 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Submodule.mul_le</a>.2 (<a>MulOpposite.rec'</a> fun m hm => <a>MulOpposite.rec'</a> fun n hn => ?_) | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m n : A
⊢ map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M ≤ map (↑(opLinearEquiv R)) (M * N) | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : op m ∈ map (↑(opLinearEquiv R)) N
n : A
hn : op n ∈ map (↑(opLinearEquiv R)) M
⊢ op m * op n ∈ map (↑(opLinearEquiv R)) (M * N) | ((:c LE.le) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c MulOpposite.instAddCommMonoid) (:fv _uniq.112892) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSem... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":10592,"sourceStart":10586,"tag":"atom"},{"children":[{"children":[{"name":"Submodule.mul_le","semanticRole":"global","source":"mul_le","sourceEnd":10599,"sourceStart":10593,"tag":"identifier"},{"source":".","sourceEnd":10600,"sourceStart":10599,"tag":"atom"},{"children":[{"so... | [] | [{"source":"mul_le.2 (MulOpposite.rec' fun m hm => MulOpposite.rec' fun n hn => ?_)","source_end":10664,"source_start":10593,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 24 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f13db95cf2159adda62b298a5d08e55c0dbf90c822c08f462cfc28521baa1af9 | f7d58af0f47d88a0f81efe0905d337ff1d9cd79aab42a6029f86462ebb4fc16a | 9a2488b7e3bf2d47477493e48caf5a674f99b833a915617c1cb43bb14358c0d1 | c7ee617df5467e33dbc89bbd7a79a5d48bf53527e99abc63691a6f754f07cc89 |
cat-searcher/leandojo-benchmark-4-random | test | 3,091 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Submodule.mem_map_equiv</a>] at hm hn ⊢ | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : op m ∈ map (↑(opLinearEquiv R)) N
n : A
hn : op n ∈ map (↑(opLinearEquiv R)) M
⊢ op m * op n ∈ map (↑(opLinearEquiv R)) (M * N) | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : (opLinearEquiv R).symm (op m) ∈ N
n : A
hn : (opLinearEquiv R).symm (op n) ∈ M
⊢ (opLinearEquiv R).symm (op m * op n) ∈ M * N | ((:c Membership.mem) ((:c MulOpposite) (:fv _uniq.112892)) ((:c Submodule) (:fv _uniq.112887) ((:c MulOpposite) (:fv _uniq.112892)) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) ((:c MulOpposite) (:fv _uniq.112892)) ((:c NonAssocSemiring.toNonUnital... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c MulOpposite) (:arg :explicit 0 (:fv FV3)))) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":10671,"sourceStart":10669,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10673,"sourceStart":10672,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Submodule.mem_ma... | [] | [{"source":"Submodule.mem_map_equiv","source_end":10696,"source_start":10673,"syntax_kind":"ident"},{"source":"hm","source_end":10703,"source_start":10701,"syntax_kind":"ident"},{"source":"hn","source_end":10706,"source_start":10704,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 25 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c57920933d64e08ecbc1b0ca71eec603fb88e5f7a8e167b3e6da91ebbad11f02 | c7ee617df5467e33dbc89bbd7a79a5d48bf53527e99abc63691a6f754f07cc89 | 96b603c792d15a156844b52cc742213272b505fe919bd2efdd71b7d5e797c45e | c7e8058155f074a6df55a6c449a5f50d79930933f5970d67293f8f0eec1547f9 |
cat-searcher/leandojo-benchmark-4-random | test | 3,092 | Submodule.map_op_mul | Mathlib/Algebra/Algebra/Operations.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Submodule.mul_mem_mul</a> hn hm | case a
ι : Sort uι
R : Type u
inst✝² : CommSemiring R
A : Type v
inst✝¹ : Semiring A
inst✝ : Algebra R A
S T : Set A
M N P Q : Submodule R A
m✝ n✝ m : A
hm : (opLinearEquiv R).symm (op m) ∈ N
n : A
hn : (opLinearEquiv R).symm (op n) ∈ M
⊢ (opLinearEquiv R).symm (op m * op n) ∈ M * N | ((:c Membership.mem) (:fv _uniq.112892) ((:c Submodule) (:fv _uniq.112887) (:fv _uniq.112892) ((:c CommSemiring.toSemiring) (:fv _uniq.112887) (:fv _uniq.112890)) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.112892) ((:c NonAssocSemiring.toNonUnitalNonAssocSemiring) (:fv _uniq.112892) ((:c Semiring.toNonA... | [{"name":"ι","sexp":"(:sort uι)"},{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝²","sexp":"((:c CommSemiring) (:fv _uniq.112887))"},{"name":"A","sexp":"(:sort (+ v 1))"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.112892))"},{"name":"inst✝","sexp":"((:c Algebra) (:fv _uniq.112887) (:fv _uniq.112892) (:fv _... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV3)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":10720,"sourceStart":10715,"tag":"atom"},{"children":[{"name":"Submodule.mul_mem_mul","semanticRole":"global","source":"mul_mem_mul","sourceEnd":10732,"sourceStart":10721,"tag":"identifier"},{"children":[{"contextIndex":18,"semanticRole":"local","source":"hn","sourceEnd":10735,... | [] | [{"source":"mul_mem_mul hn hm","source_end":10738,"source_start":10721,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.112885","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.112887","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":2,"internal... | 87 | 28 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37dcaec269697a44fc780bb0b6d5a891e1d4a6d0881e882bdcbbde599e51ef21 | c7e8058155f074a6df55a6c449a5f50d79930933f5970d67293f8f0eec1547f9 | f8cf6786e72cf33e4fe84903ad1bd89ad463580770ab25dc36d0ae7aa38647d0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,093 | CategoryTheory.Limits.biprod.isoProd_hom | Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext <;> simp [<a>CategoryTheory.Limits.biprod.isoProd</a>] | J : Type w
C : Type u
inst✝⁴ : Category.{v, u} C
inst✝³ : HasZeroMorphisms C
D : Type uD
inst✝² : Category.{uD', uD} D
inst✝¹ : HasZeroMorphisms D
P Q X Y : C
inst✝ : HasBinaryBiproduct X Y
⊢ (isoProd X Y).hom = prod.lift fst snd | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.509220) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.509220) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.509220) (:fv _uniq.509223))) ((:c CategoryTheory.Limits.biprod) (:fv _uniq.509220) (:fv _uniq.509223) (:fv _uniq.509238) (:fv _uniq.512454) (:fv _uniq.51... | [{"name":"J","sexp":"(:sort (+ w 1))"},{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝⁴","sexp":"((:c CategoryTheory.Category) (:fv _uniq.509220))"},{"name":"inst✝³","sexp":"((:c CategoryTheory.Limits.HasZeroMorphisms) (:fv _uniq.509220) (:fv _uniq.509223))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝²"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c CategoryTheory.Limits.biprod) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryThe... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.509218","is_instance":false,"is_let":false,"name":"J","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.509220","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"ext","sourceEnd":82501,"sourceStart":82498,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":82501,"sourceSt... | [] | [{"source":"biprod.isoProd","source_end":82526,"source_start":82512,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.509218","is_instance":false,"is_let":false,"user_name":"J"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.509220","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal... | 473 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5a7234ece8cbe8d668276ee0b129ce35ca409d54df0377127c57dcf98f4c3c44 | 426896e5822f164ab02ebf7330df11fcad381e8735f0969d24ea4667c67afa8b | f74d96d08a2f6be1e1883bb4c9a5b72d3369afdf5f6ac8e21bec27e6e3afc845 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,094 | CategoryTheory.Discrete.natIso_app | Mathlib/CategoryTheory/DiscreteCategory.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop_cat | α : Type u₁
C : Type u₂
inst✝ : Category.{v₂, u₂} C
I : Type u₁
F G : Discrete I ⥤ C
f : (i : Discrete I) → F.obj i ≅ G.obj i
i : Discrete I
⊢ (natIso f).app i = f i | ((:c Eq) ((:c CategoryTheory.Iso) (:fv _uniq.20943) (:fv _uniq.20946) ((:c Prefunctor.obj) ((:c CategoryTheory.Discrete) (:fv _uniq.21190)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c CategoryTheory.Discrete) (:fv _uniq.21190)) ((:c CategoryTheory.Category.toCategoryStruct) ((:c CategoryTheory.Discrete) (:fv _uni... | [{"name":"α","sexp":"(:sort (+ u₁ 1))"},{"name":"C","sexp":"(:sort (+ u₂ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.20943))"},{"name":"I","sexp":"(:sort (+ u₁ 1))"},{"name":"F","sexp":"((:c CategoryTheory.Functor) ((:c CategoryTheory.Discrete) (:fv _uniq.21190)) ((:c CategoryTheory.discreteC... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c CategoryTheory.Iso) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prefunctor.obj) (:arg :implicit-type 0 (:app (:c CategoryTheory.Discrete) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20941","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20943","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"aesop_cat","sourceEnd":9054,"sourceStart":9045,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"CategoryTheory.aesop_cat","source":"aesop_cat","sourceEnd":9054,"sourceStart":9045,"tag":"node"}],"kind":"null","source":"aesop_cat"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.20941","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.20943","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c2c68be3732a4d0902cc707722741e78d840c3066489fdbb60a3133e7f9f59c | 52f784aef0ae31813664d704750f78c764041c56c19099c146add5d425d0f6ff | 5121c016cd001463f39ee8c4444b84a277d6f4c7f9897d838d825f1c14f96636 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,095 | Part.inv_mem_inv | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Part.inv_def</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inv α
a : Part α
ma : α
ha : ma ∈ a
⊢ ma⁻¹ ∈ a⁻¹ | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inv α
a : Part α
ma : α
ha : ma ∈ a
⊢ ∃ a_1 ∈ a, a_1⁻¹ = ma⁻¹ | ((:c Membership.mem) (:fv _uniq.38640) ((:c Part) (:fv _uniq.38640)) ((:c Part.instMembership) (:fv _uniq.38640)) ((:c Inv.inv) (:fv _uniq.38640) (:fv _uniq.38740) (:fv _uniq.38742)) ((:c Inv.inv) ((:c Part) (:fv _uniq.38640)) ((:c Part.instInv) (:fv _uniq.38640) (:fv _uniq.38740)) (:fv _uniq.38741))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Inv) (:fv _uniq.38640))"},{"name":"a","sexp":"((:c Part) (:fv _uniq.38640))"},{"name":"ma","sexp":"(:fv _uniq.38640)"},{"name":"ha","sexp":"((:c Membership.mem) (:fv _uni... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Part) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 3 (:app (:c Inv.inv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38640","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38643","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":27975,"sourceStart":27971,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":27977,"sourceStart":27976,"tag":"a... | [] | [{"source":"inv_def","source_end":27984,"source_start":27977,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38640","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38643","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 258 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8220ee90bd72350f7b57d716d4e46ed9ba31fd995b3e8320a1e78ba2631750ac | 8aec7970249f700608cf53ed774059cc852a40603e1596f4022d14a1ab92a361 | 21e88490cc2c7462a8cb6b1c3ea9ad4d96a52bf2baf4e459230d3d086e3ab44d | 79ee9d709da5c5d2efaf08b5faa1de05e71ba111d91e6bb83e469310d50cb792 |
cat-searcher/leandojo-benchmark-4-random | test | 3,096 | Part.inv_mem_inv | Mathlib/Data/Part.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | aesop | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Inv α
a : Part α
ma : α
ha : ma ∈ a
⊢ ∃ a_1 ∈ a, a_1⁻¹ = ma⁻¹ | ((:c Exists) (:fv _uniq.38640) (:lambda a (:fv _uniq.38640) ((:c And) ((:c Membership.mem) (:fv _uniq.38640) ((:c Part) (:fv _uniq.38640)) ((:c Part.instMembership) (:fv _uniq.38640)) 0 (:fv _uniq.38741)) ((:c Eq) (:fv _uniq.38640) ((:c Inv.inv) (:fv _uniq.38640) (:fv _uniq.38740) 0) ((:c Inv.inv) (:fv _uniq.38640) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Inv) (:fv _uniq.38640))"},{"name":"a","sexp":"((:c Part) (:fv _uniq.38640))"},{"name":"ma","sexp":"(:fv _uniq.38640)"},{"name":"ha","sexp":"((:c Membership.mem) (:fv _uni... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Part) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38640","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38643","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"aesop","sourceEnd":27992,"sourceStart":27987,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Aesop.Frontend.Parser.aesopTactic","source":"aesop","sourceEnd":27992,"sourceStart":27987,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38640","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38643","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 258 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 29e2180b23508123154031a078c3725e0b477fe23d15bad6a8ae7b01a70c65c5 | 79ee9d709da5c5d2efaf08b5faa1de05e71ba111d91e6bb83e469310d50cb792 | bf61abd9c8c94e02103733c96be27852844483acbf580158f224257e620356a8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,097 | Int.fract_sub_nat | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Int.fract</a>] | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
n : ℕ
⊢ fract (a - ↑n) = fract a | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
n : ℕ
⊢ a - ↑n - ↑⌊a - ↑n⌋ = fract a | ((:c Eq) (:fv _uniq.160471) ((:c Int.fract) (:fv _uniq.160471) (:fv _uniq.160477) (:fv _uniq.160485) ((:c HSub.hSub) (:fv _uniq.160471) (:fv _uniq.160471) (:fv _uniq.160471) ((:c instHSub) (:fv _uniq.160471) ((:c Ring.toSub) (:fv _uniq.160471) ((:c StrictOrderedRing.toRing) (:fv _uniq.160471) ((:c LinearOrderedRing.toS... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.160471))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.160471) (:fv _uniq.160477))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Int.fract) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedRing) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 2 (:instance-of (:app (:c FloorRing) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.160468","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.160471","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":33443,"sourceStart":33441,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":33445,"sourceStart":33444,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Int.fract","sema... | [] | [{"source":"fract","source_end":33450,"source_start":33445,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.160468","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.160471","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 301 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3373b96c047bdafeaea223f34026f3eaa57de6fe8357873759d871d67f221d75 | 0a433b0ae2fba6eb5e15c40acbcbb002e9a40f0b07075007c564d65866339059 | acb829837a19b3bd7081a1a893c6cb2e1fe3b8ebece31751e7e8e1ca85fe5c9b | 1f1e78f3404e9a7b920d177b62fac3f9dee12b4ebbf1f52b1ff186977435c151 |
cat-searcher/leandojo-benchmark-4-random | test | 3,098 | Int.fract_sub_nat | Mathlib/Algebra/Order/Floor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | F : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedRing α
inst✝ : FloorRing α
z : ℤ
a✝ a : α
n : ℕ
⊢ a - ↑n - ↑⌊a - ↑n⌋ = fract a | ((:c Eq) (:fv _uniq.160471) ((:c HSub.hSub) (:fv _uniq.160471) (:fv _uniq.160471) (:fv _uniq.160471) ((:c instHSub) (:fv _uniq.160471) ((:c Ring.toSub) (:fv _uniq.160471) ((:c StrictOrderedRing.toRing) (:fv _uniq.160471) ((:c LinearOrderedRing.toStrictOrderedRing) (:fv _uniq.160471) (:fv _uniq.160477))))) ((:c HSub.hSu... | [{"name":"F","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedRing) (:fv _uniq.160471))"},{"name":"inst✝","sexp":"((:c FloorRing) (:fv _uniq.160471) (:fv _uniq.160477))"},{"name":"z","sexp":"(:c Int)"},{"name":"a✝","se... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HSub) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.160468","is_instance":false,"is_let":false,"name":"F","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.160471","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"simp","sourceEnd":33458,"sourceStart":33454,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.160468","is_instance":false,"is_let":false,"user_name":"F"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.160471","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 301 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af9384888aacee660955217697437a6fa75e9064b37d2d3290ec4b545880ca84 | 1f1e78f3404e9a7b920d177b62fac3f9dee12b4ebbf1f52b1ff186977435c151 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,099 | AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_uniq | Mathlib/Geometry/RingedSpace/OpenImmersion.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>CategoryTheory.cancel_mono</a> f, hl, <a>AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.lift_fac</a>] | C : Type u
inst✝ : Category.{v, u} C
X Y Z : PresheafedSpace C
f : X ⟶ Z
hf : IsOpenImmersion f
g : Y ⟶ Z
s : PullbackCone f g
H : Set.range ⇑g.base ⊆ Set.range ⇑f.base
l : Y ⟶ X
hl : l ≫ f = g
