dataset stringclasses 1
value | split stringclasses 1
value | row_index int64 0 4.5k | theorem stringlengths 7 81 | file_path stringclasses 723
values | repo_url stringclasses 1
value | repo_commit stringclasses 1
value | tactic stringlengths 3 2.13k | text_state stringlengths 7 2.31k | text_target_state stringlengths 0 4.07k | raw_goal_sexp stringlengths 10 11.8M | raw_hyp_sexps stringlengths 2 15.6M | model_goal_sexp stringlengths 10 2.68M | model_hyp_sexps stringlengths 2 3.62M | source_syntax stringlengths 179 164k | syntax_args stringclasses 256
values | term_ranges stringlengths 2 6.01k | local_context stringlengths 2 10.3k | unit_index int64 3 1.26k | invocation_index int64 0 357 | alignment_kind stringclasses 2
values | target_state_matches_invocation bool 2
classes | pending_goal_count int64 1 1 | hypothesis_count int64 0 77 | hypothesis_names_match bool 2
classes | raw_schema_version int64 4 4 | raw_extractor_version stringclasses 1
value | model_schema_version int64 2 2 | model_normalization stringclasses 1
value | trace_schema_version int64 3 3 | trace_extractor_version stringclasses 1
value | pantograph_commit stringclasses 1
value | model_pantograph_commit stringclasses 1
value | raw_record_sha256 stringlengths 64 64 | state_sha256 stringlengths 64 64 | tactic_sha256 stringlengths 64 64 | target_state_sha256 stringlengths 64 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cat-searcher/leandojo-benchmark-4-random | test | 4,210 | EReal.image_coe_Iio | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>Set.image_comp</a> <a>WithBot.some</a> <a>WithTop.some</a> _).<a>Eq.trans</a> ?_ | x : ℝ
⊢ Real.toEReal '' Iio x = Ioo ⊥ ↑x | x : ℝ
⊢ WithBot.some '' (WithTop.some '' Iio x) = Ioo ⊥ ↑x | ((:c Eq) ((:c Set) (:c EReal)) ((:c Set.image) (:c Real) (:c EReal) (:c Real.toEReal) ((:c Set.Iio) (:c Real) (:c Real.instPreorder) (:fv _uniq.35697))) ((:c Set.Ioo) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder)) ((:c Bot.bot) (:c EReal) (:c instERealBot)) ((:c Real.toEReal) (:fv _uniq... | [{"name":"x","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:c EReal)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c EReal)) (:arg :explicit 2 (:c Real.toEReal)) (:arg :explicit 3 (:app (:c Set.Iio) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}] | {"children":[{"source":"refine","sourceEnd":17681,"sourceStart":17675,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":17683,"sourceStart":17682,"tag":"atom"},{"children":[{"name":"Set.image_comp","semanticRole":"global","source":"image_comp","sourceEnd":17693,"sourceStart":17683,"tag":"id... | [] | [{"source":"(image_comp WithBot.some WithTop.some _).trans ?_","source_end":17731,"source_start":17682,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"user_name":"x"}] | 141 | 4 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fb4be868d9a7e4ad1765db316fb82ae25b4992d7e8ea1712cc2c5cd1386c4e61 | 5fd55ade668a949e4c137b226937e6cf541152a4a9d29cb0e5393e309792f24e | 9c42e1a95084337b5905c1e6a2202a5ef78071a20c68b60fd10453a7a7e8ba41 | ae54679d9f04bbf077c464abeaab92eb2caba7d960f061df83ade43d30efc617 |
cat-searcher/leandojo-benchmark-4-random | test | 4,211 | EReal.image_coe_Iio | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>WithTop.image_coe_Iio</a>, <a>WithBot.image_coe_Iio</a>] | x : ℝ
⊢ WithBot.some '' (WithTop.some '' Iio x) = Ioo ⊥ ↑x | x : ℝ
⊢ Ioo ⊥ ↑↑x = Ioo ⊥ ↑x | ((:c Eq) ((:c Set) ((:c WithBot) ((:c WithTop) (:c Real)))) ((:c Set.image) ((:c WithTop) (:c Real)) ((:c WithBot) ((:c WithTop) (:c Real))) ((:c WithBot.some) ((:c WithTop) (:c Real))) ((:c Set.image) (:c Real) ((:c WithTop) (:c Real)) ((:c WithTop.some) (:c Real)) ((:c Set.Iio) (:c Real) (:c Real.instPreorder) (:fv _... | [{"name":"x","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:app (:c WithTop) (:arg :explicit 0 (:c Real)))))))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:app (:c WithTop) (:arg :explicit 0 (:c Real)))) (:arg :implicit-type 1 (:app (:c WithBot) (:arg... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}] | {"children":[{"source":"rw","sourceEnd":17736,"sourceStart":17734,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":17738,"sourceStart":17737,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"WithTop.image_co... | [] | [{"source":"WithTop.image_coe_Iio","source_end":17759,"source_start":17738,"syntax_kind":"ident"},{"source":"WithBot.image_coe_Iio","source_end":17782,"source_start":17761,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"user_name":"x"}] | 141 | 5 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 583404e29675028f851a13f25948066134d28ecbbdb3b6a223158d0376906dde | ae54679d9f04bbf077c464abeaab92eb2caba7d960f061df83ade43d30efc617 | e0579bb764f6c06141b78b0f8005d6616444d64f3474a7edd2def62a4b522e7c | 3d4ff9ec9b4c6fb04fb0517fa02b81d31f456c080b4af4fbbab50f6767a4be68 |
cat-searcher/leandojo-benchmark-4-random | test | 4,212 | EReal.image_coe_Iio | Mathlib/Data/Real/EReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | x : ℝ
⊢ Ioo ⊥ ↑↑x = Ioo ⊥ ↑x | ((:c Eq) ((:c Set) ((:c WithBot) ((:c WithTop) (:c Real)))) ((:c Set.Ioo) ((:c WithBot) ((:c WithTop) (:c Real))) ((:c WithBot.preorder) ((:c WithTop) (:c Real)) ((:c WithTop.preorder) (:c Real) (:c Real.instPreorder))) ((:c Bot.bot) ((:c WithBot) ((:c WithTop) (:c Real))) ((:c WithBot.bot) ((:c WithTop) (:c Real)))) (... | [{"name":"x","sexp":"(:c Real)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c WithBot) (:arg :explicit 0 (:app (:c WithTop) (:arg :explicit 0 (:c Real)))))))) (:arg :explicit 1 (:app (:c Set.Ioo) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:app (:c WithTop) (:arg :explicit 0 (:c Real)))))) (:arg :ins... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"}] | {"children":[{"source":"rfl","sourceEnd":17789,"sourceStart":17786,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":17789,"sourceStart":17786,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.35697","is_instance":false,"is_let":false,"user_name":"x"}] | 141 | 9 | exact | true | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce8aa8cd21cdce20dbec614e91e2e0e5d048418d148d941152e133a32f479aaf | 3d4ff9ec9b4c6fb04fb0517fa02b81d31f456c080b4af4fbbab50f6767a4be68 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,213 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (atTop_basis_Ioi.tendsto_iff (<a>Filter.atTop_basis'</a> 1)).2 fun C hC₁ => ?_ | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