⊢ l = lift f g H | ((:c Eq) ((:c Quiver.Hom) ((:c AlgebraicGeometry.PresheafedSpace) (:fv _uniq.251953) (:fv _uniq.251956)) ((:c CategoryTheory.CategoryStruct.toQuiver) ((:c AlgebraicGeometry.PresheafedSpace) (:fv _uniq.251953) (:fv _uniq.251956)) ((:c CategoryTheory.Category.toCategoryStruct) ((:c AlgebraicGeometry.PresheafedSpace) (:fv... | [{"name":"C","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.251953))"},{"name":"X","sexp":"((:c AlgebraicGeometry.PresheafedSpace) (:fv _uniq.251953) (:fv _uniq.251956))"},{"name":"Y","sexp":"((:c AlgebraicGeometry.PresheafedSpace) (:fv _uniq.251953) (:fv _uniq.251956))"},{"n... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:app (:c AlgebraicGeometry.PresheafedSpace) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.Category) (:arg :explicit 0 (:fv FV0))))))) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251953","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.251956","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Categor... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":28495,"sourceStart":28493,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":28497,"sourceStart":28496,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"cancel_mono f","source_end":28514,"source_start":28501,"syntax_kind":"Lean.Parser.Term.app"},{"source":"hl","source_end":28518,"source_start":28516,"syntax_kind":"ident"},{"source":"lift_fac","source_end":28528,"source_start":28520,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.251953","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.251956","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":2,"inter... | 97 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a6ebcef5194a5cabb20ba67a829c5087c73a909fb32998e1d5bcffd83a811c0d | 8a5e7e55c230082f26a8058147d1f542287b7154898344080f625686120c2b57 | 35b49d17d42f1bce0a83342f2bc6461bc91b58f3090143aef0e66bce8bd6dcb6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,100 | Filter.Tendsto.of_tendsto_comp | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Filter.tendsto_iff_comap</a>] at hfg ⊢ | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l : Filter α
f : α → β
g : β → γ
a : Filter α
b : Filter β
c : Filter γ
hfg : Tendsto (g ∘ f) a c
hg : comap g c ≤ b
⊢ Tendsto f a b | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l : Filter α
f : α → β
g : β → γ
a : Filter α
b : Filter β
c : Filter γ
hfg : a ≤ comap (g ∘ f) c
hg : comap g c ≤ b
⊢ a ≤ comap f b | ((:c Filter.Tendsto) (:fv _uniq.227108) (:fv _uniq.227110) (:fv _uniq.227217) (:fv _uniq.227219) (:fv _uniq.227220)) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.227108))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.227108) (:fv _uniq.227110))"},{"name... | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:fv FV7)) (:arg :explicit 3 (:fv FV9)) (:arg :explicit 4 (:fv FV10))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":142945,"sourceStart":142943,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":142947,"sourceStart":142946,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Filter.tends... | [] | [{"source":"tendsto_iff_comap","source_end":142964,"source_start":142947,"syntax_kind":"ident"},{"source":"hfg","source_end":142972,"source_start":142969,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,084 | 4 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 30752f75bf5bb3246ec9d9e7c57721bcf7e04cf329278160b481b8a112719f51 | 7605fb0d93a6204dfffb3620175fec6c209fce5f64175f4ebb5fd56146068d9e | 0c32a058966e7b7170d52682516023b9b7a38a49014f95ba524825f7f967da2c | 2a1039a02f94febf3e0f2818641b556850998e54afc1bf1937865ae1dfec2414 |
cat-searcher/leandojo-benchmark-4-random | test | 3,101 | Filter.Tendsto.of_tendsto_comp | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc a ≤ <a>Filter.comap</a> (g ∘ f) c := hfg _ ≤ <a>Filter.comap</a> f b := by simpa [<a>Filter.comap_comap</a>] using <a>Filter.comap_mono</a> hg | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l : Filter α
f : α → β
g : β → γ
a : Filter α
b : Filter β
c : Filter γ
hfg : a ≤ comap (g ∘ f) c
hg : comap g c ≤ b
⊢ a ≤ comap f b | ((:c LE.le) ((:c Filter) (:fv _uniq.227108)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.227108)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.227108)) ((:c Filter.instPartialOrder) (:fv _uniq.227108)))) (:fv _uniq.227219) ((:c Filter.comap) (:fv _uniq.227108) (:fv _uniq.227110) (:fv _uniq.227217) (:fv _uniq.2... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.227108))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.227108) (:fv _uniq.227110))"},{"name... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:app (:c Filter.comap) (:arg :implicit-type 0 (:fv FV0)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"calc","sourceEnd":142983,"sourceStart":142979,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":9,"semanticRole":"local","source":"a","sourceEnd":142989,"sourceStart":142988,"tag":"identifier"},{"source":"≤","sourceEnd":142993,"sourceStart":142990,"tag":"atom"},{"children":[{"... | [] | [{"source":"a ≤ comap (g ∘ f) c","source_end":143011,"source_start":142988,"syntax_kind":"«term_≤_»"},{"source":"hfg","source_end":143018,"source_start":143015,"syntax_kind":"ident"},{"source":"_","source_end":143024,"source_start":143023,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"comap f b","source_end":143038,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,084 | 7 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e2e1b1b71a753e3c643102f566b2b4eac3cb45f8e7bf443b65cc1440d620652 | 2a1039a02f94febf3e0f2818641b556850998e54afc1bf1937865ae1dfec2414 | c41612676b0304ff10af8c52e4af03166aa87c449236766b6ac692cfdb5e4460 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,102 | Filter.Tendsto.of_tendsto_comp | Mathlib/Order/Filter/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [<a>Filter.comap_comap</a>] using <a>Filter.comap_mono</a> hg | α : Type u
β : Type v
γ : Type w
δ : Type u_1
ι : Sort x
l : Filter α
f : α → β
g : β → γ
a : Filter α
b : Filter β
c : Filter γ
hfg : a ≤ comap (g ∘ f) c
hg : comap g c ≤ b
⊢ comap (g ∘ f) c ≤ comap f b | ((:c LE.le) ((:c Filter) (:fv _uniq.227108)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.227108)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.227108)) ((:c Filter.instPartialOrder) (:fv _uniq.227108)))) ((:c Filter.comap) (:fv _uniq.227108) (:fv _uniq.227112) ((:c Function.comp) (:fv _uniq.227108) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort x)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.227108))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.227108) (:fv _uniq.227110))"},{"name... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Filter.comap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":143050,"sourceStart":143045,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [{"source":"comap_comap","source_end":143063,"source_start":143052,"syntax_kind":"ident"},{"source":"comap_mono hg","source_end":143084,"source_start":143071,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.227108","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.227110","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 1,084 | 10 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ed17dbfefae77f5f3f6c3185c327accc147e2dcb29dc3d26cfe55a3f40c5921 | 63b675a0bc109f6079a5be36058ceb3f8c3ecd0275e90e1e67cdbf9086da8d54 | bac7a153fa0520f20420c71a07bf28e5f0c144ce01dcaa08a0b8365e4605e329 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,103 | Polynomial.eval_comp | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | induction p using <a>Polynomial.induction_on'</a> with | h_add r s hr hs => simp [<a>Polynomial.add_comp</a>, hr, hs] | h_monomial n a => simp | R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝¹ : CommSemiring R
p q : R[X]
x : R
inst✝ : CommSemiring S
f : R →+* S
⊢ eval x (p.comp q) = eval (eval x q) p | ((:c Eq) (:fv _uniq.246253) ((:c Polynomial.eval) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) (:fv _uniq.246437) ((:c Polynomial.comp) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) (:fv _uniq.246431) (:fv _uniq.246435))) ((:c Polynomi... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.246253)"},{"name":"b","sexp":"(:fv _uniq.246253)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"induction","sourceEnd":42129,"sourceStart":42120,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"p","sourceEnd":42131,"sourceStart":42130,"tag":"identifier"}],"kind":"null","source":"p","sourceEnd":42131,"sourceStart":42130,"ta... | [] | [{"source":"p","source_end":42131,"source_start":42130,"syntax_kind":"ident"},{"source":"Polynomial.induction_on'","source_end":42162,"source_start":42138,"syntax_kind":"ident"},{"source":"add_comp","source_end":42209,"source_start":42201,"syntax_kind":"ident"},{"source":"hr","source_end":42213,"source_start":42211,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 378 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37bd042fbe996ce33b37c54fef5f81a7b36b600955c4bee4496bdbd9842a37ec | af20b3ffee8516bbfbc4d161028e9d06bf430aba6c85862a5540415addc8ee05 | e664a5f7b47b7fd35f8be615ce00ec6b446e03b416a4d0de00c229a6064f19e3 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,104 | Polynomial.eval_comp | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Polynomial.add_comp</a>, hr, hs] | case h_add
R : Type u
S : Type v
T : Type w
ι : Type y
a b : R
m n : ℕ
inst✝¹ : CommSemiring R
p q : R[X]
x : R
inst✝ : CommSemiring S
f : R →+* S
r s : R[X]
hr : eval x (r.comp q) = eval (eval x q) r
hs : eval x (s.comp q) = eval (eval x q) s
⊢ eval x ((r + s).comp q) = eval (eval x q) (r + s) | ((:c Eq) (:fv _uniq.246253) ((:c Polynomial.eval) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) (:fv _uniq.246437) ((:c Polynomial.comp) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) ((:c HAdd.hAdd) ((:c Polynomial) (:fv _uniq.246253) (... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a","sexp":"(:fv _uniq.246253)"},{"name":"b","sexp":"(:fv _uniq.246253)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":42199,"sourceStart":42195,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"add_comp","source_end":42209,"source_start":42201,"syntax_kind":"ident"},{"source":"hr","source_end":42213,"source_start":42211,"syntax_kind":"ident"},{"source":"hs","source_end":42217,"source_start":42215,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 378 | 7 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2fda0664ee5ea24d97547fac4631110a372a53b4371ef156d2fe393909bf8587 | 28ff2e0f972b5c6245dcd847575073b25dbffc9c14f79acf77f8271436913283 | e7921bf5cf50011925e48aead586685d62f0e8eed6a5bbc450238caf39a81dd4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,105 | Polynomial.eval_comp | Mathlib/Algebra/Polynomial/Eval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h_monomial
R : Type u
S : Type v
T : Type w
ι : Type y
a✝ b : R
m n✝ : ℕ
inst✝¹ : CommSemiring R
p q : R[X]
x : R
inst✝ : CommSemiring S
f : R →+* S
n : ℕ
a : R
⊢ eval x (((monomial n) a).comp q) = eval (eval x q) ((monomial n) a) | ((:c Eq) (:fv _uniq.246253) ((:c Polynomial.eval) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) (:fv _uniq.246437) ((:c Polynomial.comp) (:fv _uniq.246253) ((:c CommSemiring.toSemiring) (:fv _uniq.246253) (:fv _uniq.246270)) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.246253)... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"T","sexp":"(:sort (+ w 1))"},{"name":"ι","sexp":"(:sort (+ y 1))"},{"name":"a✝","sexp":"(:fv _uniq.246253)"},{"name":"b","sexp":"(:fv _uniq.246253)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n✝","sexp":"(:c Nat)"},{"name":"inst✝¹","sex... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Polynomial.eval) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV11)) (:arg :explicit 3 (:app (:c Polynomial.comp) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":42249,"sourceStart":42245,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.246253","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.246255","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 378 | 11 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4e01bc3157475b0f01edc1d33677780f0779e5fa77312fab160cb3ad5df37dab | d6c207528869b80f9514c8074f23dcb19ac041334aba7c434a12fa2751c5cf89 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,106 | LinearMap.adjoint_adjoint | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext v | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁹ : RCLike 𝕜
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedAddCommGroup G
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : InnerProductSpace 𝕜 F
inst✝³ : InnerProductSpace 𝕜 G
inst✝² : FiniteDimensional 𝕜 E
inst✝¹ : FiniteDimensional 𝕜 ... | case h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁹ : RCLike 𝕜
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedAddCommGroup G
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : InnerProductSpace 𝕜 F
inst✝³ : InnerProductSpace 𝕜 G
inst✝² : FiniteDimensional 𝕜 E
inst✝¹ : FiniteDimensio... | ((:c Eq) ((:c LinearMap) (:fv _uniq.928434) (:fv _uniq.928434) ((:c DivisionSemiring.toSemiring) (:fv _uniq.928434) ((:c Semifield.toDivisionSemiring) (:fv _uniq.928434) ((:c Field.toSemifield) (:fv _uniq.928434) ((:c NormedField.toField) (:fv _uniq.928434) ((:c DenselyNormedField.toNormedField) (:fv _uniq.928434) ((:c... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.928434))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.928437))"},{"name":"inst✝⁷","sexp":"(... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 4 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext","sourceEnd":18187,"sourceStart":18184,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"v","sourceEnd":18189,"sourceStart":18188,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"v","sourceEnd":18189,"sourceStart":18188,"tag... | [{"role":"fresh_name","source":"v","source_end":18189,"source_start":18188,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 111 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7058a0fdbd8500d70fad6c5bc0e7c1c4c18967a1d0766c6e912b815f532aa0e9 | 994bff2cfb11cc0be400f3ca4cef83c57d68aaa04228941b300f2ae90524b61f | 9c1b09e55060ad790220fd901d8783ce0b42139a60f02e92db4aafbab81eb8d7 | e999944babafeefd1e1e466fce90a1d69b053dd5c4586d075b9d6d17ada3aef5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,107 | LinearMap.adjoint_adjoint | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>ext_inner_left</a> 𝕜 fun w => ?_ | case h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁹ : RCLike 𝕜
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedAddCommGroup G
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : InnerProductSpace 𝕜 F
inst✝³ : InnerProductSpace 𝕜 G
inst✝² : FiniteDimensional 𝕜 E
inst✝¹ : FiniteDimensio... | case h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁹ : RCLike 𝕜
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedAddCommGroup G
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : InnerProductSpace 𝕜 F
inst✝³ : InnerProductSpace 𝕜 G
inst✝² : FiniteDimensional 𝕜 E
inst✝¹ : FiniteDimensio... | ((:c Eq) (:fv _uniq.928440) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.928434) (:fv _uniq.928434) ((:c DivisionSemiring.toSemiring) (:fv _uniq.928434) ((:c Semifield.toDivisionSemiring) (:fv _uniq.928434) ((:c Field.toSemifield) (:fv _uniq.928434) ((:c NormedField.toField) (:fv _uniq.928434) ((:c DenselyNormedField.... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.928434))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.928437))"},{"name":"inst✝⁷","sexp":"(... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":18198,"sourceStart":18192,"tag":"atom"},{"children":[{"name":"ext_inner_left","semanticRole":"global","source":"ext_inner_left","sourceEnd":18213,"sourceStart":18199,"tag":"identifier"},{"children":[{"contextIndex":0,"semanticRole":"local","source":"𝕜","sourceEnd":18218,"sou... | [] | [{"source":"ext_inner_left 𝕜 fun w => ?_","source_end":18230,"source_start":18199,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 111 | 5 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42f9237eb754c7e7216acefd107d8bc9cb4d5b33e420249e22ce3fc55a962335 | e999944babafeefd1e1e466fce90a1d69b053dd5c4586d075b9d6d17ada3aef5 | 7cc9322e216b2b38a6de664dac056007e6398666a4e86202a31c4db4df721ce2 | b95718a0592d415df59595a32af6978fc26a3bf0db37707569a6f9a65736c81c |
cat-searcher/leandojo-benchmark-4-random | test | 3,108 | LinearMap.adjoint_adjoint | Mathlib/Analysis/InnerProductSpace/Adjoint.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>LinearMap.adjoint_inner_right</a>, <a>LinearMap.adjoint_inner_left</a>] | case h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁹ : RCLike 𝕜
inst✝⁸ : NormedAddCommGroup E
inst✝⁷ : NormedAddCommGroup F
inst✝⁶ : NormedAddCommGroup G
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : InnerProductSpace 𝕜 F
inst✝³ : InnerProductSpace 𝕜 G
inst✝² : FiniteDimensional 𝕜 E
inst✝¹ : FiniteDimensio... | ((:c Eq) (:fv _uniq.928434) ((:c Inner.inner) (:fv _uniq.928434) (:fv _uniq.928440) ((:c InnerProductSpace.toInner) (:fv _uniq.928434) (:fv _uniq.928440) (:fv _uniq.928446) (:fv _uniq.928452) (:fv _uniq.928481)) (:fv _uniq.935306) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.928434) (:fv _uniq.928434) ((:c DivisionSem... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"G","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁹","sexp":"((:c RCLike) (:fv _uniq.928434))"},{"name":"inst✝⁸","sexp":"((:c NormedAddCommGroup) (:fv _uniq.928437))"},{"name":"inst✝⁷","sexp":"(... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Inner.inner) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Inner) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2))))) (:arg :explicit 3 (:fv FV17)) (:arg :explicit 4 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":18235,"sourceStart":18233,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":18237,"sourceStart":18236,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"LinearMap.adjoin... | [] | [{"source":"adjoint_inner_right","source_end":18256,"source_start":18237,"syntax_kind":"ident"},{"source":"adjoint_inner_left","source_end":18276,"source_start":18258,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.928434","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.928437","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 111 | 6 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 69d56ec345902f369f1068008da42a3972247ddaa1eeabf2d3be246c92a16703 | b95718a0592d415df59595a32af6978fc26a3bf0db37707569a6f9a65736c81c | 730362ce527e00bbb5cfc09f5d98e42b84177e57b3ddefacec976e5f55d60e5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,109 | contDiff_top_iff_deriv | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>contDiffOn_univ</a>, ← <a>differentiableOn_univ</a>, ← <a>derivWithin_univ</a>] | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | ((:c Iff) ((:c ContDiff) (:fv _uniq.2093016) (:fv _uniq.2093019) (:fv _uniq.2093016) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.2093016) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.2093016) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.2093016) ((:c NormedField.toNormedComm... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.2093016))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2093021))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.2093016) (:fv _uniq.2093021) ((:c... | (:app (:c Iff) (:arg :explicit 0 (:app (:c ContDiff) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093016","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2093019","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"simp","sourceEnd":111194,"sourceStart":111190,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":111199,"sourceStart":111195,"tag":"atom"}],"kind":"null","source":"only","sourceEnd"... | [] | [{"source":"contDiffOn_univ","source_end":111220,"source_start":111205,"syntax_kind":"ident"},{"source":"differentiableOn_univ","source_end":111247,"source_start":111226,"syntax_kind":"ident"},{"source":"derivWithin_univ","source_end":111269,"source_start":111253,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093016","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2093019","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"... | 520 | 4 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9832ee5d994b19d33008f160c999f8f3c7482393175328048f053b96c5485a4f | 435f4b248dcfa5b0522643ae7267d86d2645c70e1deebef3b4aa66544f2297dd | b9ed6aa4249a7e7983ce09189e3643f97bdb04db099bc7454d36f6c2af3ca343 | 5ec66d1db41309c8810df126cd093a10f0f1d3a590b6d8c479147c79a37f51ff |
cat-searcher/leandojo-benchmark-4-random | test | 3,110 | contDiff_top_iff_deriv | Mathlib/Analysis/Calculus/ContDiff/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>contDiffOn_top_iff_derivWithin</a> <a>uniqueDiffOn_univ</a>] | 𝕜 : Type u_1
inst✝¹⁰ : NontriviallyNormedField 𝕜
D : Type uD
inst✝⁹ : NormedAddCommGroup D
inst✝⁸ : NormedSpace 𝕜 D
E : Type uE
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type uF
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type uG
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜... | ((:c Iff) ((:c ContDiffOn) (:fv _uniq.2093016) (:fv _uniq.2093019) (:fv _uniq.2093016) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.2093016) ((:c NonUnitalNormedCommRing.toNonUnitalNormedRing) (:fv _uniq.2093016) ((:c NormedCommRing.toNonUnitalNormedCommRing) (:fv _uniq.2093016) ((:c NormedField.toNormedCo... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.2093016))"},{"name":"D","sexp":"(:sort (+ uD 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.2093021))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.2093016) (:fv _uniq.2093021) ((:c... | (:app (:c Iff) (:arg :explicit 0 (:app (:c ContDiffOn) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093016","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2093019","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNorme... | {"children":[{"source":"rw","sourceEnd":111275,"sourceStart":111273,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":111277,"sourceStart":111276,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":... | [] | [{"source":"contDiffOn_top_iff_derivWithin uniqueDiffOn_univ","source_end":111325,"source_start":111277,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093016","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.2093019","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"... | 520 | 5 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e01253cc963d94f66a6355beb57e98407b3cbaf41754f6047c0d3d291fe06e4 | 5ec66d1db41309c8810df126cd093a10f0f1d3a590b6d8c479147c79a37f51ff | 87365a58af5b8fbd2f2241485062344e9ef83f3e83b1f0066a054f3698e58353 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,111 | WeierstrassCurve.ΨSq_odd | Mathlib/AlgebraicGeometry/EllipticCurve/DivisionPolynomial/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | erw [<a>WeierstrassCurve.ΨSq_ofNat</a>, <a>WeierstrassCurve.preΨ'_odd</a>, <a>if_neg</a> (m + 2).<a>Nat.not_even_two_mul_add_one</a>, <a>mul_one</a>] | R : Type r
S : Type s
inst✝¹ : CommRing R
inst✝ : CommRing S
W : WeierstrassCurve R
m : ℕ
⊢ W.ΨSq (2 * (↑m + 2) + 1) =
((W.preΨ' (m + 4) * W.preΨ' (m + 2) ^ 3 * if Even m then W.Ψ₂Sq ^ 2 else 1) -
W.preΨ' (m + 1) * W.preΨ' (m + 3) ^ 3 * if Even m then 1 else W.Ψ₂Sq ^ 2) ^
2 | ((:c Eq) ((:c Polynomial) (:fv _uniq.84383) ((:c CommSemiring.toSemiring) (:fv _uniq.84383) ((:c CommRing.toCommSemiring) (:fv _uniq.84383) (:fv _uniq.84388)))) ((:c WeierstrassCurve.ΨSq) (:fv _uniq.84383) (:fv _uniq.84388) (:fv _uniq.84394) ((:c HAdd.hAdd) (:c Int) (:c Int) (:c Int) ((:c instHAdd) (:c Int) (:c Int.ins... | [{"name":"R","sexp":"(:sort (+ r 1))"},{"name":"S","sexp":"(:sort (+ s 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.84383))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.84385))"},{"name":"W","sexp":"((:c WeierstrassCurve) (:fv _uniq.84383))"},{"name":"m","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 1 (:app (:c WeierstrassCurve.ΨSq) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84383","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84385","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"children":[{"children":[{"children":[{"source":"erw","sourceEnd":10789,"sourceStart":10786,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10791,"sourceStart":10790,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WeierstrassCurve.ΨSq_ofNat","se... | [] | [{"source":"ΨSq_ofNat","source_end":10801,"source_start":10791,"syntax_kind":"ident"},{"source":"preΨ'_odd","source_end":10813,"source_start":10803,"syntax_kind":"ident"},{"source":"if_neg (m + 2).not_even_two_mul_add_one","source_end":10854,"source_start":10815,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_one"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.84383","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.84385","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 51 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07ac0571b4e8641ce288d4c53e4ba83fc151dd92beaf49e63e37767baccc3fae | 0ca960bb6e8399ab75ec54d56219be522c909f03215d0f2d20e75117e21b71b9 | 92dc7329b9425d338aff9ac54087d86bdcef7c878993c5a1dca0c7cece869144 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,112 | ProbabilityTheory.IdentDistrib.evariance_eq | Mathlib/Probability/IdentDistrib.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert (h.sub_const (∫ x, f x ∂μ)).nnnorm.coe_nnreal_ennreal.sq.lintegral_eq | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
μ : Measure α
ν : Measure β
f✝ : α → γ
g✝ : β → γ
f : α → ℝ
g : β → ℝ
h : IdentDistrib f g μ ν
⊢ evariance f μ = evariance g ν | case h.e'_3
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
μ : Measure α
ν : Measure β
f✝ : α → γ
g✝ : β → γ
f : α → ℝ
g : β → ℝ
h : IdentDistrib f g μ ν
⊢ evariance g ν = ∫⁻ (x : β), ↑‖g x - ∫ (x : α), f x ∂... | ((:c Eq) (:c ENNReal) ((:c ProbabilityTheory.evariance) (:fv _uniq.28693) (:fv _uniq.28705) (:fv _uniq.28891) (:fv _uniq.28723)) ((:c ProbabilityTheory.evariance) (:fv _uniq.28696) (:fv _uniq.28708) (:fv _uniq.28892) (:fv _uniq.28732))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c MeasurableSpace) (:fv _uniq.28693))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.28696))"},{"name":"inst✝¹","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ProbabilityTheory.evariance) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV13)) (:arg :explicit 3 (:fv FV8)))) (:arg :explicit 2 (:app (:c ProbabilityTheory.evariance) (:arg :implicit-type 0 (:fv FV1)) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"convert","sourceEnd":16287,"sourceStart":16280,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"(","sourceEnd":16289,"sourceStart":16288,"tag":"atom"},{"children":[{"source":"h.sub_con... | [] | [{"source":"(h.sub_const (∫ x, f x ∂μ)).nnnorm.coe_nnreal_ennreal.sq.lintegral_eq","source_end":16362,"source_start":16288,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66410ecc3ecf4e175015e664ee050a157ad968af41ecb4b3791355a02c7f5753 | 3d6d0c06bc25cfc5116340117ee482ebce3482aa7661781aa627cc50803f8b28 | cef70e8b9f7dd9ee6b0f5e419005ab7f81b9cae7f5f47dd31089a4eb2492355f | a03ba159dc3c9923e726a64e5c998adbf126e1cff6f4641fe58071c995f14a56 |
cat-searcher/leandojo-benchmark-4-random | test | 3,113 | ProbabilityTheory.IdentDistrib.evariance_eq | Mathlib/Probability/IdentDistrib.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h.integral_eq] | case h.e'_3
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
μ : Measure α
ν : Measure β
f✝ : α → γ
g✝ : β → γ
f : α → ℝ
g : β → ℝ
h : IdentDistrib f g μ ν
⊢ evariance g ν = ∫⁻ (x : β), ↑‖g x - ∫ (x : α), f x ∂... | case h.e'_3
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
μ : Measure α
ν : Measure β
f✝ : α → γ
g✝ : β → γ
f : α → ℝ
g : β → ℝ
h : IdentDistrib f g μ ν
⊢ evariance g ν = ∫⁻ (x : β), ↑‖g x - ∫ (x : β), g x ∂... | ((:c Eq) (:c ENNReal) ((:c ProbabilityTheory.evariance) (:fv _uniq.28696) (:fv _uniq.28708) (:fv _uniq.28892) (:fv _uniq.28732)) ((:c MeasureTheory.lintegral) (:fv _uniq.28696) (:fv _uniq.28708) (:fv _uniq.28732) (:lambda x (:fv _uniq.28696) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c MeasurableSpace) (:fv _uniq.28693))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.28696))"},{"name":"inst✝¹","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ProbabilityTheory.evariance) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV9)))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV1)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":16367,"sourceStart":16365,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16369,"sourceStart":16368,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ProbabilityTheor... | [] | [{"source":"h.integral_eq","source_end":16382,"source_start":16369,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 5 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6126d590ed8c79ee52fdd26e191e9c4a979990bd0e600f6dc02e1ff473e2dea5 | a03ba159dc3c9923e726a64e5c998adbf126e1cff6f4641fe58071c995f14a56 | 1f3cb7b01cffed7b86f7901afd72dd530444579b89dec8a54487e39e3acb5234 | 8cee069e9ebeb52fcde5f09f6a2278a8d58ed40ac436038e02a2490664201b38 |
cat-searcher/leandojo-benchmark-4-random | test | 3,114 | ProbabilityTheory.IdentDistrib.evariance_eq | Mathlib/Probability/IdentDistrib.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case h.e'_3
α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
inst✝³ : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
μ : Measure α
ν : Measure β
f✝ : α → γ
g✝ : β → γ
f : α → ℝ
g : β → ℝ
h : IdentDistrib f g μ ν
⊢ evariance g ν = ∫⁻ (x : β), ↑‖g x - ∫ (x : β), g x ∂... | ((:c Eq) (:c ENNReal) ((:c ProbabilityTheory.evariance) (:fv _uniq.28696) (:fv _uniq.28708) (:fv _uniq.28892) (:fv _uniq.28732)) ((:c MeasureTheory.lintegral) (:fv _uniq.28696) (:fv _uniq.28708) (:fv _uniq.28732) (:lambda x (:fv _uniq.28696) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝³","sexp":"((:c MeasurableSpace) (:fv _uniq.28693))"},{"name":"inst✝²","sexp":"((:c MeasurableSpace) (:fv _uniq.28696))"},{"name":"inst✝¹","sexp"... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c ProbabilityTheory.evariance) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV14)) (:arg :explicit 3 (:fv FV9)))) (:arg :explicit 2 (:app (:c MeasureTheory.lintegral) (:arg :implicit-type 0 (:fv FV1)) (:arg :impl... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rfl","sourceEnd":16389,"sourceStart":16386,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":16389,"sourceStart":16386,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.28693","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.28696","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 79 | 8 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 36b8a816a60ca1169c5800b6572c755d17e40352569268c5091d642c711e1747 | 8cee069e9ebeb52fcde5f09f6a2278a8d58ed40ac436038e02a2490664201b38 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,115 | Basis.sumCoords_reindex | Mathlib/LinearAlgebra/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | ι : Type u_1
ι' : Type u_2
R : Type u_3
R₂ : Type u_4
K : Type u_5
M : Type u_6
M' : Type u_7
M'' : Type u_8
V : Type u
V' : Type u_9
inst✝⁴ : Semiring R
inst✝³ : AddCommMonoid M
inst✝² : Module R M
inst✝¹ : AddCommMonoid M'
inst✝ : Module R M'
b b₁ : Basis ι R M
i : ι
c : R
x : M
b' : Basis ι' R M'
e : ι ≃ ι'
⊢ (b.rei... | case h
ι : Type u_1
ι' : Type u_2
R : Type u_3
R₂ : Type u_4
K : Type u_5
M : Type u_6
M' : Type u_7
M'' : Type u_8
V : Type u
V' : Type u_9
inst✝⁴ : Semiring R
inst✝³ : AddCommMonoid M
inst✝² : Module R M
inst✝¹ : AddCommMonoid M'
inst✝ : Module R M'
b b₁ : Basis ι R M
i : ι
c : R
x✝ : M
b' : Basis ι' R M'
e : ι ≃ ι'
... | ((:c Eq) ((:c LinearMap) (:fv _uniq.138249) (:fv _uniq.138249) (:fv _uniq.138272) (:fv _uniq.138272) ((:c RingHom.id) (:fv _uniq.138249) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.138249) (:fv _uniq.138272))) (:fv _uniq.138258) (:fv _uniq.138249) (:fv _uniq.138275) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"R₂","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M'","sexp":"(:sort (+ u_7 1))"},{"name":"M''","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:app (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"ext","sourceEnd":17543,"sourceStart":17540,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":17545,"sourceStart":17544,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":17545,"sourceStart":17544,"tag... | [{"role":"fresh_name","source":"x","source_end":17545,"source_start":17544,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 136 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b3c09607acfa9562d8241867baa5e60e2813b25e7d51924fde3a6ce0a1362f9 | a3c4714d127bdc0d2cb3215b0a60fd4ef91d1b93b53536a13f2ad101d7364b7a | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | ff7abc43d51013c176e29496b1d2f0eb8b308d51542664402983c88c97752f8f |
cat-searcher/leandojo-benchmark-4-random | test | 3,116 | Basis.sumCoords_reindex | Mathlib/LinearAlgebra/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Basis.coe_sumCoords</a>, <a>Basis.repr_reindex</a>] | case h
ι : Type u_1
ι' : Type u_2
R : Type u_3
R₂ : Type u_4
K : Type u_5
M : Type u_6
M' : Type u_7
M'' : Type u_8
V : Type u
V' : Type u_9
inst✝⁴ : Semiring R
inst✝³ : AddCommMonoid M
inst✝² : Module R M
inst✝¹ : AddCommMonoid M'
inst✝ : Module R M'
b b₁ : Basis ι R M
i : ι
c : R
x✝ : M
b' : Basis ι' R M'
e : ι ≃ ι'
... | case h
ι : Type u_1
ι' : Type u_2
R : Type u_3
R₂ : Type u_4
K : Type u_5
M : Type u_6
M' : Type u_7
M'' : Type u_8
V : Type u
V' : Type u_9
inst✝⁴ : Semiring R
inst✝³ : AddCommMonoid M
inst✝² : Module R M
inst✝¹ : AddCommMonoid M'
inst✝ : Module R M'
b b₁ : Basis ι R M
i : ι
c : R
x✝ : M
b' : Basis ι' R M'
e : ι ≃ ι'
... | ((:c Eq) (:fv _uniq.138249) ((:c DFunLike.coe) ((:c LinearMap) (:fv _uniq.138249) (:fv _uniq.138249) (:fv _uniq.138272) (:fv _uniq.138272) ((:c RingHom.id) (:fv _uniq.138249) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.138249) (:fv _uniq.138272))) (:fv _uniq.138258) (:fv _uniq.138249) (:fv _uniq.138275) ((:c NonUnital... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"R₂","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M'","sexp":"(:sort (+ u_7 1))"},{"name":"M''","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c LinearMap) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":17552,"sourceStart":17548,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":17557,"sourceStart":17553,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":175... | [] | [{"source":"coe_sumCoords","source_end":17572,"source_start":17559,"syntax_kind":"ident"},{"source":"repr_reindex","source_end":17586,"source_start":17574,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 136 | 5 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66b02e6cce4df8c8602c88c12650e451058f052022f12ba86354625b831f7820 | ff7abc43d51013c176e29496b1d2f0eb8b308d51542664402983c88c97752f8f | 789c5019c9826c4588e081dd9011da240ac29a06386030ff7ae094e6bc38f5d8 | fa393c56f60d80bf66e1b0df484546395c5fc912d00f62a5307b6707d5198a34 |
cat-searcher/leandojo-benchmark-4-random | test | 3,117 | Basis.sumCoords_reindex | Mathlib/LinearAlgebra/Basis.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Finsupp.sum_mapDomain_index</a> (fun _ => <a>rfl</a>) fun _ _ _ => <a>rfl</a> | case h
ι : Type u_1
ι' : Type u_2
R : Type u_3
R₂ : Type u_4
K : Type u_5
M : Type u_6
M' : Type u_7
M'' : Type u_8
V : Type u
V' : Type u_9
inst✝⁴ : Semiring R
inst✝³ : AddCommMonoid M
inst✝² : Module R M
inst✝¹ : AddCommMonoid M'
inst✝ : Module R M'
b b₁ : Basis ι R M
i : ι
c : R
x✝ : M
b' : Basis ι' R M'
e : ι ≃ ι'