⊢ Tendsto (fun x => rexp x / x ^ n) atTop atTop | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | ((:c Filter.Tendsto) (:c Real) (:c Real) (:lambda x (:c Real) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) 0) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Filter.Tendsto) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :explicit 2 (:lambda x :explicit (:c Real) (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"refine","sourceEnd":9988,"sourceStart":9982,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":9990,"sourceStart":9989,"tag":"atom"},{"children":[{"source":"atTop_basis_Ioi.tendsto_iff","sourceEnd":10017,"sourceStart":9990,"tag":"identifier"},{"children":[{"children":... | [] | [{"source":"(atTop_basis_Ioi.tendsto_iff (atTop_basis' 1)).2 fun C hC₁ => ?_","source_end":10055,"source_start":9989,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1da6ce6008c265c78f89e61a2a7104d53a2924153e47c31894fea79fdf68114d | 1179fd631f8864781e126694b5f0d60f18172cfd09995d877bea8593bcdaf441 | f439af88962c551ade0678da0490545874663671169555ac4706a38ddf4cadfb | 14c6b0958a03f1d7ab8fe5589579336f4a70d13446b1bb1925e394c4ad62c3be |
cat-searcher/leandojo-benchmark-4-random | test | 4,214 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hC₀ : 0 < C := zero_lt_one.trans_le hC₁ | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | ((:c Exists) (:c Real) (:lambda ia (:c Real) ((:c And) (:c True) (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ioi) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilattic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda ia :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:c True)) (:arg :explicit 1 (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"have","sourceEnd":10062,"sourceStart":10058,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hC₀","sourceEnd":10068,"sourceStart":10063,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hC₀","sourceEnd":10068,"sourceStart":10063,"tag":"n... | [] | [{"source":"0 < C","source_end":10076,"source_start":10071,"syntax_kind":"«term_<_»"},{"source":"zero_lt_one.trans_le hC₁","source_end":10106,"source_start":10080,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 088c81c0b5bb683940956796e5cc9638b95451cacfd18c3f3745f2085c1c90cd | 14c6b0958a03f1d7ab8fe5589579336f4a70d13446b1bb1925e394c4ad62c3be | 76b4af85002195682203aa96310dba0e9b41fb6ab42cc2d67d3424a5b4be2af5 | a3ff6c5f989b433c5d92c736b4935d5f11fbb6327d9ef14bd4ddecc446f65058 |
cat-searcher/leandojo-benchmark-4-random | test | 4,215 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : 0 < (<a>Real.exp</a> 1 * C)⁻¹ := <a>inv_pos</a>.2 (<a>mul_pos</a> (<a>Real.exp_pos</a> _) hC₀) | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | ((:c Exists) (:c Real) (:lambda ia (:c Real) ((:c And) (:c True) (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ioi) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilattic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda ia :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:c True)) (:arg :explicit 1 (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"have","sourceEnd":10113,"sourceStart":10109,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":10114,"sourceStart":10114,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":10114,"sourceStart":10114,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"0 < (exp 1 * C)⁻¹","source_end":10136,"source_start":10116,"syntax_kind":"«term_<_»"},{"source":"inv_pos.2 (mul_pos (exp_pos _) hC₀)","source_end":10177,"source_start":10140,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 6 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cb781afa10633332ea5015d4224303a7b45513a9af61a5f97f34e9fc5d56dad0 | a3ff6c5f989b433c5d92c736b4935d5f11fbb6327d9ef14bd4ddecc446f65058 | 38cbb3234d38a052452abf249444bfee938b8632ff0e1ef72d30fbd6a4c9aee0 | 68477d269c2e498d29b16848d31ea43071c17cb52ec1969e741f46b0a3abf319 |
cat-searcher/leandojo-benchmark-4-random | test | 4,216 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨N, hN⟩ : ∃ N : ℕ, ∀ k ≥ N, (↑k : ℝ) ^ n / <a>Real.exp</a> 1 ^ k < (<a>Real.exp</a> 1 * C)⁻¹ := <a>Filter.eventually_atTop</a>.1 ((<a>tendsto_pow_const_div_const_pow_of_one_lt</a> n (<a>Real.one_lt_exp_iff</a>.2 <a>zero_lt_one</a>)).<a>Filter.Tendsto.eventually</a> (<a>gt_mem_nhds</a> this)) | α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n / rexp 1 ^ k < (rexp 1 * C)⁻¹
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | ((:c Exists) (:c Real) (:lambda ia (:c Real) ((:c And) (:c True) (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ioi) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilattic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda ia :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:c True)) (:arg :explicit 1 (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"obtain","sourceEnd":10186,"sourceStart":10180,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":10190,"sourceStart":10187,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"N","sourceEn... | [] | [{"source":"∃ N : ℕ, ∀ k ≥ N, (↑k : ℝ) ^ n / exp 1 ^ k < (exp 1 * C)⁻¹","source_end":10274,"source_start":10201,"syntax_kind":"«term∃_,_»"},{"source":"eventually_atTop.1\n ((tendsto_pow_const_div_const_pow_of_one_lt n (one_lt_exp_iff.2 zero_lt_one)).eventually\n (gt_mem_nhds this))","source_end":10423,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 96826f06307453f10aabf438de35581a53862970300f85b588ce6f4c8a170168 | 68477d269c2e498d29b16848d31ea43071c17cb52ec1969e741f46b0a3abf319 | fb242a750933a68c931c4388406936b3a3360e9867080392a67df26c23546377 | 294da3495900181c3b6f45bc11b274f3c659f6e9fbe3e3b5963b823cdd6458e4 |
cat-searcher/leandojo-benchmark-4-random | test | 4,217 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Real.exp_nat_mul</a>, <a>mul_one</a>, <a>div_lt_iff</a>, <a>Real.exp_pos</a>, ← <a>div_eq_inv_mul</a>] at hN | case intro
α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n / rexp 1 ^ k < (rexp 1 * C)⁻¹
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | ((:c Exists) (:c Real) (:lambda ia (:c Real) ((:c And) (:c True) (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ioi) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilattic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda ia :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:c True)) (:arg :explicit 1 (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"simp","sourceEnd":10430,"sourceStart":10426,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10435,"sourceStart":10431,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":104... | [] | [{"source":"exp_nat_mul","source_end":10452,"source_start":10441,"syntax_kind":"ident"},{"source":"mul_one","source_end":10461,"source_start":10454,"syntax_kind":"ident"},{"source":"div_lt_iff","source_end":10473,"source_start":10463,"syntax_kind":"ident"},{"source":"exp_pos","source_end":10482,"source_start":10475,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 8 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2509c2cab7465a6c3ba90a55fb3befec40e16226be8dd9551eecf6c54c762c62 | 294da3495900181c3b6f45bc11b274f3c659f6e9fbe3e3b5963b823cdd6458e4 | 5d955d7c959d92eb4752181e24b55284c6b7acc2700dfa8689265024077e8ae7 | ddab4d3d7d2cbff4d0dc732c152bf5708506bc0826e63661e56e5b424bbe17f7 |
cat-searcher/leandojo-benchmark-4-random | test | 4,218 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨N, <a>trivial</a>, fun x hx => ?_⟩ | case intro
α : Type u_1
x y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
⊢ ∃ ia, True ∧ ∀ x ∈ Set.Ioi ia, rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : x ∈ Set.Ioi ↑N
⊢ rexp x / x ^ n ∈ Set.Ici C | ((:c Exists) (:c Real) (:lambda ia (:c Real) ((:c And) (:c True) (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ioi) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeSup.toPartialOrder) (:c Real) (:c Real.instSemilattic... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda ia :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:c True)) (:arg :explicit 1 (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"refine","sourceEnd":10518,"sourceStart":10512,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":10522,"sourceStart":10519,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"N","sourceEnd":10523,"sourceStart":10522,"tag":"identifier"},{"source":",","sourceEnd":10524... | [] | [{"source":"⟨N, trivial, fun x hx => ?_⟩","source_end":10551,"source_start":10519,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 80 | 9 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 16765f1ad09a6888449cab74e345c4d73818a08afe9834873c585d8f7fbbbded | ddab4d3d7d2cbff4d0dc732c152bf5708506bc0826e63661e56e5b424bbe17f7 | 91adcd635c5c792ea10430d5a2f9e58f84935cb03f3fe8abcae7982d5181efdf | 727d7669da9a5569b69fffcad8bf0189703256ec7a43b69069676e49d609ba4a |
cat-searcher/leandojo-benchmark-4-random | test | 4,219 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Ioi</a>] at hx | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : x ∈ Set.Ioi ↑N
⊢ rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
⊢ rexp x / x ^ n ∈ Set.Ici C | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) (:fv _uniq.39808)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c i... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":10556,"sourceStart":10554,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10558,"sourceStart":10557,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Ioi","se... | [] | [{"source":"Set.mem_Ioi","source_end":10569,"source_start":10558,"syntax_kind":"ident"},{"source":"hx","source_end":10576,"source_start":10574,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 10 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2c360a9a3ee5c2605bc32ca0d9924cad84caf7ce907abe1fc6121fe03a6875c9 | 727d7669da9a5569b69fffcad8bf0189703256ec7a43b69069676e49d609ba4a | 8f59bbfb9da17e559ddb3b6bd0f2e1040ff327f1ce51c1aec349d0afe1e8927a | ab7bd676cde4c48852cac8d24367c4bd5a4c577fc498f9002a630b539e6aa69b |
cat-searcher/leandojo-benchmark-4-random | test | 4,220 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hx₀ : 0 < x := (<a>Nat.cast_nonneg</a> N).<a>LE.le.trans_lt</a> hx | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
⊢ rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ rexp x / x ^ n ∈ Set.Ici C | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) (:fv _uniq.39808)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c i... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"have","sourceEnd":10583,"sourceStart":10579,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hx₀","sourceEnd":10589,"sourceStart":10584,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hx₀","sourceEnd":10589,"sourceStart":10584,"tag":"n... | [] | [{"source":"0 < x","source_end":10597,"source_start":10592,"syntax_kind":"«term_<_»"},{"source":"(Nat.cast_nonneg N).trans_lt hx","source_end":10632,"source_start":10601,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 13 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c809dad578a988697e33ff17064100920ecde9ec9dd7c40198100eebea00ac2 | ab7bd676cde4c48852cac8d24367c4bd5a4c577fc498f9002a630b539e6aa69b | e9df63a082fcafdc7017296d9658c783a98abf1a2d6d01e49a9b7ee205d96310 | 4e9dabf6ed86306730a783ff2f4f3c5ef3f4f10fcdeaa2d926d91a83648afa44 |
cat-searcher/leandojo-benchmark-4-random | test | 4,221 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Ici</a>, <a>le_div_iff</a> (<a>pow_pos</a> hx₀ _), ← <a>le_div_iff'</a> hC₀] | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ rexp x / x ^ n ∈ Set.Ici C | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ x ^ n ≤ rexp x / C | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) (:fv _uniq.39808)) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c i... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c HDiv.hDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rw","sourceEnd":10637,"sourceStart":10635,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10639,"sourceStart":10638,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Ici","se... | [] | [{"source":"Set.mem_Ici","source_end":10650,"source_start":10639,"syntax_kind":"ident"},{"source":"le_div_iff (pow_pos hx₀ _)","source_end":10680,"source_start":10652,"syntax_kind":"Lean.Parser.Term.app"},{"source":"le_div_iff' hC₀","source_end":10703,"source_start":10686,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 14 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5e146ad6c8e5a042711c499e629e7a3321c359d46e88f0b1dd8d246d20a4e56 | 4e9dabf6ed86306730a783ff2f4f3c5ef3f4f10fcdeaa2d926d91a83648afa44 | f49786ca3c629b70ef2c76f818d61572dddbb66438cfadc446d8dfb657fbf168 | f04a51d547ae8e4a960f3719fcd69752d56342ddfc6f787592e5d1ed73093169 |