... | ((:c Eq) (:fv _uniq.138249) ((:c Finsupp.sum) (:fv _uniq.138246) (:fv _uniq.138249) (:fv _uniq.138249) ((:c MonoidWithZero.toZero) (:fv _uniq.138249) ((:c Semiring.toMonoidWithZero) (:fv _uniq.138249) (:fv _uniq.138272))) ((:c NonUnitalNonAssocSemiring.toAddCommMonoid) (:fv _uniq.138249) ((:c NonAssocSemiring.toNonUnit... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"ι'","sexp":"(:sort (+ u_2 1))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"R₂","sexp":"(:sort (+ u_4 1))"},{"name":"K","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M'","sexp":"(:sort (+ u_7 1))"},{"name":"M''","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Finsupp.sum) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Zero) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 4 (:instance-of (:app (:c AddComm... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"name":"ι'","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":17595,"sourceStart":17590,"tag":"atom"},{"children":[{"name":"Finsupp.sum_mapDomain_index","semanticRole":"global","source":"Finsupp.sum_mapDomain_index","sourceEnd":17623,"sourceStart":17596,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":17625,"source... | [] | [{"source":"Finsupp.sum_mapDomain_index (fun _ => rfl) fun _ _ _ => rfl","source_end":17655,"source_start":17596,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.138243","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.138246","is_instance":false,"is_let":false,"user_name":"ι'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 136 | 6 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3cce98c0850d21cbf25d243dab138c46bf71e2e8d9fddb45545a3e078fafa964 | fa393c56f60d80bf66e1b0df484546395c5fc912d00f62a5307b6707d5198a34 | facbbc90a4d2c686766cb039b76976aa51694be7610a46dd24acfe8e1d8757de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,118 | Monoid.exponent_dvd | Mathlib/GroupTheory/Exponent.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Monoid.exponent_dvd_iff_forall_pow_eq_one</a>, <a>orderOf_dvd_iff_pow_eq_one</a>] | G : Type u
inst✝ : Monoid G
n : ℕ
⊢ exponent G ∣ n ↔ ∀ (g : G), orderOf g ∣ n | ((:c Iff) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c Monoid.exponent) (:fv _uniq.19346) (:fv _uniq.19349)) (:fv _uniq.19412)) (:forall g (:fv _uniq.19346) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) ((:c orderOf) (:fv _uniq.19346) (:fv _uniq.19349) 0) (:fv _uniq.19412)))) | [{"name":"G","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c Monoid) (:fv _uniq.19346))"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Monoid.exponent) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0)))))))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19346","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19349","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c Monoid) (:arg :explicit ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":9799,"sourceStart":9792,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9801,"sourceStart":9800,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":""... | [] | [{"source":"exponent_dvd_iff_forall_pow_eq_one","source_end":9835,"source_start":9801,"syntax_kind":"ident"},{"source":"orderOf_dvd_iff_pow_eq_one","source_end":9863,"source_start":9837,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19346","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.19349","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"interna... | 61 | 2 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 53afb625e33bfe37b5997e359350d8232a06e07f283b165b0080f34f2e522cd2 | e4a563080530f00b55cd3a3cd51197227b4d62a3e8f8614a576562b32c686286 | 822a4ea1c90cbd4dcc377238125bfe6d7f1953253f3d4377b41701a279a87dc9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,119 | JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>inf_comm</a>] | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
x y : X
hxz : IsMaximal x (x ⊔ y)
hyz : IsMaximal y (x ⊔ y)
⊢ IsMaximal (x ⊓ y) y | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
x y : X
hxz : IsMaximal x (x ⊔ y)
hyz : IsMaximal y (x ⊔ y)
⊢ IsMaximal (y ⊓ x) y | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.677) (:fv _uniq.680) (:fv _uniq.693) ((:c Inf.inf) (:fv _uniq.677) ((:c Lattice.toInf) (:fv _uniq.677) (:fv _uniq.680)) (:fv _uniq.897) (:fv _uniq.898)) (:fv _uniq.898)) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.677))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.677) (:fv _uniq.680))"},{"name":"x","sexp":"(:fv _uniq.677)"},{"name":"y","sexp":"(:fv _uniq.677)"},{"name":"hxz","sexp":"((:c JordanHolderLattice.IsMaximal) (:fv... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explicit 0 ... | {"children":[{"source":"rw","sourceEnd":5353,"sourceStart":5351,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5355,"sourceStart":5354,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"inf_comm","semanticR... | [] | [{"source":"inf_comm","source_end":5363,"source_start":5355,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,"i... | 8 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1fa98b570878fd6a7e6a11a8a59f39d1cbfa07b45af9401e477c2ae34b128703 | a98debe4b85406e607d45650738c7e1184817f6ffd4d88134df3d2b4f8e4b46f | 63e8a526b60bd6c20b3d1dcc0dbcd41194c08bbc0a453f08757774f3d7f44bc3 | c9f36c1c907e0c16c4fd5eb99015b9651e3380472b028783642b056b01c2d655 |
cat-searcher/leandojo-benchmark-4-random | test | 3,120 | JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>sup_comm</a>] at hxz hyz | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
x y : X
hxz : IsMaximal x (x ⊔ y)
hyz : IsMaximal y (x ⊔ y)
⊢ IsMaximal (y ⊓ x) y | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
x y : X
hxz : IsMaximal x (y ⊔ x)
hyz : IsMaximal y (y ⊔ x)
⊢ IsMaximal (y ⊓ x) y | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.677) (:fv _uniq.680) (:fv _uniq.693) ((:c Inf.inf) (:fv _uniq.677) ((:c SemilatticeInf.toInf) (:fv _uniq.677) ((:c Lattice.toSemilatticeInf) (:fv _uniq.677) (:fv _uniq.680))) (:fv _uniq.898) (:fv _uniq.897)) (:fv _uniq.898)) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.677))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.677) (:fv _uniq.680))"},{"name":"x","sexp":"(:fv _uniq.677)"},{"name":"y","sexp":"(:fv _uniq.677)"},{"name":"hxz","sexp":"((:c JordanHolderLattice.IsMaximal) (:fv... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explicit 0 ... | {"children":[{"source":"rw","sourceEnd":5369,"sourceStart":5367,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5371,"sourceStart":5370,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"sup_comm","semanticR... | [] | [{"source":"sup_comm","source_end":5379,"source_start":5371,"syntax_kind":"ident"},{"source":"hxz","source_end":5387,"source_start":5384,"syntax_kind":"ident"},{"source":"hyz","source_end":5391,"source_start":5388,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,"i... | 8 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7582d85e67d975312e9dd05ee5628f8ed7fbb55f0169d790e93a98fd63566c61 | c9f36c1c907e0c16c4fd5eb99015b9651e3380472b028783642b056b01c2d655 | c6438625fb7aec5ef0e4b998e2f55fadd3ebaf2e1d134ff08ea26c9800800d42 | e6bf94077b385272c1ef71379119e44b6f9339fd428bb3d9196f5d77ff3c13f8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,121 | JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup | Mathlib/Order/JordanHolder.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>JordanHolderLattice.isMaximal_inf_left_of_isMaximal_sup</a> hyz hxz | X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
x y : X
hxz : IsMaximal x (y ⊔ x)
hyz : IsMaximal y (y ⊔ x)
⊢ IsMaximal (y ⊓ x) y | ((:c JordanHolderLattice.IsMaximal) (:fv _uniq.677) (:fv _uniq.680) (:fv _uniq.693) ((:c Inf.inf) (:fv _uniq.677) ((:c SemilatticeInf.toInf) (:fv _uniq.677) ((:c Lattice.toSemilatticeInf) (:fv _uniq.677) (:fv _uniq.680))) (:fv _uniq.898) (:fv _uniq.897)) (:fv _uniq.898)) | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c Lattice) (:fv _uniq.677))"},{"name":"inst✝","sexp":"((:c JordanHolderLattice) (:fv _uniq.677) (:fv _uniq.680))"},{"name":"x","sexp":"(:fv _uniq.677)"},{"name":"y","sexp":"(:fv _uniq.677)"},{"name":"hxz","sexp":"((:c JordanHolderLattice.IsMaximal) (:fv... | (:app (:c JordanHolderLattice.IsMaximal) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c JordanHolderLattice) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Lattice) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Lattice) (:arg :explicit 0 ... | {"children":[{"source":"exact","sourceEnd":5399,"sourceStart":5394,"tag":"atom"},{"children":[{"name":"JordanHolderLattice.isMaximal_inf_left_of_isMaximal_sup","semanticRole":"global","source":"isMaximal_inf_left_of_isMaximal_sup","sourceEnd":5435,"sourceStart":5400,"tag":"identifier"},{"children":[{"contextIndex":7,"s... | [] | [{"source":"isMaximal_inf_left_of_isMaximal_sup hyz hxz","source_end":5443,"source_start":5400,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.677","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.680","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":2,"i... | 8 | 10 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b0991e28216483d2254c6a349d04e08ad7e4ec727a4e7988156a49ca0ee4e6f8 | e6bf94077b385272c1ef71379119e44b6f9339fd428bb3d9196f5d77ff3c13f8 | 1fa13cbdfd35a332d3ecfae2182b018e29be05eb8ba4c936e531ab7376e46fb9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,122 | FirstOrder.Language.LHom.setOf_realize_onFormula | Mathlib/ModelTheory/Semantics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | L : Language
L' : Language
M : Type w
N : Type u_1
P : Type u_2
inst✝⁴ : L.Structure M
inst✝³ : L.Structure N
inst✝² : L.Structure P
α : Type u'
β : Type v'
γ : Type u_3
n : ℕ
inst✝¹ : L'.Structure M
φ : L →ᴸ L'
inst✝ : φ.IsExpansionOn M
ψ : L.Formula α
⊢ setOf (φ.onFormula ψ).Realize = setOf ψ.Realize | case h
L : Language
L' : Language
M : Type w
N : Type u_1
P : Type u_2
inst✝⁴ : L.Structure M
inst✝³ : L.Structure N
inst✝² : L.Structure P
α : Type u'
β : Type v'
γ : Type u_3
n : ℕ
inst✝¹ : L'.Structure M
φ : L →ᴸ L'
inst✝ : φ.IsExpansionOn M
ψ : L.Formula α
x✝ : α → M
⊢ x✝ ∈ setOf (φ.onFormula ψ).Realize ↔ x✝ ∈ setO... | ((:c Eq) ((:c Set) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275))) ((:c setOf) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275)) ((:c FirstOrder.Language.Formula.Realize) (:fv _uniq.149273) (:fv _uniq.149275) (:fv _uniq.149476) (:fv _uniq.149304) ((:c FirstOrder.Language.LHom.onFormula) (:fv _uniq.149269) (:fv _uniq... | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.149269) (:fv _uniq.149275))"},{"na... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:forall _ :explicit (:fv FV8) (:fv FV2))))) (:arg :explicit 1 (:app (:c setOf) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV8) (:fv FV2))) (:arg :explicit 1 (:app (:c FirstOrder.Language.Formula.Realize) (:arg :implicit 0) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149269","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149273","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bi... | {"children":[{"source":"ext","sourceEnd":33382,"sourceStart":33379,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":33382,"sourceStart":33379,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149269","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149273","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 159 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c0f12a56b27ae27f91d3b2a134390dbfb2c62802d66eaac18b4ce90bb18b688 | a89fbb1f4b5ade010de39e9a4d2686b9711d50f3ce52b6932a606a05d339d7da | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 7efdc3456e40932ed5e53516ea79f079d10c1f971afe5c75b44ad693dd466ca0 |
cat-searcher/leandojo-benchmark-4-random | test | 3,123 | FirstOrder.Language.LHom.setOf_realize_onFormula | Mathlib/ModelTheory/Semantics.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
L : Language
L' : Language
M : Type w
N : Type u_1
P : Type u_2
inst✝⁴ : L.Structure M
inst✝³ : L.Structure N
inst✝² : L.Structure P
α : Type u'
β : Type v'
γ : Type u_3
n : ℕ
inst✝¹ : L'.Structure M
φ : L →ᴸ L'
inst✝ : φ.IsExpansionOn M
ψ : L.Formula α
x✝ : α → M
⊢ x✝ ∈ setOf (φ.onFormula ψ).Realize ↔ x✝ ∈ setO... | ((:c Iff) ((:c Membership.mem) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275)) ((:c Set) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275))) ((:c Set.instMembership) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275))) (:fv _uniq.149503) ((:c setOf) (:forall _ (:fv _uniq.149304) (:fv _uniq.149275)) ((:c FirstOrder.Langu... | [{"name":"L","sexp":"(:c FirstOrder.Language)"},{"name":"L'","sexp":"(:c FirstOrder.Language)"},{"name":"M","sexp":"(:sort (+ w 1))"},{"name":"N","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c FirstOrder.Language.Structure) (:fv _uniq.149269) (:fv _uniq.149275))"},{"na... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:forall _ :explicit (:fv FV8) (:fv FV2))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:forall _ :explicit (:fv FV8) (:fv FV2))))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:forall _ :explicit (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149269","is_instance":false,"is_let":false,"name":"L","sexp":"(:c FirstOrder.Language)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149273","is_instance":false,"is_let":false,"name":"L'","sexp":"(:c FirstOrder.Language)"},{"bi... | {"children":[{"source":"simp","sourceEnd":33389,"sourceStart":33385,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.149269","is_instance":false,"is_let":false,"user_name":"L"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.149273","is_instance":false,"is_let":false,"user_name":"L'"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 159 | 5 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b448240966dda6e1feddf46a35998c198fc5ac6c8c3ed6b78c655cd27269f308 | 7efdc3456e40932ed5e53516ea79f079d10c1f971afe5c75b44ad693dd466ca0 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,124 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases hc₅₁₂ : <a>Collinear</a> ℝ ({p₅, p₁, p₂} : <a>Set</a> P) | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"by_cases","sourceEnd":43810,"sourceStart":43802,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"hc₅₁₂","sourceEnd":43822,"sourceStart":43811,"tag":"identifier"},{"source":":","sourceEnd":43824,"sourceStart":43823,"tag":"atom"}],"kind":"null","source":"hc₅₁₂ :","sourceEnd":438... | [] | [{"source":"Collinear ℝ ({p₅, p₁, p₂} : Set P)","source_end":43867,"source_start":43825,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a79fb8df1b13d87e60f87ff97e545bfc6783a3fd34715b4a736fb9b6d5718749 | ee219af670f87dbd50d13ec170341037b086c02ca5436cc75887b06f8097e00a | c17eb33cde2829fc5bb1e4fd206f2c880cb72efe2d12ee2f1b141e58da55f895 | fbe0d42272b3909abced4d62926f3ec53ec276d927b50f9b2ba01f95de20161b |
cat-searcher/leandojo-benchmark-4-random | test | 3,125 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hc₅₁₂₃₄ : <a>Collinear</a> ℝ ({p₅, p₁, p₂, p₃, p₄} : <a>Set</a> P) := (hc.collinear_insert_iff_of_ne (<a>Set.mem_insert</a> _ _) (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert</a> _ _)) hp₁p₂).2 hc₅₁₂ | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":43877,"sourceStart":43873,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hc₅₁₂₃₄","sourceEnd":43895,"sourceStart":43878,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hc₅₁₂₃₄","sourceEnd":43895,"sourceStart":43878,... | [] | [{"source":"Collinear ℝ ({p₅, p₁, p₂, p₃, p₄} : Set P)","source_end":43952,"source_start":43898,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(hc.collinear_insert_iff_of_ne (Set.mem_insert _ _)\n (Set.mem_insert_of_mem _ (Set.mem_insert _ _)) hp₁p₂).2 hc₅₁₂","source_end":44093,"source_start":43962,"syntax_kin... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 9 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | daec80747ea238fa5264e7b38f2f83fa4d9e767cfb91a98f4be2c3bdfbcbb4d9 | ee48076f2b71c23a68912e8dc872d76d93c5336977604bfa31ba7e8589495e7a | 72717787ca0d75b0016fefcfb5cb929912ce9548fef6e033f4c969ca803aa369 | e181edb82926ca907b52b431b7d0917154570247a17c9aa7748b670ee9f4b977 |
cat-searcher/leandojo-benchmark-4-random | test | 3,126 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hc₅₃₄ : <a>Collinear</a> ℝ ({p₅, p₃, p₄} : <a>Set</a> P) := (hc.collinear_insert_iff_of_ne (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert</a> _ _))) (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_singleton</a> _)))) hp... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":44102,"sourceStart":44098,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hc₅₃₄","sourceEnd":44114,"sourceStart":44103,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hc₅₃₄","sourceEnd":44114,"sourceStart":44103,"tag... | [] | [{"source":"Collinear ℝ ({p₅, p₃, p₄} : Set P)","source_end":44159,"source_start":44117,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(hc.collinear_insert_iff_of_ne\n (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_insert _ _)))\n (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 10 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8108c690612c0dc098c49df174aff7988e52a582e4f7b9f662555c66009941e8 | e181edb82926ca907b52b431b7d0917154570247a17c9aa7748b670ee9f4b977 | 6cdea8c8590d9ddbb9c1c89fe7944c24cb4b7a6312dc181b93d7614e84a4eacb | bed6967e74a27a2fd386079df597044401a142b8ec51e16356d72bf9d07c5646 |
cat-searcher/leandojo-benchmark-4-random | test | 3,127 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.insert_comm</a>] at hc₅₁₂ hc₅₃₄ | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":44436,"sourceStart":44434,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44438,"sourceStart":44437,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.insert_comm"... | [] | [{"source":"Set.insert_comm","source_end":44453,"source_start":44438,"syntax_kind":"ident"},{"source":"hc₅₁₂","source_end":44469,"source_start":44458,"syntax_kind":"ident"},{"source":"hc₅₃₄","source_end":44481,"source_start":44470,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 11 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3060727aa8fa152d826cde9521a281a2880734eaec5bd32a25846fe6c04cb48c | bed6967e74a27a2fd386079df597044401a142b8ec51e16356d72bf9d07c5646 | 2c6f71106c620f02aac9def7077c61917e2d945173ea8f8f0e6ac665e79587f8 | 77b035f7193aa13308e4b24fdae0d40ef45d1f6597749e40ef1699755e8aab3c |
cat-searcher/leandojo-benchmark-4-random | test | 3,128 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hs₁₅₂ := <a>EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear</a>.2 hc₅₁₂ | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":44490,"sourceStart":44486,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hs₁₅₂","sourceEnd":44502,"sourceStart":44491,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hs₁₅₂","sourceEnd":44502,"sourceStart":44491,"tag... | [] | [{"source":"oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₁₂","source_end":44557,"source_start":44506,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 14 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a7fbf9ac517830b8f8031c4b3cc65fa6f48e786c9fae8216f217ccef543edab | 77b035f7193aa13308e4b24fdae0d40ef45d1f6597749e40ef1699755e8aab3c | db6dba13e4ef610476dc518d93380fb923269e1a0bf1e0f99c19e92a6b98f294 | a72bf7d3c204592d1750ef0556703b25fd448a0eb112fbd2b98ec06255b8ad75 |
cat-searcher/leandojo-benchmark-4-random | test | 3,129 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hs₃₅₄ := <a>EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear</a>.2 hc₅₃₄ | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":44566,"sourceStart":44562,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hs₃₅₄","sourceEnd":44578,"sourceStart":44567,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hs₃₅₄","sourceEnd":44578,"sourceStart":44567,"tag... | [] | [{"source":"oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₃₄","source_end":44633,"source_start":44582,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 15 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6026bb8a5a6679fba4439035d173c9c7e44d3b93d74bdd2864b81eec6b3ad63 | a72bf7d3c204592d1750ef0556703b25fd448a0eb112fbd2b98ec06255b8ad75 | 5d515650107a7bfc7fe73b1a76d0273e68094722208cbaa7cf07acbc63aaf23b | 72270e709e4a108712bc134d3f0a0787af466c126f458f64eec5df233eb28605 |
cat-searcher/leandojo-benchmark-4-random | test | 3,130 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.Angle.sign_eq_zero_iff</a>] at hs₁₅₂ hs₃₅₄ | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":44640,"sourceStart":44638,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44642,"sourceStart":44641,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":44645,"sourceSt... | [] | [{"source":"Real.Angle.sign_eq_zero_iff","source_end":44673,"source_start":44646,"syntax_kind":"ident"},{"source":"hs₁₅₂","source_end":44689,"source_start":44678,"syntax_kind":"ident"},{"source":"hs₃₅₄","source_end":44701,"source_start":44690,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 16 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97f5ab6dc0f08be72d7ae9e7b1d78a07755ab33698962a71fbb1981734b5bca4 | 72270e709e4a108712bc134d3f0a0787af466c126f458f64eec5df233eb28605 | 56c55e939b05fb0432ea6e448753adec1b9b237025ef09f09af1f97f57df1620 | 53dd95f4568b06dc74594ade36542b2330d6c3eeca8224b64d30a07fd6c62e3c |
cat-searcher/leandojo-benchmark-4-random | test | 3,131 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [hs₁₅₂, hs₃₅₄] | case pos
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":44708,"sourceStart":44706,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":44710,"sourceStart":44709,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":21,"seman... | [] | [{"source":"hs₁₅₂","source_end":44721,"source_start":44710,"syntax_kind":"ident"},{"source":"hs₃₅₄","source_end":44734,"source_start":44723,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 19 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7726bc227de3b54b4383811334de62e2a996a601c50c49aba401e74b3fbccac | 53dd95f4568b06dc74594ade36542b2330d6c3eeca8224b64d30a07fd6c62e3c | 5b390ac0272d930e8d7cbb69db2b43b67d032a635b9a6bfa4810fd18ee1ad849 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,132 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let s : <a>Set</a> (P × P × P) := (fun x : line[ℝ, p₁, p₂] × V => (x.1, p₅, x.2 +ᵥ (x.1 : P))) '' <a>Set.univ</a> ×ˢ {v | <a>SameRay</a> ℝ (p₂ -ᵥ p₁) v ∧ v ≠ 0} | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"let","sourceEnd":44744,"sourceStart":44741,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":44746,"sourceStart":44745,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":4474... | [] | [{"source":"Set (P × P × P)","source_end":44766,"source_start":44749,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(fun x : line[ℝ, p₁, p₂] × V => (x.1, p₅, x.2 +ᵥ (x.1 : P))) ''\n Set.univ ×ˢ {v | SameRay ℝ (p₂ -ᵥ p₁) v ∧ v ≠ 0}","source_end":44921,"source_start":44776,"syntax_kind":"Set.term_''_"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 27 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c05b5da7bc467550298d35b0d0374f304a01965d8cc7412feb661e7d20c8970a | 4cf8b602fc2da252d0ec47adf6c6dd31a191a46485e4ca5ff47b1d63c2c5751e | e3af262959ed69146574a607af7158d498cd181ebd33e3fd1a8e214fcc5e8289 | d0b5a85a6dffcd24d8d0ff558dd2125420ecdaa067429a5a552bce5acbd5f6ac |
cat-searcher/leandojo-benchmark-4-random | test | 3,133 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hco : <a>IsConnected</a> s := haveI : <a>ConnectedSpace</a> line[ℝ, p₁, p₂] := <a>AddTorsor.connectedSpace</a> _ _ (isConnected_univ.prod (<a>isConnected_setOf_sameRay_and_ne_zero</a> (<a>vsub_ne_zero</a>.2 hp₁p₂.symm))).<a>IsConnected.image</a> _ (continuous_fst.subtype_val.prod_mk (continuous_const.prod_mk (cont... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":44930,"sourceStart":44926,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hco","sourceEnd":44934,"sourceStart":44931,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hco","sourceEnd":44934,"sourceStart":44931,"tag":"n... | [] | [{"source":"IsConnected s","source_end":44950,"source_start":44937,"syntax_kind":"Lean.Parser.Term.app"},{"source":"haveI : ConnectedSpace line[ℝ, p₁, p₂] := AddTorsor.connectedSpace _ _\n (isConnected_univ.prod (isConnected_setOf_sameRay_and_ne_zero\n (vsub_ne_zero.2 hp₁p₂.symm))).image _\n (continu... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 28 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9aee1cb38b74497db247b3a147ffeaca120ea791ab06d43f18ff95e6cfd79c7 | d0b5a85a6dffcd24d8d0ff558dd2125420ecdaa067429a5a552bce5acbd5f6ac | 1ffdd738e81af5d264dcf84c4b1fed013a1227ec4fe9f9e6631cbf57c08f7d4a | 4a052c4035af3dd78150526a046ecf24d2be616be6e2c5e80ca8de6bd0c402f5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,134 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hp₁p₂s : (p₁, p₅, p₂) ∈ s := by simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_setOf</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] refine ⟨⟨⟨p₁, <a>left_mem_affineSpan_pair</a> ℝ _ _⟩, p₂ -ᵥ p₁⟩, ⟨<a>SameRay.rfl</a>, <a>vsub_ne_zero</a>.2 hp₁p₂.symm⟩, ?_⟩ simp | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":47307,"sourceStart":47303,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hp₁p₂s","sourceEnd":47318,"sourceStart":47308,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hp₁p₂s","sourceEnd":47318,"sourceStart":47308,"t... | [] | [{"source":"(p₁, p₅, p₂) ∈ s","source_end":47345,"source_start":47321,"syntax_kind":"«term_∈_»"},{"source":"s","source_end":47368,"source_start":47367,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":47383,"source_start":47370,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":47397,"source_start... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 131 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eba4e4fea20797d0ca49f2910db1c98b05ddb1531924782ec8605f38230b4b38 | 57f17ea58d885a5363b2faaca589362b80024324d0472aea88963eaae47c26a0 | 9abd300f06dd5ada8d3a7858a87f2238bef1f915406228af9174e52c3cbab1d0 | b9c01a6208fc280bea3e049c5b72ad1fa570036c7fec604a1cf9f5fdca916953 |
cat-searcher/leandojo-benchmark-4-random | test | 3,135 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hp₃p₄s : (p₃, p₅, p₄) ∈ s := by simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_setOf</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] refine ⟨⟨⟨p₃, hc.mem_affineSpan_of_mem_of_ne (<a>Set.mem_insert</a> _ _) (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert</a> _ _)) (<a>Set.m... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"have","sourceEnd":47631,"sourceStart":47627,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hp₃p₄s","sourceEnd":47642,"sourceStart":47632,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hp₃p₄s","sourceEnd":47642,"sourceStart":47632,"t... | [] | [{"source":"(p₃, p₅, p₄) ∈ s","source_end":47669,"source_start":47645,"syntax_kind":"«term_∈_»"},{"source":"s","source_end":47692,"source_start":47691,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":47707,"source_start":47694,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":47721,"source_start... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 144 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48e3dd0c36aa61834eaaf8907208b7a85b31852475fa66dc20ae8572f8b1148d | b9c01a6208fc280bea3e049c5b72ad1fa570036c7fec604a1cf9f5fdca916953 | c546fdab0d13d47a7af5efa5942d513c2e4d98fec17a33e48060de8a8d9928c2 | d57c0ad2a55a71e6e16bfb2a2d69abdf92ddce8c04870a063e8338031f6f34b8 |
cat-searcher/leandojo-benchmark-4-random | test | 3,136 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>Real.Angle.sign_eq_of_continuousOn</a> hco hf hsp hp₃p₄s hp₁p₂s | case neg
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ ... | ((:c Eq) (:c SignType) ((:c Real.Angle.sign) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.401018) (:fv _uniq.401022) (:fv _uniq.401019))) ((:c Real.Angle.sign) ((:c Euclid... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Eq) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:app (:c Real.Angle.sign) (:arg :explicit 0 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"convert","sourceEnd":48114,"sourceStart":48107,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Real.Angle.sign_eq_of_continuousOn","semanticRole":"global","source":"Real.Angle.sign_eq_of_continuousO... | [] | [{"source":"Real.Angle.sign_eq_of_continuousOn hco hf hsp hp₃p₄s hp₁p₂s","source_end":48182,"source_start":48115,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 157 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e46d1f1ecab9d0c2ae38d359685c93446367afb2f981cb391165d2ffda0538c2 | d57c0ad2a55a71e6e16bfb2a2d69abdf92ddce8c04870a063e8338031f6f34b8 | 8e72cf6907aefedc84e405d3dc570e10ccc516b26c7d9e6f9674fab192ef24a2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,137 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>ContinuousAt.continuousOn</a> fun p hp => <a>EuclideanGeometry.continuousAt_oangle</a> ?_ ?_ | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | case refine_1
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p... | ((:c ContinuousOn) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341))) (:c Real.Angle) ((:c instTopologicalSpaceProd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.397341) ((:c PseudoMetricSpace.toUniformSpace) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c ContinuousOn) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :implicit-type 1 (:c Real.Angle)) (:arg :instance 2 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:app (:c Prod... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":45391,"sourceStart":45385,"tag":"atom"},{"children":[{"name":"ContinuousAt.continuousOn","semanticRole":"global","source":"ContinuousAt.continuousOn","sourceEnd":45417,"sourceStart":45392,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":45421,"sourceS... | [] | [{"source":"ContinuousAt.continuousOn fun p hp => continuousAt_oangle ?_ ?_","source_end":45455,"source_start":45392,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 31 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6370937f62d4e325b96b79b724d06b541a0cf5aedeb4c87961172ebb7cc1fd42 | de72fb82d1529b86105816d34b72270489951b9a9508a59bacde108f9d7a0d8a | d43f822a55e99f0ec7b426932f82c54a958011e8e95e0d5098b7f707599a8f68 | b2a2cdee53db6060b75b061776d1da81449a3c7c6aabf31324085accbf57e845 |
cat-searcher/leandojo-benchmark-4-random | test | 3,139 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] at hp | case refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p... | case refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p... | ((:c Ne) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) (:fv _uniq.420602))) ((:c Prod.fst) (:fv _uniq.397341) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":45487,"sourceStart":45480,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45489,"sourceStart":45488,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"... | [] | [{"source":"hp","source_end":45568,"source_start":45566,"syntax_kind":"ident"},{"source":"s","source_end":45490,"source_start":45489,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":45505,"source_start":45492,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":45519,"source_start":45507,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 52 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87c64b080d13a2caf6b70e87a01b922f9dc53a5ececb8d8d4d7acc71575a2bc5 | 625764b79e5b617edf4fbae0e3fa507242147d7f0117b507e4997b011bbd6e11 | 98c2772e5a1107c97ac1af1becbb90a3bc878d5fb738bbf8c81c3616d39d89ea | 7fcaa26573bbb3ca769de52940c53c213505b455a4ae33ef089bbdadc7296ad5 |
cat-searcher/leandojo-benchmark-4-random | test | 3,140 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨q₁, q₅, q₂⟩ := p | case refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p... | case refine_2.mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRa... | ((:c Ne) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) (:fv _uniq.420602))) ((:c Prod.fst) (:fv _uniq.397341) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":45583,"sourceStart":45577,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":45587,"sourceStart":45584,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"q₁","sourceE... | [] | [{"source":"p","source_end":45611,"source_start":45610,"syntax_kind":"ident"},{"source":"⟨q₁, q₅, q₂⟩","source_end":45606,"source_start":45584,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 60 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 133f3f6b8002b6a370bcd1eb52f30e46d288ab11e15b2fa873d9b81524395b1a | 7fcaa26573bbb3ca769de52940c53c213505b455a4ae33ef089bbdadc7296ad5 | c8b8f1a1008b75da8ff1fccca523a36034e391d02413d8250cb234225dea81e2 | fc2e57f6c3eff70ac786517581df09d12a379adf676c7a8043ddb7b8a36049bd |
cat-searcher/leandojo-benchmark-4-random | test | 3,141 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only at hp ⊢ | case refine_2.mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRa... | case refine_2.mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRa... | ((:c Ne) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) (:fv _uniq.397341) ((:c Prod.snd) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) ((:c Prod.mk) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) (:fv _uniq.425801) ((:c Prod.mk) (:fv _uniq.397341) (:fv _uniq.397341) (... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Prod.snd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"dsimp","sourceEnd":45625,"sourceStart":45620,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":45630,"sourceStart":45626,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":45... | [] | [{"source":"hp","source_end":45636,"source_start":45634,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 61 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fe27654b8cb2b52bad5bd8d4b576956e608899518789fdc6172de2c68ae40dc0 | fc2e57f6c3eff70ac786517581df09d12a379adf676c7a8043ddb7b8a36049bd | 2de08369763010a55613c467f581f1de9ad7bbec105768ab0a454cccab442ea8 | fa36d2a2e68aa9d496dc0c7d7d8477705c3515fa8c8137c3beb051919cf7ba7c |
cat-searcher/leandojo-benchmark-4-random | test | 3,142 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp | case refine_2.mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRa... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ... | ((:c Ne) (:fv _uniq.397341) (:fv _uniq.425824) (:fv _uniq.425823)) | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV23)) (:arg :explicit 2 (:fv FV22))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":45655,"sourceStart":45649,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":45659,"sourceStart":45656,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":45662,"sourceStart":45659,"... | [] | [{"source":"hp","source_end":45707,"source_start":45705,"syntax_kind":"ident"},{"source":"⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩","source_end":45701,"source_start":45656,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 62 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9531aca839b3cafaf30933498493c3d391793d2b9e8a63211e256bdd451be8b2 | fa36d2a2e68aa9d496dc0c7d7d8477705c3515fa8c8137c3beb051919cf7ba7c | 0e5b94f570ca2deda88ba1d1580da48945cb7ac2bf9912c22d58fe349ee39eb4 | cc85b12ec95d2586fdd8ef1756225dacfea377d2dc44d89c32f24f5bf22d770b |