cat-searcher/leandojo-benchmark-4-random | test | 4,222 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc x ^ n ≤ ⌈x⌉₊ ^ n := mod_cast <a>pow_le_pow_left</a> hx₀.le (<a>Nat.le_ceil</a> _) _ _ ≤ <a>Real.exp</a> ⌈x⌉₊ / (<a>Real.exp</a> 1 * C) := mod_cast (hN _ (<a>Nat.lt_ceil</a>.2 hx).<a>LT.lt.le</a>).<a>LT.lt.le</a> _ ≤ <a>Real.exp</a> (x + 1) / (<a>Real.exp</a> 1 * C) := by gcongr; exact (<a>Nat.ceil_lt_add_one</a> h... | case intro
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ x ^ n ≤ rexp x / C | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"calc","sourceEnd":10711,"sourceStart":10707,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":13,"semanticRole":"local","source":"x","sourceEnd":10717,"sourceStart":10716,"tag":"identifier"},{"source":"^","sourceEnd":10719,"sourceStart":10718,"tag":"atom"},{"conte... | [] | [{"source":"x ^ n ≤ ⌈x⌉₊ ^ n","source_end":10740,"source_start":10716,"syntax_kind":"«term_≤_»"},{"source":"mod_cast pow_le_pow_left hx₀.le (Nat.le_ceil _) _","source_end":10795,"source_start":10744,"syntax_kind":"Lean.modCast"},{"source":"_","source_end":10801,"source_start":10800,"syntax_kind":"Lean.Parser.Term.hole"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 19 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cda18e243104209b89f2a6e50e65cc377f5e029ecd401c805cdc2434ffb4e3c8 | f04a51d547ae8e4a960f3719fcd69752d56342ddfc6f787592e5d1ed73093169 | 6f19c420c866a501c0172ceb7777051e3ecf1d3083ca5efe549371adf2bcc79b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,223 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ rexp ↑⌈x⌉₊ / (rexp 1 * C) ≤ rexp (x + 1) / (rexp 1 * C) | case hab.h
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ ↑⌈x⌉₊ ≤ x + 1 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:c Nat.ceil) (:c Real) (:c Real.orderedSemiring) ((:c FloorRing.toFloo... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"gcongr","sourceEnd":10927,"sourceStart":10921,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":10927,"sourceStart":10921,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 24 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cdfd5b5db3a01467bb39bd1838c1df8e0807b9bcbbca678741d7e77b169d2ddc | 8a3878ff04e8354f8d4327e1e219d80da2ae6c94da9984ba357382084900b5b5 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 0df75ff8fa31c95f1d0abfe76f990cd61dd928202bb46d78989c138ac383a38b |
cat-searcher/leandojo-benchmark-4-random | test | 4,224 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>Nat.ceil_lt_add_one</a> hx₀.le).<a>LT.lt.le</a> | case hab.h
α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ ↑⌈x⌉₊ ≤ x + 1 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:c Nat.ceil) (:c Real) (:c Real.orderedSemiring) ((:c FloorRing.toFloorSemiring) (:c Real) (:c Real.instLinearOrderedRing) (:c Real.instFloorRing)) (:fv _uniq.39808))) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.ceil... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":10934,"sourceStart":10929,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":10936,"sourceStart":10935,"tag":"atom"},{"children":[{"name":"Nat.ceil_lt_add_one","semanticRole":"global","source":"Nat.ceil_lt_add_one","sourceEnd":10955,"sourceStart":10936,"tag":"id... | [] | [{"source":"(Nat.ceil_lt_add_one hx₀.le).le","source_end":10968,"source_start":10935,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 26 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 05701d417e9c735cec5157801ef890522f22839a2e02d30da9a669997ae04f59 | 0df75ff8fa31c95f1d0abfe76f990cd61dd928202bb46d78989c138ac383a38b | c98b264e7a3cbf21b08acfa8faaf1c95e426f8981a03b5e07e788f02c0045d6c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,225 | Real.tendsto_exp_div_pow_atTop | Mathlib/Analysis/SpecialFunctions/Exp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_comm</a>, <a>Real.exp_add</a>, <a>mul_div_mul_left</a> _ _ (<a>Real.exp_pos</a> _).<a>LT.lt.ne'</a>] | α : Type u_1
x✝ y z : ℝ
l : Filter α
n : ℕ
C : ℝ
hC₁ : 1 ≤ C
hC₀ : 0 < C
this : 0 < (rexp 1 * C)⁻¹
N : ℕ
hN : ∀ k ≥ N, ↑k ^ n < rexp ↑k / (rexp 1 * C)
x : ℝ
hx : ↑N < x
hx₀ : 0 < x
⊢ rexp (x + 1) / (rexp 1 * C) = rexp x / C | ((:c Eq) (:c Real) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.exp) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) (:fv _uniq.39808) ((:c OfNat.ofNat) (:c Real) (:l... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"z","sexp":"(:c Real)"},{"name":"l","sexp":"((:c Filter) (:fv _uniq.36407))"},{"name":"n","sexp":"(:c Nat)"},{"name":"C","sexp":"(:c Real)"},{"name":"hC₁","sexp":"((:c LE.le) (:c Real) ((:c Preorder.toLE) (... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":10995,"sourceStart":10993,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10997,"sourceStart":10996,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"add_comm","source_end":11005,"source_start":10997,"syntax_kind":"ident"},{"source":"exp_add","source_end":11014,"source_start":11007,"syntax_kind":"ident"},{"source":"mul_div_mul_left _ _ (exp_pos _).ne'","source_end":11052,"source_start":11016,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.36407","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.36409","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 80 | 29 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c1f23e78327dace7a8fc0b40ca2f6ffb0e774a721a5057e4c93f36c13b2ff7e1 | 8bce9b15cef31ef61b6afed68419f13b0f06ee2323861c1fc66c5531c24a7a5c | cdc23062da64a18cc3206dc9cef3dc4188f032b0bf59a9d3380d797f6fd70eaa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,226 | FractionalIdeal.count_zero | Mathlib/RingTheory/DedekindDomain/Factorization.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>FractionalIdeal.count</a>, <a>dif_pos</a>] | R : Type u_1