cat-searcher/leandojo-benchmark-4-random | test | 3,143 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>Subtype.coe_mk</a>, <a>Set.mem_setOf</a>] at hv ⊢ | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ... | ((:c Ne) (:fv _uniq.397341) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397341) ((:c instHVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c AddAction.toVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.397338) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.397338) ((:... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HVAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"dsimp","sourceEnd":45721,"sourceStart":45716,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":45726,"sourceStart":45722,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":45... | [] | [{"source":"Subtype.coe_mk","source_end":45742,"source_start":45728,"syntax_kind":"ident"},{"source":"Set.mem_setOf","source_end":45757,"source_start":45744,"syntax_kind":"ident"},{"source":"hv","source_end":45764,"source_start":45762,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 63 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 927ea52278412d973212107bd00223869fa555d2e79bb639268e11cc3db68062 | cc85b12ec95d2586fdd8ef1756225dacfea377d2dc44d89c32f24f5bf22d770b | 2f83830c189476b9c5afda6547c0e34637acf17140c72dab499948db0a271806 | 46993a8fa41b5bedbb5d05b4e3b647a96c2f9c40f21f72a3b9f887769a1c3c3a |
cat-searcher/leandojo-benchmark-4-random | test | 3,144 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨hvr, -⟩ := hv | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Coll... | ((:c Ne) (:fv _uniq.397341) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397341) ((:c instHVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c AddAction.toVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.397338) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.397338) ((:... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HVAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":45783,"sourceStart":45777,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":45787,"sourceStart":45784,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hvr","source... | [] | [{"source":"hv","source_end":45802,"source_start":45800,"syntax_kind":"ident"},{"source":"⟨hvr, -⟩","source_end":45796,"source_start":45784,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 64 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0dd1ac2e38978b1e1543707ac4c06b9b30e738b14a8add3bbe43910181e106e4 | 46993a8fa41b5bedbb5d05b4e3b647a96c2f9c40f21f72a3b9f887769a1c3c3a | 9a94e744fa9a0bad2d04ae2bea38006ec5d85dbf356ad21d23c346c7090136f2 | a7c0cb058a3c71d7cd9dde75a319197d05309f5abef6a58fc95224042e62f75d |
cat-searcher/leandojo-benchmark-4-random | test | 3,145 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro rfl | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Coll... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | ((:c Ne) (:fv _uniq.397341) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397341) ((:c instHVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c AddAction.toVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.397338) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.397338) ((:... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HVAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rintro","sourceEnd":45817,"sourceStart":45811,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":45821,"sourceStart":45818,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"rfl","sourceEnd":45821,"sourceStart":458... | [] | [{"source":"rfl","source_end":45821,"source_start":45818,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 65 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f54aa5dca3ae4c50f46901e2378e8620dba969966903df177d3e1bb5da169007 | a7c0cb058a3c71d7cd9dde75a319197d05309f5abef6a58fc95224042e62f75d | 09e128cd6787f35d3c063b643315aff1382388dafa4e55b6546fbf9dcecb02da | 92a10f0c046414943c5f402bf000a467b8c905316b5d3461c21785ea05e26044 |
cat-searcher/leandojo-benchmark-4-random | test | 3,146 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hc₅₁₂ ((<a>collinear_insert_iff_of_mem_affineSpan</a> ?_).2 (<a>collinear_pair</a> _ _ _)) | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | (:c False) | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":45836,"sourceStart":45830,"tag":"atom"},{"children":[{"contextIndex":21,"semanticRole":"local","source":"hc₅₁₂","sourceEnd":45848,"sourceStart":45837,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":45850,"sourceStart":45849,"tag":"atom"},{"children":[{... | [] | [{"source":"hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan ?_).2 (collinear_pair _ _ _))","source_end":45919,"source_start":45837,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 66 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fa7779e0ed470a0095091664849ec565df63a9d603d2588b1d43177ef8d03e9f | 92a10f0c046414943c5f402bf000a467b8c905316b5d3461c21785ea05e26044 | 467d42ddd5bbe9d08b609ee2a68fb3e9b729201f35a41fad50e55c5f6a338560 | 52f3e8ad2afa807ab2fcc12ede87b984b2a0dd51d11a69b5da6c27b15287433c |
cat-searcher/leandojo-benchmark-4-random | test | 3,147 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hq | case refine_1.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | ((:c Membership.mem) (:fv _uniq.397341) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing)) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.397338) (:c Real.nor... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":45934,"sourceStart":45929,"tag":"atom"},{"contextIndex":19,"semanticRole":"local","source":"hq","sourceEnd":45937,"sourceStart":45935,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hq","sourceEnd":45937,"sourceStar... | [] | [{"source":"hq","source_end":45937,"source_start":45935,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 69 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3596e902770b71361601ba3644d242c5670575d89413bed0d943332b8e46ed5d | 952d69dc8ccfc5498f8d84a8ce0cbc73b11a6a687472ca18eec8d6f3b2830707 | d7b853abf6de1e0c685decd105315dff0d57e71cbf540757a028d67909738630 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,148 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>AffineSubspace.vadd_mem_of_mem_direction</a> ?_ hq | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | ((:c Membership.mem) (:fv _uniq.397341) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing)) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.397338) (:c Real.nor... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":45953,"sourceStart":45947,"tag":"atom"},{"children":[{"name":"AffineSubspace.vadd_mem_of_mem_direction","semanticRole":"global","source":"vadd_mem_of_mem_direction","sourceEnd":45979,"sourceStart":45954,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":4... | [] | [{"source":"vadd_mem_of_mem_direction ?_ hq","source_end":45985,"source_start":45954,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 76 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc4fe8c462a18c4c3d1f70393f44deafea8998ad6c47961e21670fb451288ec3 | 52f3e8ad2afa807ab2fcc12ede87b984b2a0dd51d11a69b5da6c27b15287433c | b68755fb937e23e21a98976b7f58318220221e59fe6cedb43c3873dd9d4d5442 | ebc724c9ddb975db4b897752fd35523eb1d5758d1f6d640d2be0b2fd8c6885fa |
cat-searcher/leandojo-benchmark-4-random | test | 3,149 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>exists_nonneg_left_iff_sameRay</a> (<a>vsub_ne_zero</a>.2 hp₁p₂.symm)] at hvr | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":45996,"sourceStart":45994,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":45998,"sourceStart":45997,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":46001,"sourceSt... | [] | [{"source":"hvr","source_end":46072,"source_start":46069,"syntax_kind":"ident"},{"source":"exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)","source_end":46064,"source_start":46002,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 77 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 538410afc70e1bd3f6199a9280b0b1181e3040c3a512fac7115581ee34dd3f5a | ebc724c9ddb975db4b897752fd35523eb1d5758d1f6d640d2be0b2fd8c6885fa | b422b3cbb72adf9de65d249ea5ed2f07f775ef8eab2bd1353979b480f60e2cbf | 05dcf79ecab0a0f079e6b003e27075096f28840f7c9ca433966833f1a6556f8c |
cat-searcher/leandojo-benchmark-4-random | test | 3,150 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨r, -, rfl⟩ := hvr | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Colline... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":46087,"sourceStart":46081,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46091,"sourceStart":46088,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"r","sourceEn... | [] | [{"source":"hvr","source_end":46110,"source_start":46107,"syntax_kind":"ident"},{"source":"⟨r, -, rfl⟩","source_end":46103,"source_start":46088,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 80 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9faa622a0fb39c8873251f6d27cf0ce0ab64d14e5d4ddffc2d1a4e87c41dae92 | 05dcf79ecab0a0f079e6b003e27075096f28840f7c9ca433966833f1a6556f8c | 5082b3e4a278099e0785c453d156e424bde65a687436b61a061cf3d34132538c | 4a12be6ed25ed19984e13602853104b7190fe3d0b5e4048c086dd8953eaf6dac |
cat-searcher/leandojo-benchmark-4-random | test | 3,151 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>direction_affineSpan</a>] | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
... | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":46121,"sourceStart":46119,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46123,"sourceStart":46122,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"direction_affine... | [] | [{"source":"direction_affineSpan","source_end":46143,"source_start":46123,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 81 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf735a639b8d46a13759ff662b707c3653ffa08c509414123db3c7050a24a8bc | 4a12be6ed25ed19984e13602853104b7190fe3d0b5e4048c086dd8953eaf6dac | 83a0700cae12d67c7683a2782a7e56db979267ea8e209c71d3acfadc4b2e987c | 7ce8a7775a79f5cb2d1f49d6a6bcb340adb90b7e1be9468ae08d6eaa9bd909ab |
cat-searcher/leandojo-benchmark-4-random | test | 3,152 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>smul_vsub_rev_mem_vectorSpan_pair</a> _ _ _ | case refine_2.mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing))) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":46158,"sourceStart":46153,"tag":"atom"},{"children":[{"name":"smul_vsub_rev_mem_vectorSpan_pair","semanticRole":"global","source":"smul_vsub_rev_mem_vectorSpan_pair","sourceEnd":46192,"sourceStart":46159,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":4... | [] | [{"source":"smul_vsub_rev_mem_vectorSpan_pair _ _ _","source_end":46198,"source_start":46159,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 84 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d68dacb6bb5f76bf56f570d1d7304b9365d2d6e5b65aeebfcf7548ab4d8d78c1 | 7ce8a7775a79f5cb2d1f49d6a6bcb340adb90b7e1be9468ae08d6eaa9bd909ab | 995f65b60c52631599367c73df2cd75fdede6ffb653ae67d4251683a7f6bf960 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,153 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro p hp | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | (:forall p ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341))) (:forall _ ((:c Membership.mem) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341))) ((:c Set) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)))) ((:c Set.instMembership... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:forall p :explicit (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1))))) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"intro","sourceEnd":46321,"sourceStart":46316,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"p","sourceEnd":46323,"sourceStart":46322,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hp","sourceEnd":46326,"sourceStart":46324,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"p","source_end":46323,"source_start":46322,"syntax_kind":"ident"},{"role":"fresh_name","source":"hp","source_end":46326,"source_start":46324,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 87 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2320b19bfa0f7cdb611a40f9d5fa8bac8569c3c207b7b334533a789d9f03b224 | 63377648d542d7eeeb96dcf08c32f9d4f9d44a1099d2a099d1f04653bc3cd260 | a42621e01ce9e8896da55f357f5a262e8c26624a251adf40dffbbfdbf4b87cd0 | c74b52440211e4ec166cfbda404516627b7a754dee0279d1e27241e3a7b52739 |
cat-searcher/leandojo-benchmark-4-random | test | 3,154 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_setOf</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] at hp | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) ((:c Prod.fst) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) (:fv _uniq.431958)... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":46340,"sourceStart":46333,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46342,"sourceStart":46341,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"... | [] | [{"source":"hp","source_end":46444,"source_start":46442,"syntax_kind":"ident"},{"source":"s","source_end":46343,"source_start":46342,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":46358,"source_start":46345,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":46372,"source_start":46360,"syntax_ki... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 88 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d8e5fc5961a8dca2fddb5390ff165d6a58f6d0a354e01dee840977ffea1a1a8 | c74b52440211e4ec166cfbda404516627b7a754dee0279d1e27241e3a7b52739 | 14287be443f3ca27295c04488245a9dcd5b859e236a94f6f314fb6d7563589cf | b09cb104d7d7d527d96e2c80af7089f49658df211e0856086c7813f1cf65f52b |
cat-searcher/leandojo-benchmark-4-random | test | 3,155 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨q₁, q₅, q₂⟩ := p | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | case mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) ((:c Prod.fst) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) (:fv _uniq.431958)... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":46457,"sourceStart":46451,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46461,"sourceStart":46458,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"q₁","sourceE... | [] | [{"source":"p","source_end":46485,"source_start":46484,"syntax_kind":"ident"},{"source":"⟨q₁, q₅, q₂⟩","source_end":46480,"source_start":46458,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 97 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b0d1a44f0bcbfb42ef743714d56244f781c3c0d759acd0f79b8355b64e4a040 | b09cb104d7d7d527d96e2c80af7089f49658df211e0856086c7813f1cf65f52b | c8b8f1a1008b75da8ff1fccca523a36034e391d02413d8250cb234225dea81e2 | 10e5db820c034f0ef0f50d47e238286262d909f165a74176e965a630a64a6283 |
cat-searcher/leandojo-benchmark-4-random | test | 3,156 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only at hp ⊢ | case mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -... | case mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) ((:c Prod.fst) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)) ((:c Prod.mk) (:fv... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"dsimp","sourceEnd":46497,"sourceStart":46492,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":46502,"sourceStart":46498,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":46... | [] | [{"source":"hp","source_end":46508,"source_start":46506,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 98 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e478e8bc98171f33f005ede2bc0c0337672f0b6d06873ba636935802603cf927 | 10e5db820c034f0ef0f50d47e238286262d909f165a74176e965a630a64a6283 | 2de08369763010a55613c467f581f1de9ad7bbec105768ab0a454cccab442ea8 | 4f0fa0cad51074f4ad39c4063efa1e71d81a1e0222dfd51762d965fbda03120a |
cat-searcher/leandojo-benchmark-4-random | test | 3,157 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp | case mk.mk
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -... | case mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433219) (:fv _uniq.433241) (:fv _uniq.433242)) ((:c OfNat.ofNat) (:c Real.Angle) (:lit 0) (... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":46525,"sourceStart":46519,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46529,"sourceStart":46526,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46532,"sourceStart":46529,"... | [] | [{"source":"hp","source_end":46577,"source_start":46575,"syntax_kind":"ident"},{"source":"⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩","source_end":46571,"source_start":46526,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 99 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f88de3f7f41c5a614d444fdc2993a426ad45edc3908696826bcc7d668ee65516 | 4f0fa0cad51074f4ad39c4063efa1e71d81a1e0222dfd51762d965fbda03120a | 0e5b94f570ca2deda88ba1d1580da48945cb7ac2bf9912c22d58fe349ee39eb4 | a7eb57777ec7e5df9701abe4b9b4b005b8b971d62f59895c989ec385ad482a32 |
cat-searcher/leandojo-benchmark-4-random | test | 3,158 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only [<a>Subtype.coe_mk</a>, <a>Set.mem_setOf</a>] at hv ⊢ | case mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂... | case mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) ((:c Subtype.val) (:fv _uniq.397341) (:lambda x (:fv _uniq.397341) ((:c Membership.mem) (:fv _uniq.397... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"dsimp","sourceEnd":46589,"sourceStart":46584,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":46594,"sourceStart":46590,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":46... | [] | [{"source":"Subtype.coe_mk","source_end":46610,"source_start":46596,"syntax_kind":"ident"},{"source":"Set.mem_setOf","source_end":46625,"source_start":46612,"syntax_kind":"ident"},{"source":"hv","source_end":46632,"source_start":46630,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 100 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32ec49e237e3c45cd3434a9e51e90d771ab5b2ef541336e5c6f496c0f4e17a0e | a7eb57777ec7e5df9701abe4b9b4b005b8b971d62f59895c989ec385ad482a32 | 2f83830c189476b9c5afda6547c0e34637acf17140c72dab499948db0a271806 | e8b1f06b74ca1c9ef1d2156f31583413da332864fb958b8f4a32a6229fe6e444 |