inst✝⁴ : CommRing R
K : Type u_2
inst✝³ : Field K
inst✝² : Algebra R K
inst✝¹ : IsFractionRing R K
inst✝ : IsDedekindDomain R
v : HeightOneSpectrum R
⊢ count K v 0 = 0 | ((:c Eq) (:c Int) ((:c FractionalIdeal.count) (:fv _uniq.58993) (:fv _uniq.58996) (:fv _uniq.58999) (:fv _uniq.59002) (:fv _uniq.59254) (:fv _uniq.59291) (:fv _uniq.59300) (:fv _uniq.59309) ((:c OfNat.ofNat) ((:c FractionalIdeal) (:fv _uniq.58993) (:fv _uniq.58996) ((:c nonZeroDivisors) (:fv _uniq.58993) ((:c Semiring.... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c CommRing) (:fv _uniq.58993))"},{"name":"K","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Field) (:fv _uniq.58999))"},{"name":"inst✝²","sexp":"((:c Algebra) (:fv _uniq.58993) (:fv _uniq.58999) ((:c CommRing.toCommSemiring) (:fv _uniq.5899... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c FractionalIdeal.count) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Field) (:arg :explicit 0 (:fv FV2... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.58993","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.58996","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c CommRing) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":14978,"sourceStart":14974,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":14983,"sourceStart":14979,"tag":"atom"}],"kind"... | [] | [{"source":"count","source_end":14990,"source_start":14985,"syntax_kind":"ident"},{"source":"dif_pos","source_end":14999,"source_start":14992,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.58993","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.58996","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 43 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 369bde84048de2637366601dd2c624445e93c9db2c6591ba9ea53e9378e67469 | 111f5abcddd06ab17267621a3a0d3ad4ad154bc5b720cce6ae158f9eaf3628ef | 6074fc33a73298867469cbb802379ff60253acc10ffe21be7e5fc4bd75a4ef6a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,227 | CategoryTheory.eqToHom_comp_iff | Mathlib/CategoryTheory/EqToHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | C : Type u₁
inst✝ : Category.{v₁, u₁} C
X X' Y : C
p : X = X'
f : X ⟶ Y
g : X' ⟶ Y
h : eqToHom p ≫ g = f
⊢ g = eqToHom ⋯ ≫ eqToHom p ≫ g | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.1643) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1643) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1643) (:fv _uniq.1646))) (:fv _uniq.1931) (:fv _uniq.1932)) (:fv _uniq.1935) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.1643) ((:c CategoryTheory.Ca... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1643))"},{"name":"X","sexp":"(:fv _uniq.1643)"},{"name":"X'","sexp":"(:fv _uniq.1643)"},{"name":"Y","sexp":"(:fv _uniq.1643)"},{"name":"p","sexp":"((:c Eq) (:fv _uniq.1643) (:fv _uniq.1930) (:fv _uniq.1931))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV4)) (:arg :explicit 3 (:fv FV5)))) (:arg :explicit 1 (:fv FV8)) (:arg :explicit 2 (:app (:c CategoryTheory.CategoryStruc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1643","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1646","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2596,"sourceStart":2592,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1643","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1646","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 14 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ef63f20c267e9e27408e4c1af7cafaf98dc9923ad64fbf4713993013a8431256 | e32d6defd5dc117f3f05647551dab05aa3dab56a039ef9e7d0e955998d3032a6 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,228 | CategoryTheory.eqToHom_comp_iff | Mathlib/CategoryTheory/EqToHom.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>CategoryTheory.whisker_eq</a> _ h] | C : Type u₁
inst✝ : Category.{v₁, u₁} C
X X' Y : C
p : X = X'
f : X ⟶ Y
g : X' ⟶ Y
h : g = eqToHom ⋯ ≫ f
⊢ eqToHom p ≫ eqToHom ⋯ ≫ f = f | ((:c Eq) ((:c Quiver.Hom) (:fv _uniq.1643) ((:c CategoryTheory.CategoryStruct.toQuiver) (:fv _uniq.1643) ((:c CategoryTheory.Category.toCategoryStruct) (:fv _uniq.1643) (:fv _uniq.1646))) (:fv _uniq.1930) (:fv _uniq.1932)) ((:c CategoryTheory.CategoryStruct.comp) (:fv _uniq.1643) ((:c CategoryTheory.Category.toCategory... | [{"name":"C","sexp":"(:sort (+ u₁ 1))"},{"name":"inst✝","sexp":"((:c CategoryTheory.Category) (:fv _uniq.1643))"},{"name":"X","sexp":"(:fv _uniq.1643)"},{"name":"X'","sexp":"(:fv _uniq.1643)"},{"name":"Y","sexp":"(:fv _uniq.1643)"},{"name":"p","sexp":"((:c Eq) (:fv _uniq.1643) (:fv _uniq.1930) (:fv _uniq.1931))"},{"nam... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Quiver.Hom) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Quiver) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV3)) (:arg :explicit 3 (:fv FV5)))) (:arg :explicit 1 (:app (:c CategoryTheory.CategoryStruct.comp) (:arg :implicit-type ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1643","is_instance":false,"is_let":false,"name":"C","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1646","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c CategoryTheory.Category) (... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":2630,"sourceStart":2626,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"whisker_eq _ h","source_end":2646,"source_start":2632,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1643","is_instance":false,"is_let":false,"user_name":"C"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1646","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 14 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b77046ea6c49ca1acbcd017dceced22bf4160e6f40a9e9e6777537dc25d46b0 | b4cd36e2e49f5dd66bf272539f07ad28bbced5b8ee0e2141d9ff6fb10d6be20e | e6aa7f86f34e7ddf51838c6d4ecc990ed134728f738e25651d6cc12bde083250 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,229 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hn' : 0 < (n : ℝ) := mod_cast hn.bot_lt | z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"have","sourceEnd":41380,"sourceStart":41376,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hn'","sourceEnd":41384,"sourceStart":41381,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hn'","sourceEnd":41384,"sourceStart":41381,"tag":"n... | [] | [{"source":"0 < (n : ℝ)","source_end":41400,"source_start":41387,"syntax_kind":"«term_<_»"},{"source":"mod_cast hn.bot_lt","source_end":41422,"source_start":41404,"syntax_kind":"Lean.modCast"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6027c31306a06968e3d60dc33cef44da45c312e81fc5dc41d27efbdda66c3b27 | 32be4fa2600e5eedb7b4745dc2546507836262af2315095390f1f215478c1be6 | 329c4da23fd5c57fc7669d0ca7bd2d69ca26d84410ef4c23f13e1309debc999e | f8c46144abfbd3fc3a7f135f1a75acd1b7114ac3f7ba3fb7ddf83bcbca471640 |
cat-searcher/leandojo-benchmark-4-random | test | 4,230 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨q, hxq, hqy⟩ := <a>exists_rat_btwn</a> (<a>Real.rpow_lt_rpow</a> (<a>le_max_left</a> 0 x) (<a>max_lt</a> hy h) <| inv_pos.mpr hn') | z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"obtain","sourceEnd":41431,"sourceStart":41425,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":41435,"sourceStart":41432,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"q","sourceEn... | [] | [{"source":"exists_rat_btwn (rpow_lt_rpow (le_max_left 0 x) (max_lt hy h) <| inv_pos.mpr hn')","source_end":41538,"source_start":41457,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨q, hxq, hqy⟩","source_end":41449,"source_start":41432,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 5 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7111ef41496f0f5f503e5631871806d21c7ef68fc6c05155faaf487bdc4d5fde | f8c46144abfbd3fc3a7f135f1a75acd1b7114ac3f7ba3fb7ddf83bcbca471640 | ddeac4bd7c0b96c3ed9b210b820929c4c2d9516c988a97d49c4941d95550d95b | d8b72fbe35d54f719d09fedc24cd0345b4c749c021c6fa23c04b42d13151ad59 |
cat-searcher/leandojo-benchmark-4-random | test | 4,231 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>Real.rpow_nonneg</a> (<a>le_max_left</a> 0 x) n⁻¹ | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"have","sourceEnd":41545,"sourceStart":41541,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":41546,"sourceStart":41546,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":41546,"sourceStart":41546,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"rpow_nonneg (le_max_left 0 x) n⁻¹","source_end":41585,"source_start":41549,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 6 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77bc12929fe8677de56e987e2e94625c4aaa143d3fe898c40b3657eda6d8a3ed | d8b72fbe35d54f719d09fedc24cd0345b4c749c021c6fa23c04b42d13151ad59 | 6cf7c2646397998bfd418b8d07de91f53ebbbf40ffe52c42ab70cb775b66a5ce | 49091eef8bc65df37a072ead78f689e91eaefaf2640bbafb1c911fcb684627d6 |
cat-searcher/leandojo-benchmark-4-random | test | 4,232 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hq := this.trans_lt hxq | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"have","sourceEnd":41592,"sourceStart":41588,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hq","sourceEnd":41595,"sourceStart":41593,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hq","sourceEnd":41595,"sourceStart":41593,"tag":"nod... | [] | [{"source":"this.trans_lt hxq","source_end":41616,"source_start":41599,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 7 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fef1dc6129bcf4741cb7c637e41294e60c9f1b30f3664e4375eb3150356b06d7 | 49091eef8bc65df37a072ead78f689e91eaefaf2640bbafb1c911fcb684627d6 | f4cd44093c8856df8e9f6de6949aa5b4513371c5a2691d4a39002420571c6de8 | 472aa9f6d22b05dc32f34be4b470ac461c2b77110790574986639d7484d591a3 |
cat-searcher/leandojo-benchmark-4-random | test | 4,233 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace hxq := <a>Real.rpow_lt_rpow</a> this hxq hn' | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hxq : max 0 x ^ (↑n)⁻¹ < ↑q
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : (max 0 x ^ (↑n)⁻¹) ^ ↑n < ↑q ^ ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"replace","sourceEnd":41626,"sourceStart":41619,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hxq","sourceEnd":41630,"sourceStart":41627,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hxq","sourceEnd":41630,"sourceStart":41627,"tag"... | [] | [{"source":"rpow_lt_rpow this hxq hn'","source_end":41659,"source_start":41634,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 8 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 56f4a8e3846c7cadde4f61cfac68ffc6a919dee57571fea033b62bfd0ac3f9b4 | 472aa9f6d22b05dc32f34be4b470ac461c2b77110790574986639d7484d591a3 | 92146ac6fec7a64ba9c44248525aef37b57147736ee0f22b08559e87e1be7a88 | e4cc157f5442badc0269a6946f555ab6cd0793e3f8be87c26abf49139d0cac97 |
cat-searcher/leandojo-benchmark-4-random | test | 4,234 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace hqy := <a>Real.rpow_lt_rpow</a> hq.le hqy hn' | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
hqy : ↑q < y ^ (↑n)⁻¹
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : (max 0 x ^ (↑n)⁻¹) ^ ↑n < ↑q ^ ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : (max 0 x ^ (↑n)⁻¹) ^ ↑n < ↑q ^ ↑n
hqy : ↑q ^ ↑n < (y ^ (↑n)⁻¹) ^ ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"replace","sourceEnd":41669,"sourceStart":41662,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hqy","sourceEnd":41673,"sourceStart":41670,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hqy","sourceEnd":41673,"sourceStart":41670,"tag"... | [] | [{"source":"rpow_lt_rpow hq.le hqy hn'","source_end":41703,"source_start":41677,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 9 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9101c0aecd7884b53e41620fc6cb1291b0bfc1f89159fc5d0721c4947c3390ee | e4cc157f5442badc0269a6946f555ab6cd0793e3f8be87c26abf49139d0cac97 | fd0180217512612375b35fc78598af9eeffe07cdc0813aff6d3e3615f4acd477 | e170be7c7229f0bd1bd74d85b466599dbf5ef8494617599c48ca2213c1820c26 |