cat-searcher/leandojo-benchmark-4-random | test | 3,159 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨hvr, hv0⟩ := hv | case mk.mk.intro.mk.mk.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂... | case mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433325) (:fv _uniq.401022) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":46649,"sourceStart":46643,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46653,"sourceStart":46650,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hvr","source... | [] | [{"source":"hv","source_end":46670,"source_start":46668,"syntax_kind":"ident"},{"source":"⟨hvr, hv0⟩","source_end":46664,"source_start":46650,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 101 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e89d07fe3bbcd8c58ebeb1f154362a8740705926db3206b6b0046c028289dba3 | e8b1f06b74ca1c9ef1d2156f31583413da332864fb958b8f4a32a6229fe6e444 | ae64fa64cd3b0a032fa0c1d5ada339bacc7b6da5c1cf725a973a26a1a9854c42 | 025f2d984385523e0a1f3f9996a6635637afc5d85ff6995234d34a3602007641 |
cat-searcher/leandojo-benchmark-4-random | test | 3,160 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>exists_nonneg_left_iff_sameRay</a> (<a>vsub_ne_zero</a>.2 hp₁p₂.symm)] at hvr | case mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {... | case mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433325) (:fv _uniq.401022) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":46679,"sourceStart":46677,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46681,"sourceStart":46680,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":46684,"sourceSt... | [] | [{"source":"hvr","source_end":46755,"source_start":46752,"syntax_kind":"ident"},{"source":"exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)","source_end":46747,"source_start":46685,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 102 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d592cf7e118ecaab1ccfa0ba7cfbe685ae2bc058bf6ecae3469983f309f0442f | 025f2d984385523e0a1f3f9996a6635637afc5d85ff6995234d34a3602007641 | b422b3cbb72adf9de65d249ea5ed2f07f775ef8eab2bd1353979b480f60e2cbf | a98c3a9dfd9457af15be0bc93e8976a467e09f174e2b8cc765fc6fd6ecb1b9f6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,161 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨r, -, rfl⟩ := hvr | case mk.mk.intro.mk.mk.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433325) (:fv _uniq.401022) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"obtain","sourceEnd":46768,"sourceStart":46762,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":46772,"sourceStart":46769,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"r","sourceEn... | [] | [{"source":"hvr","source_end":46791,"source_start":46788,"syntax_kind":"ident"},{"source":"⟨r, -, rfl⟩","source_end":46784,"source_start":46769,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 105 | exact | true | 1 | 26 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | af23d5a2426298e3d5bf747b78e930091a49771090c82d1a3796d5280da4e769 | a98c3a9dfd9457af15be0bc93e8976a467e09f174e2b8cc765fc6fd6ecb1b9f6 | 5082b3e4a278099e0785c453d156e424bde65a687436b61a061cf3d34132538c | d8bf6fe8761e394f13017982169bbc9689554a237fbf7a69d0046f1202ab22b4 |
cat-searcher/leandojo-benchmark-4-random | test | 3,162 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | change q ∈ line[ℝ, p₁, p₂] at hq | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433325) (:fv _uniq.401022) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"change","sourceEnd":46804,"sourceStart":46798,"tag":"atom"},{"children":[{"contextIndex":22,"semanticRole":"local","source":"q","sourceEnd":46806,"sourceStart":46805,"tag":"identifier"},{"source":"∈","sourceEnd":46810,"sourceStart":46807,"tag":"atom"},{"children":[{"source":"line[","sourceEnd":4... | [] | [{"source":"hq","source_end":46838,"source_start":46836,"syntax_kind":"ident"},{"source":"q ∈ line[ℝ, p₁, p₂]","source_end":46832,"source_start":46805,"syntax_kind":"«term_∈_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 106 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f617086a266aa6249264e7e255352d7a7eee3051898c47dc9e0ee35b8ca0e523 | d8bf6fe8761e394f13017982169bbc9689554a237fbf7a69d0046f1202ab22b4 | 79c8015f64dec01f80f74b9fd0434442c18488bb3fb60df38a775769575849ce | 5a354f923d0e67811fe80b75a95309f70f43d5e6b054b9a7b00364fb224273c3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,163 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent</a>] | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | ((:c And) ((:c Ne) (:c Real.Angle) ((:c EuclideanGeometry.oangle) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397344) (:fv _uniq.397357) (:fv _uniq.397360) (:fv _uniq.397648) (:fv _uniq.397905) (:fv _uniq.398598) (:fv _uniq.433325) (:fv _uniq.401022) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _un... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Real.Angle)) (:arg :explicit 1 (:app (:c EuclideanGeometry.oangle) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":46847,"sourceStart":46845,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":46849,"sourceStart":46848,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"EuclideanGeometr... | [] | [{"source":"oangle_ne_zero_and_ne_pi_iff_affineIndependent","source_end":46895,"source_start":46849,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 107 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 06b8bcd3cb4581bcc3a96dbc35843124142b73d7e107d95814dab6413bd9b349 | 5a354f923d0e67811fe80b75a95309f70f43d5e6b054b9a7b00364fb224273c3 | a8f891d490f161c8888e31b2f918640a72ae45d381e3e31d90ac047ab9976483 | 93632d361e612bb64033fac98d5072cdfabf8c211a13712786be7a45998c63af |
cat-searcher/leandojo-benchmark-4-random | test | 3,164 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>affineIndependent_of_ne_of_mem_of_not_mem_of_mem</a> ?_ hq (fun h => hc₅₁₂ ((<a>collinear_insert_iff_of_mem_affineSpan</a> h).2 (<a>collinear_pair</a> _ _ _))) ?_ | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : C... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_1
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | ((:c AffineIndependent) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.397338) (:c Real.normedField) ((:c NormedAddCommGroup.toSeminormedAddCommGroup) (:fv _uniq.397338) (:f... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c AffineIndependent) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (:c AddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 5 (:instan... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":46909,"sourceStart":46903,"tag":"atom"},{"children":[{"name":"affineIndependent_of_ne_of_mem_of_not_mem_of_mem","semanticRole":"global","source":"affineIndependent_of_ne_of_mem_of_not_mem_of_mem","sourceEnd":46958,"sourceStart":46910,"tag":"identifier"},{"children":[{"childre... | [] | [{"source":"affineIndependent_of_ne_of_mem_of_not_mem_of_mem ?_ hq\n (fun h => hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan h).2 (collinear_pair _ _ _))) ?_","source_end":47070,"source_start":46910,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 110 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f1518a6359aa2b24323f63fb7d26407e38d3cfcf9341535d602da1005c045908 | 93632d361e612bb64033fac98d5072cdfabf8c211a13712786be7a45998c63af | f3a62e5c372662337279b8d030032ec37f8af90b7c34ca35d76ba70ba0bf2eed | 9d43c7bea64efc751c917b7923ca236c21a326346ed14ebec451f50ec97e6dc6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,165 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← @<a>vsub_ne_zero</a> V, <a>vsub_vadd_eq_vsub_sub</a>, <a>vsub_self</a>, <a>zero_sub</a>, <a>neg_ne_zero</a>] | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_1
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | ((:c Ne) (:fv _uniq.397341) (:fv _uniq.433325) ((:c HVAdd.hVAdd) (:fv _uniq.397338) (:fv _uniq.397341) (:fv _uniq.397341) ((:c instHVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c AddAction.toVAdd) (:fv _uniq.397338) (:fv _uniq.397341) ((:c SubNegMonoid.toAddMonoid) (:fv _uniq.397338) ((:c AddGroup.toSubNegMonoid) (:f... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:fv FV22)) (:arg :explicit 2 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HVAdd) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":47083,"sourceStart":47080,"tag":"atom"},{"children":[{"source":"[","sourceEnd":47085,"sourceStart":47084,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":47088,"sourceStart":47085,"tag... | [] | [{"source":"@vsub_ne_zero V","source_end":47104,"source_start":47089,"syntax_kind":"Lean.Parser.Term.app"},{"source":"vsub_vadd_eq_vsub_sub","source_end":47127,"source_start":47106,"syntax_kind":"ident"},{"source":"vsub_self","source_end":47138,"source_start":47129,"syntax_kind":"ident"},{"source":"zero_sub","source_en... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 113 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08a7f253464286c74efce03a42fa11825496729dc102e60f59912aff5e84c737 | 1f1d73b232a5b1f44ec9be66074791c035c06454b1bf384f2b1bb0246987418a | 6e49665cebd53ae187e3a286e50e55f22c077e4de39923ca38d986bde2ace625 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,166 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>AffineSubspace.vadd_mem_of_mem_direction</a> ?_ hq | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | ((:c Membership.mem) (:fv _uniq.397341) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) ((:c DivisionRing.toRing) (:c Real) (:c Real.instDivisionRing)) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.397338) (:c Real.nor... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c Ring) (:arg :explicit 0 (:c Real))))) (:arg :instance 4 (:instance-of (:app (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":47178,"sourceStart":47172,"tag":"atom"},{"children":[{"name":"AffineSubspace.vadd_mem_of_mem_direction","semanticRole":"global","source":"vadd_mem_of_mem_direction","sourceEnd":47204,"sourceStart":47179,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":4... | [] | [{"source":"vadd_mem_of_mem_direction ?_ hq","source_end":47210,"source_start":47179,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 126 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b913c9884b7f01e108c34dab08ee7ba46cae460cff986f5dbcb9fc2f4cecd18e | 85024375cb1e970fbea7991319f1b9e1b4b225a1f27b57ee35b706c4c6f20442 | b68755fb937e23e21a98976b7f58318220221e59fe6cedb43c3873dd9d4d5442 | 47fc0f5442590ad333b80af098f2dacfa59f49f3a63c28716daa277df09b62a3 |
cat-searcher/leandojo-benchmark-4-random | test | 3,167 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>direction_affineSpan</a>] | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) (:c Real.instRing)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.3... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"rw","sourceEnd":47221,"sourceStart":47219,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":47223,"sourceStart":47222,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"direction_affine... | [] | [{"source":"direction_affineSpan","source_end":47243,"source_start":47223,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 127 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50458d7503c49d81c00000e3bcc576d098d6806dd5e9ac46d30dd3955df36d22 | 47fc0f5442590ad333b80af098f2dacfa59f49f3a63c28716daa277df09b62a3 | 83a0700cae12d67c7683a2782a7e56db979267ea8e209c71d3acfadc4b2e987c | 03f5ea98a184f3a53819a9aa571b5d71ed909abf019e88d194793d13887f6395 |
cat-searcher/leandojo-benchmark-4-random | test | 3,168 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>smul_vsub_rev_mem_vectorSpan_pair</a> _ _ _ | case mk.mk.intro.mk.mk.intro.intro.intro.intro.intro.intro.refine_2
V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ ... | ((:c Membership.mem) (:fv _uniq.397338) ((:c Submodule) (:c Real) (:fv _uniq.397338) ((:c Ring.toSemiring) (:c Real) (:c Real.instRing)) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.397338) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344))) ((:c NormedSpace.toModule) (:c Real) (:fv _uniq.3... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Submodule) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Real))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"exact","sourceEnd":47258,"sourceStart":47253,"tag":"atom"},{"children":[{"name":"smul_vsub_rev_mem_vectorSpan_pair","semanticRole":"global","source":"smul_vsub_rev_mem_vectorSpan_pair","sourceEnd":47292,"sourceStart":47259,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":4... | [] | [{"source":"smul_vsub_rev_mem_vectorSpan_pair _ _ _","source_end":47298,"source_start":47259,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 130 | exact | true | 1 | 25 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5bc50f28289bdbd91d3bb9417b756d4f258926c37f2d5fc9f2d30280fc117d31 | 03f5ea98a184f3a53819a9aa571b5d71ed909abf019e88d194793d13887f6395 | 995f65b60c52631599367c73df2cd75fdede6ffb653ae67d4251683a7f6bf960 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,169 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_setOf</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341))) ((:c Set) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)))) ((:c Prod.mk) (:fv ... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c P... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":47365,"sourceStart":47358,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":47367,"sourceStart":47366,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"... | [] | [{"source":"s","source_end":47368,"source_start":47367,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":47383,"source_start":47370,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":47397,"source_start":47385,"syntax_kind":"ident"},{"source":"Set.mem_setOf","source_end":47412,"source_start":47399... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 133 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6cf11776e645868bb31d3f1470df0107fedcafc5d1ab8c2a21f161ecd46fdfed | 9229709cb6e9a13dec53c06acf90739c4464fe5c0ec1ac57edcbf2f7f6b2edd1 | f06d045d689590c8ef15df3da48c70615aeee34e160ef92d57e38d78afbefc85 | 0cf8f1f60f785299a50ba6e7c4cdf7a8c2016629d79298a16a615d69bdc63df7 |
cat-searcher/leandojo-benchmark-4-random | test | 3,170 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨⟨p₁, <a>left_mem_affineSpan_pair</a> ℝ _ _⟩, p₂ -ᵥ p₁⟩, ⟨<a>SameRay.rfl</a>, <a>vsub_ne_zero</a>.2 hp₁p₂.symm⟩, ?_⟩ | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c Exists) ((:c Prod) ((:c Subtype) (:fv _uniq.397341) (:lambda x (:fv _uniq.397341) ((:c Membership.mem) (:fv _uniq.397341) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule)... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":47476,"sourceStart":47470,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":47480,"sourceStart":47477,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":47483,"sourceStart":47480,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":47486,"source... | [] | [{"source":"⟨⟨⟨p₁, left_mem_affineSpan_pair ℝ _ _⟩, p₂ -ᵥ p₁⟩,\n ⟨SameRay.rfl, vsub_ne_zero.2 hp₁p₂.symm⟩, ?_⟩","source_end":47611,"source_start":47477,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 142 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 604b73581714c849f66d58570504435e050ae92657ef7165219985897da9c44e | 0cf8f1f60f785299a50ba6e7c4cdf7a8c2016629d79298a16a615d69bdc63df7 | 86cef9b9730164cb58aaf47cd8c4b9f2c2b7ff4fe9de4c77bfc6b534a6f83d04 | f04c0133e5e874da5e5e4b48298d587b41602bbce006cca2fbbe007376840b7a |
cat-searcher/leandojo-benchmark-4-random | test | 3,171 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c And) ((:c Eq) (:fv _uniq.397341) ((:c Subtype.val) (:fv _uniq.397341) (:lambda x (:fv _uniq.397341) ((:c Membership.mem) (:fv _uniq.397341) ((:c Set) (:fv _uniq.397341)) ((:c Set.instMembership) (:fv _uniq.397341)) 0 ((:c SetLike.coe) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) (:c Real.in... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Prod.fst) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":47622,"sourceStart":47618,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 143 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 058dde31d47b44f23d225d4c71b91b6f036fb4c9daef25f5eb6f68ae3510ce30 | f04c0133e5e874da5e5e4b48298d587b41602bbce006cca2fbbe007376840b7a | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,172 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [s, <a>Set.mem_image</a>, <a>Set.mem_prod</a>, <a>Set.mem_setOf</a>, <a>Set.mem_univ</a>, <a>true_and_iff</a>, <a>Prod.ext_iff</a>] | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c Membership.mem) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341))) ((:c Set) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)))) ((:c Set.instMembership) ((:c Prod) (:fv _uniq.397341) ((:c Prod) (:fv _uniq.397341) (:fv _uniq.397341)))) ((:c Prod.mk) (:fv ... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV1)))))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c P... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp_rw","sourceEnd":47689,"sourceStart":47682,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":47691,"sourceStart":47690,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":19,"... | [] | [{"source":"s","source_end":47692,"source_start":47691,"syntax_kind":"ident"},{"source":"Set.mem_image","source_end":47707,"source_start":47694,"syntax_kind":"ident"},{"source":"Set.mem_prod","source_end":47721,"source_start":47709,"syntax_kind":"ident"},{"source":"Set.mem_setOf","source_end":47736,"source_start":47723... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 146 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 97c7d08165db1477307214e1c0b935d18d3c60eb0c7291e21996a17013c8eb08 | 3ad29e19e62f5bfa1f7c01114088f50158398278e790f5f07e0ca25abd626c96 | f06d045d689590c8ef15df3da48c70615aeee34e160ef92d57e38d78afbefc85 | 967d841e17410aac25cc229f183e059b8eef8a97975b298c786d50f76e9c6c3b |