cat-searcher/leandojo-benchmark-4-random | test | 4,235 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.rpow_natCast</a>, <a>Real.rpow_natCast</a>, <a>Real.rpow_inv_natCast_pow</a> _ hn] at hxq hqy | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : (max 0 x ^ (↑n)⁻¹) ^ ↑n < ↑q ^ ↑n
hqy : ↑q ^ ↑n < (y ^ (↑n)⁻¹) ^ ↑n
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : max 0 x < ↑q ^ n
hqy : ↑q ^ n < y
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq... | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"source":"rw","sourceEnd":41708,"sourceStart":41706,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41710,"sourceStart":41709,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Real.rpow_natCas... | [] | [{"source":"rpow_natCast","source_end":41722,"source_start":41710,"syntax_kind":"ident"},{"source":"hxq","source_end":41771,"source_start":41768,"syntax_kind":"ident"},{"source":"hqy","source_end":41775,"source_start":41772,"syntax_kind":"ident"},{"source":"rpow_natCast","source_end":41736,"source_start":41724,"syntax_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 10 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ba94dccb1113b665ff270980a9aada428f0cf9e4d25ecb3110e40ae60ef02a7d | e170be7c7229f0bd1bd74d85b466599dbf5ef8494617599c48ca2213c1820c26 | 8840d387dba026ba8afca1b3db2f5f2d07dabe6440218853efc5646a4862914b | 8b65f3b53ec35af9385a3ebffa6ca3710528ef632028ddc5612b9b2437647dd5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,236 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨q, mod_cast hq, (<a>le_max_right</a> _ _).<a>LE.le.trans_lt</a> hxq, hqy⟩ | case intro.intro
z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : max 0 x < ↑q ^ n
hqy : ↑q ^ n < y
⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y | ((:c Exists) (:c Rat) (:lambda q (:c Rat) ((:c And) ((:c LT.lt) (:c Rat) (:c Rat.instLT) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) 0) ((:c And) ((:c LT.lt) (:c Real) (:c Real.instLT) (:fv _uniq.179611) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.to... | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c Exists) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lambda q :explicit (:c Rat) (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":41786,"sourceStart":41781,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":41790,"sourceStart":41787,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"q","sourceEnd":41791,"sourceStart":41790,"tag":"identi... | [] | [{"source":"⟨q, mod_cast hq, (le_max_right _ _).trans_lt hxq, hqy⟩","source_end":41845,"source_start":41787,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 17 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e19f42001ecf19ff70b32f7553e1a170aaf957d07a1ed7f35ab11577e069ea77 | 591c1cd2a5e72eb274545aba96b0af79f315832f308134d3df5353dc897b1c7a | 42cc32589ec544c3a16c2c30ea6bc0930fefa03effd0018adb21b4e08685d6e9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,237 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hy.le | z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : max 0 x < ↑q ^ n
hqy : ↑q ^ n < (y ^ (↑n)⁻¹) ^ n
⊢ 0 ≤ y | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.179612)) | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":41856,"sourceStart":41851,"tag":"atom"},{"name":"LT.lt.le","semanticRole":"global","source":"hy.le","sourceEnd":41862,"sourceStart":41857,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact hy.le","sourceEnd":41862,"sou... | [] | [{"source":"hy.le","source_end":41862,"source_start":41857,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 22 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 16ef5dddf7094a8d77992a009bcf8febbaea0277ee9d276777c25511100eda6e | 8f6cef220dccb694383e5b6bc93eb045e2f5244e89b821a39f1590f6d57697a0 | d449e8c9fcf03f16d374272a19410826e006d8b2ae4311bc272aaaad81669b5d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,238 | Real.exists_rat_pow_btwn_rat_aux | Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_max_left</a> _ _ | z x✝ y✝ : ℝ
n : ℕ
hn : n ≠ 0
x y : ℝ
h : x < y
hy : 0 < y
hn' : 0 < ↑n
q : ℚ
this : 0 ≤ max 0 x ^ (↑n)⁻¹
hq : 0 < ↑q
hxq : (max 0 x ^ (↑n)⁻¹) ^ n < ↑q ^ n
hqy : ↑q ^ n < (y ^ (↑n)⁻¹) ^ n
⊢ 0 ≤ max 0 x | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Max.max) (:c Real) ((:c LinearOrder.toMax) (:c Real) (:c Real.linearOrder)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.179611))) | [{"name":"z","sexp":"(:c Real)"},{"name":"x✝","sexp":"(:c Real)"},{"name":"y✝","sexp":"(:c Real)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hn","sexp":"((:c Ne) (:c Nat) (:fv _uniq.179379) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"}... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"name":"z","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","contex... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":41873,"sourceStart":41868,"tag":"atom"},{"children":[{"name":"le_max_left","semanticRole":"global","source":"le_max_left","sourceEnd":41885,"sourceStart":41874,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":41887,... | [] | [{"source":"le_max_left _ _","source_end":41889,"source_start":41874,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.179373","is_instance":false,"is_let":false,"user_name":"z"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.179375","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 289 | 27 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bc574a454ae06f7085fe159409c3e582aef8107c549e8797e513d8c4bac03a8 | 435deb83c1135f43e426dc06f6a01ae933ea7704e9d5d278d660f8d3a59775b7 | ab0c933fdd1abf7ec37c13bdae4541363cabc8d1dfc120cf683585eece254cd8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,239 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>UniqueFactorizationMonoid.normalizedFactors</a>, <a>UniqueFactorizationMonoid.factors</a>] | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
⊢ ∀ x ∈ normalizedFactors a, normalize x = x | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