cat-searcher/leandojo-benchmark-4-random | test | 3,173 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨⟨⟨p₃, hc.mem_affineSpan_of_mem_of_ne (<a>Set.mem_insert</a> _ _) (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert</a> _ _)) (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert_of_mem</a> _ (<a>Set.mem_insert</a> _ _))) hp₁p₂⟩, p₄ -ᵥ p₃⟩, ⟨hr, <a>vsub_ne_zero</a>.2 hp₃p₄.symm⟩, ?_⟩ | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c Exists) ((:c Prod) ((:c Subtype) (:fv _uniq.397341) (:lambda x (:fv _uniq.397341) ((:c Membership.mem) (:fv _uniq.397341) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) (:c Real.instRing) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.397338) (:fv _uniq.397344)) ((:c NormedSpace.toModule)... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :explicit (:fv FV1) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c AffineSubspace) (:arg :explicit 0 (:c Real)) (:arg... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"refine","sourceEnd":47800,"sourceStart":47794,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":47804,"sourceStart":47801,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":47807,"sourceStart":47804,"tag":"atom"},{"children":[{"children":[{"source":"⟨","sourceEnd":47810,"source... | [] | [{"source":"⟨⟨⟨p₃, hc.mem_affineSpan_of_mem_of_ne (Set.mem_insert _ _)\n (Set.mem_insert_of_mem _ (Set.mem_insert _ _))\n (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_insert _ _))) hp₁p₂⟩, p₄ -ᵥ p₃⟩,\n ⟨hr, vsub_ne_zero.2 hp₃p₄.symm⟩, ?_⟩","source_end":48091,"source_start":47801,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 155 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 70fdb8e35cae08da8a141f175a6c711472db7ae5c8fdbe206b18c0d8a110c32e | 967d841e17410aac25cc229f183e059b8eef8a97975b298c786d50f76e9c6c3b | 65635474c207ed362f97564be69e5912c535d79f07f2d4be9b911aa347fbdea7 | 7f9725b87237919565cc37287d4ac56364f27d48f4d85bc53a7d3391d32bb8da |
cat-searcher/leandojo-benchmark-4-random | test | 3,174 | Collinear.oangle_sign_of_sameRay_vsub | Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | V : Type u_1
P : Type u_2
inst✝⁴ : NormedAddCommGroup V
inst✝³ : InnerProductSpace ℝ V
inst✝² : MetricSpace P
inst✝¹ : NormedAddTorsor V P
hd2 : Fact (finrank ℝ V = 2)
inst✝ : Module.Oriented ℝ V (Fin 2)
p₁ p₂ p₃ p₄ p₅ : P
hp₁p₂ : p₁ ≠ p₂
hp₃p₄ : p₃ ≠ p₄
hc : Collinear ℝ {p₁, p₂, p₃, p₄}
hr : SameRay ℝ (p₂ -ᵥ p₁) (p₄ -... | ((:c And) ((:c Eq) (:fv _uniq.397341) ((:c Subtype.val) (:fv _uniq.397341) (:lambda x (:fv _uniq.397341) ((:c Membership.mem) (:fv _uniq.397341) ((:c Set) (:fv _uniq.397341)) ((:c Set.instMembership) (:fv _uniq.397341)) 0 ((:c SetLike.coe) ((:c AffineSubspace) (:c Real) (:fv _uniq.397338) (:fv _uniq.397341) (:c Real.in... | [{"name":"V","sexp":"(:sort (+ u_1 1))"},{"name":"P","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁴","sexp":"((:c NormedAddCommGroup) (:fv _uniq.397338))"},{"name":"inst✝³","sexp":"((:c InnerProductSpace) (:c Real) (:fv _uniq.397338) (:c Real.RCLike) (:fv _uniq.397344))"},{"name":"inst✝²","sexp":"((:c MetricSpace) (:fv _u... | (:app (:c And) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c Prod.fst) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:lambda x :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"name":"P","sexp":"(:sort Type)"},{"binder_role":":instance-imp... | {"children":[{"source":"simp","sourceEnd":48102,"sourceStart":48098,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.397338","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.397341","is_instance":false,"is_let":false,"user_name":"P"},{"binder_role":":instance-implicit","context_index":2,"internal... | 189 | 156 | exact | true | 1 | 23 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae618b2993e26bee9e460102dc95c19b32a53e662dc1161bd18eecebe36f4b9f | 7f9725b87237919565cc37287d4ac56364f27d48f4d85bc53a7d3391d32bb8da | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,175 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro F hF r hr | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
⊢ μ.InnerRegularWRT p MeasurableSet | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c MeasureTheory.Measure.InnerRegularWRT) (:fv _uniq.92228) (:fv _uniq.92234) (:fv _uniq.92673) (:fv _uniq.92250) ((:c MeasurableSet) (:fv _uniq.92228) (:fv _uniq.92234))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c MeasureTheory.Measure.InnerRegularWRT) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV12)) (:arg :explicit 3 (:fv FV5)) (:arg :explicit 4 (:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"intro","sourceEnd":32154,"sourceStart":32149,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"F","sourceEnd":32156,"sourceStart":32155,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hF","sourceEnd":32159,"sourceStart":32157,"tag":"identifier"},{"semanticRole":"sc... | [{"role":"fresh_name","source":"F","source_end":32156,"source_start":32155,"syntax_kind":"ident"},{"role":"fresh_name","source":"hF","source_end":32159,"source_start":32157,"syntax_kind":"ident"},{"role":"fresh_name","source":"r","source_end":32161,"source_start":32160,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 4 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4dc32fcf64b3b395e390847e112e0dbea0791eedbdf6528ab11fd7b074509c0d | 3f49f887710adc95eb06cfac5bf65b76387620136f2c3d634f34946064823e39 | 0d90c8cf1f645ec703730178c10b233ed00bcb1781f8df75fe7da3d37510252a | c999520fdbddfc399011cd283fcf3166a6d74504b19ab361b22afdf1ceb17c16 |
cat-searcher/leandojo-benchmark-4-random | test | 3,176 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hBU : ⋃ n, F ∩ s n = F := by rw [← <a>Set.inter_iUnion</a>, univ_subset_iff.mp hs, <a>Set.inter_univ</a>] | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":32171,"sourceStart":32167,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hBU","sourceEnd":32175,"sourceStart":32172,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hBU","sourceEnd":32175,"sourceStart":32172,"tag":"n... | [] | [{"source":"⋃ n, F ∩ s n = F","source_end":32198,"source_start":32178,"syntax_kind":"«term_=_»"},{"source":"inter_iUnion","source_end":32226,"source_start":32214,"syntax_kind":"ident"},{"source":"univ_subset_iff.mp hs","source_end":32249,"source_start":32228,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inter_univ",... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 5 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d600926b18de02c0de1b29054c82b172a96e5ee2b5806e41e062a25f065a2035 | c999520fdbddfc399011cd283fcf3166a6d74504b19ab361b22afdf1ceb17c16 | 84e91ffe20b088d04d47b4c1927cf27914d7e868ce38baa920f2d8ab48bdffc6 | 2a66b5779bdf9e637811b03ecba0ed2d3c2f3c6803163fb1fddd0184cefbd46c |
cat-searcher/leandojo-benchmark-4-random | test | 3,177 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : μ F = ⨆ n, μ (F ∩ s n) := by rw [← <a>MeasureTheory.measure_iUnion_eq_iSup</a>, hBU] exact <a>Monotone.directed_le</a> fun m n h ↦ <a>Set.inter_subset_inter_right</a> _ (hmono h) | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":32269,"sourceStart":32265,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":32270,"sourceStart":32270,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":32270,"sourceStart":32270,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"μ F = ⨆ n, μ (F ∩ s n)","source_end":32300,"source_start":32272,"syntax_kind":"«term_=_»"},{"source":"measure_iUnion_eq_iSup","source_end":32341,"source_start":32319,"syntax_kind":"ident"},{"source":"hBU","source_end":32346,"source_start":32343,"syntax_kind":"ident"},{"source":"Monotone.directed_le fun m n ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 12 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b71f37635b21bc8660ffe815d69d7ccfba5308e80a85f98e6504b145ff2f14e | 2a66b5779bdf9e637811b03ecba0ed2d3c2f3c6803163fb1fddd0184cefbd46c | 62b9b6709c0cbae809b2071b2a7db0b49b3701aca1ad5bd4d13b8fe677aafbc1 | d51ada0413da4ee6c0b181f665d3dace3ac00efebe6f1300086903cab9350f3c |
cat-searcher/leandojo-benchmark-4-random | test | 3,178 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] at hr | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":32434,"sourceStart":32432,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32436,"sourceStart":32435,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":22,"seman... | [] | [{"source":"this","source_end":32440,"source_start":32436,"syntax_kind":"ident"},{"source":"hr","source_end":32447,"source_start":32445,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 19 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6d184e39f3b2daa7979180dce41791e66a2c63f984599d664e571cdad707408 | d51ada0413da4ee6c0b181f665d3dace3ac00efebe6f1300086903cab9350f3c | 05e36f9d6c7cfbeb97c89fd6ea657ad63d6a9be1576d9c5df3c4910a8416d1ec | 049fd1d0ec16d7552851d432fa6c707fa479c283922e474472ee48bd546ab7d6 |
cat-searcher/leandojo-benchmark-4-random | test | 3,179 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>lt_iSup_iff</a>.1 hr with ⟨n, hn⟩ | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | case intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":32456,"sourceStart":32450,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"name":"lt_iSup_iff","semanticRole":"global","source":"lt_iSup_iff","sourceEnd":32468,"sourceStart":32457,"tag":"identifier"},{"... | [] | [{"source":"lt_iSup_iff.1 hr","source_end":32473,"source_start":32457,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨n, hn⟩","source_end":32490,"source_start":32479,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 22 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9950e4a2d697c260dc565c0dc10ed2144f3fc73bda2ea085cb0b142c945d2f31 | 049fd1d0ec16d7552851d432fa6c707fa479c283922e474472ee48bd546ab7d6 | 8c4ce073f882fbf6085ece27d3a8b1cb33b38323728bb5cc3bfbe6b885d86edb | 4b581ea1cb1ec59366ea697a531514a171498ce6105c505ab374381e897479e2 |
cat-searcher/leandojo-benchmark-4-random | test | 3,180 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.Measure.restrict_apply</a> hF] at hn | case intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ... | case intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":32495,"sourceStart":32493,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32497,"sourceStart":32496,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32500,"sourceSt... | [] | [{"source":"hn","source_end":32525,"source_start":32523,"syntax_kind":"ident"},{"source":"restrict_apply hF","source_end":32518,"source_start":32501,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 23 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6cf64c15b3b8c7a4a57d90188a503d13a8652a5dd484237e15df16c2d5e1f3ca | 4b581ea1cb1ec59366ea697a531514a171498ce6105c505ab374381e897479e2 | 00825519022c7d9e92f30cfd68d060a37f9239439e6d7aaa4c10e0ec173d4c86 | 71c26e507946a10e9c2c0d4a539689e6d1aa08b7a5a84cfdddc41fcfb97ac12a |
cat-searcher/leandojo-benchmark-4-random | test | 3,181 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases h n hF _ hn with ⟨K, KF, hKp, hK⟩ | case intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ... | case intro.intro.intro.intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : Mea... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":32534,"sourceStart":32528,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"h","sourceEnd":32536,"sourceStart":32535,"tag":"identifier"},{"children":[{"contextIndex":... | [] | [{"source":"h n hF _ hn","source_end":32546,"source_start":32535,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨K, KF, hKp, hK⟩","source_end":32572,"source_start":32552,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 26 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 46d533bf5dddbf764b3b0ad8bd189e47aa233b563039dae4ef25fbac62e343e7 | 71c26e507946a10e9c2c0d4a539689e6d1aa08b7a5a84cfdddc41fcfb97ac12a | 546206fe85bbefd8972f09afd2c10fc02e505e7e59380e8e86061894aa5bcc8f | 72c036b6dcceb16cfb45b28ab7cf40d02839ea5fd1588bddf81050dce937b73e |
cat-searcher/leandojo-benchmark-4-random | test | 3,182 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨K, KF, hKp, hK.trans_le (<a>MeasureTheory.Measure.restrict_apply_le</a> _ _)⟩ | case intro.intro.intro.intro
α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : Mea... | ((:c Exists) ((:c Set) (:fv _uniq.92228)) (:lambda K ((:c Set) (:fv _uniq.92228)) ((:c And) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.92228)) ((:c Set.instHasSubset) (:fv _uniq.92228)) 0 (:fv _uniq.92681)) ((:c And) ((:fv _uniq.92250) 0) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPr... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda K :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":32580,"sourceStart":32575,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":32584,"sourceStart":32581,"tag":"atom"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"K","sourceEnd":32585,"sourceStart":32584,"tag":"identifier"},{"source":",","sourceEnd":32586,... | [] | [{"source":"⟨K, KF, hKp, hK.trans_le (restrict_apply_le _ _)⟩","source_end":32634,"source_start":32581,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 27 | exact | true | 1 | 28 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 13f7ce45bda6d4f77afb95db165f06608702b2c2e8c055b9d3515c4f9eaeefd7 | 72c036b6dcceb16cfb45b28ab7cf40d02839ea5fd1588bddf81050dce937b73e | 239077c94506611cccd80edfa332fa9ce7b7cb4f35fd2e9bb1b326e07098f614 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,183 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Set.inter_iUnion</a>, univ_subset_iff.mp hs, <a>Set.inter_univ</a>] | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c Eq) ((:c Set) (:fv _uniq.92228)) ((:c Set.iUnion) (:fv _uniq.92228) (:c Nat) (:lambda n (:c Nat) ((:c Inter.inter) ((:c Set) (:fv _uniq.92228)) ((:c Set.instInter) (:fv _uniq.92228)) (:fv _uniq.92681) ((:fv _uniq.92674) 0)))) (:fv _uniq.92681)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:c Nat)) (:arg :explicit 2 (:lambda n :explicit (:c Nat) (:app (:c Inter.inter) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":32208,"sourceStart":32206,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32210,"sourceStart":32209,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32213,"sourceSt... | [] | [{"source":"inter_iUnion","source_end":32226,"source_start":32214,"syntax_kind":"ident"},{"source":"univ_subset_iff.mp hs","source_end":32249,"source_start":32228,"syntax_kind":"Lean.Parser.Term.app"},{"source":"inter_univ","source_end":32261,"source_start":32251,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 7 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dc7cd31e66d316feb293550ce42d73f5f6c9bdb9bdbd212c4896842a713226fc | 4c17c35c9660201e7dc08320ea594b29a5920e1f38ab9654a19731d58d876099 | 522ebdd9a8fd2295b10220651aa3a0606535f0fe8a70428d9288694d87884e0c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 3,184 | MeasureTheory.Measure.InnerRegularWRT.of_restrict | Mathlib/MeasureTheory/Measure/Regular.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>MeasureTheory.measure_iUnion_eq_iSup</a>, hBU] | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | α : Type u_1
β : Type u_2
inst✝¹ : MeasurableSpace α
inst✝ : TopologicalSpace α
μ✝ : Measure α
p q : Set α → Prop
U s✝ : Set α
ε r✝ : ℝ≥0∞
μ : Measure α
s : ℕ → Set α
h : ∀ (n : ℕ), (μ.restrict (s n)).InnerRegularWRT p MeasurableSet
hs : univ ⊆ ⋃ n, s n
hmono : Monotone s
F : Set α
hF : MeasurableSet F
r : ℝ≥0∞
hr : r ... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234)) ((:c Set) (:fv _uniq.92228)) (:lambda _ ((:c Set) (:fv _uniq.92228)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.92228) (:fv _uniq.92234)) (:fv _uniq.92673) (:fv _uniq.92681)) ((:c iSup) (:c EN... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c MeasurableSpace) (:fv _uniq.92228))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.92228))"},{"name":"μ✝","sexp":"((:c MeasureTheory.Measure) (:fv _uniq.92228) (:fv _uniq.92234))"},{"name":"p","se... | (: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.92228","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rw","sourceEnd":32313,"sourceStart":32311,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32315,"sourceStart":32314,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32318,"sourceSt... | [] | [{"source":"measure_iUnion_eq_iSup","source_end":32341,"source_start":32319,"syntax_kind":"ident"},{"source":"hBU","source_end":32346,"source_start":32343,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.92228","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.92231","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 66 | 14 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9423447120e30c3f4a7af8a8db90f770a9dd280493769cf48f928104aab2953d | 41044873163fa79975e3fa2ee8f972828d8c51082e3f654fd44289b8e31770bc | 2d7cfa9a9fbe813871fd87e7ae903770c4e97841d9adcd5ed9fc5a7748ed39c7 | 55ceaac86f1f0d72174e03c857fa0bad0879f86cfdc8660ffb2b44dbb664a423 |
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