⊢ ∀ x ∈ Multiset.map (⇑normalize) (if h : a = 0 then 0 else Classical.choose ⋯), normalize x = x | (:forall x (:fv _uniq.140490) (:forall _ ((:c Membership.mem) (:fv _uniq.140490) ((:c Multiset) (:fv _uniq.140490)) ((:c Multiset.instMembership) (:fv _uniq.140490)) 0 ((:c UniqueFactorizationMonoid.normalizedFactors) (:fv _uniq.140490) (:fv _uniq.140493) (:fv _uniq.140502) (:fv _uniq.140509) (:fv _uniq.140677))) ((:c ... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"rw","sourceEnd":29384,"sourceStart":29382,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":29386,"sourceStart":29385,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"UniqueFactorizat... | [] | [{"source":"normalizedFactors","source_end":29403,"source_start":29386,"syntax_kind":"ident"},{"source":"factors","source_end":29412,"source_start":29405,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dcefc7056c3c5d36e42880f5c2c466639b906e2f072844b8ef034b8795b95424 | fc070bb78c9ebf7b235116979f048108d1a2ef5a92e55b8802b840804057eede | 228c863e8cbadd737ab5113db653d6d07e2cb7ecf701ff339e3c8801a1a09bd0 | 9cc33f0222c28f1c9f4e24130e41d0eea0e833c61822377fe18ffc18ea81fe38 |
cat-searcher/leandojo-benchmark-4-random | test | 4,240 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | split_ifs with h | α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
⊢ ∀ x ∈ Multiset.map (⇑normalize) (if h : a = 0 then 0 else Classical.choose ⋯), normalize x = x | case pos
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : a = 0
⊢ ∀ x ∈ Multiset.map (fun x => normalize x) 0, normalize x = x
case neg
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorization... | (:forall x (:fv _uniq.140490) (:forall _ ((:c Membership.mem) (:fv _uniq.140490) ((:c Multiset) (:fv _uniq.140490)) ((:c Multiset.instMembership) (:fv _uniq.140490)) 0 ((:c Multiset.map) (:fv _uniq.140490) (:fv _uniq.140490) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) (:fv _uniq.140490) (:fv _uniq.140490) ((:c MonoidWit... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"split_ifs","sourceEnd":29425,"sourceStart":29416,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":29430,"sourceStart":29426,"tag":"atom"},{"children":[{"children":[{"source":"h","sourceEnd":29432,"sourceStart":29431,"tag":"identifier"... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 8 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3800599d0a373524b8bc5562080851fa13561ea36432818500c5d73c14fd9302 | 9cc33f0222c28f1c9f4e24130e41d0eea0e833c61822377fe18ffc18ea81fe38 | 4384516da9879e95125096635779b1b98675db82dd9560bb5f86d9ca5296b84d | 64401f541dedf2ecc9400f47fa96a9ba9e8819e170f34ffca3fcd2b0206e82cf |
cat-searcher/leandojo-benchmark-4-random | test | 4,241 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x hx | case neg
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : ¬a = 0
⊢ ∀ x ∈ Multiset.map (fun x => normalize x) (Classical.choose ⋯), normalize x = x | case neg
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : ¬a = 0
x : α
hx : x ∈ Multiset.map (fun x => normalize x) (Classical.choose ⋯)
⊢ normalize x = x | (:forall x (:fv _uniq.140490) (:forall _ ((:c Membership.mem) (:fv _uniq.140490) ((:c Multiset) (:fv _uniq.140490)) ((:c Multiset.instMembership) (:fv _uniq.140490)) 0 ((:c Multiset.map) (:fv _uniq.140490) (:fv _uniq.140490) (:lambda x (:fv _uniq.140490) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) (:fv _uniq.140490) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"intro","sourceEnd":29449,"sourceStart":29444,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":29451,"sourceStart":29450,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hx","sourceEnd":29454,"sourceStart":29452,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"x","source_end":29451,"source_start":29450,"syntax_kind":"ident"},{"role":"fresh_name","source":"hx","source_end":29454,"source_start":29452,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 15 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f4c26ec38bf1d2c96f8c1966ba8f6d7c6f807fb423a9519425e0e92fda32bdf4 | 31b7097d9174a7606b5b6a32d56d44265efda733e2ad162a4ff8564c1148a290 | 65777af1f444837568ec00c3040db2bdc96178d91d8bf83037116b747be939ac | e607ae11dfd7229bf7f29c64e519e03ae63a40418fc45291db5c6c490c23f336 |
cat-searcher/leandojo-benchmark-4-random | test | 4,242 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨y, _, rfl⟩ := <a>Multiset.mem_map</a>.1 hx | case neg
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : ¬a = 0
x : α
hx : x ∈ Multiset.map (fun x => normalize x) (Classical.choose ⋯)
⊢ normalize x = x | case neg.intro.intro
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : ¬a = 0
y : α
left✝ : y ∈ Classical.choose ⋯
hx : normalize y ∈ Multiset.map (fun x => normalize x) (Classical.choose ⋯)
⊢ normalize (normalize y) = normalize y | ((:c Eq) (:fv _uniq.140490) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) (:fv _uniq.140490) (:fv _uniq.140490) ((:c MonoidWithZero.toMulZeroOneClass) (:fv _uniq.140490) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.140490) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.140490) (:fv _uniq.140493))))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidWithZeroHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c MulZeroOneClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"obtain","sourceEnd":29463,"sourceStart":29457,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":29467,"sourceStart":29464,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"y","sourceEn... | [] | [{"source":"Multiset.mem_map.1 hx","source_end":29504,"source_start":29483,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨y, _, rfl⟩","source_end":29479,"source_start":29464,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 16 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 416e7cc9f192d0d037896ede7a66576600453676444c8751548c380008bd0b19 | e607ae11dfd7229bf7f29c64e519e03ae63a40418fc45291db5c6c490c23f336 | b0cbaadef59a143a4fa3b331846161c47c7292d96ddcc4ec66dd33c5c18a7f42 | b5a435f4c8d121b827dde02d39f79a19060eb4e11c6733a5e2ee64e83ccbb484 |
cat-searcher/leandojo-benchmark-4-random | test | 4,243 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>normalize_idem</a> | case neg.intro.intro
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : ¬a = 0
y : α
left✝ : y ∈ Classical.choose ⋯
hx : normalize y ∈ Multiset.map (fun x => normalize x) (Classical.choose ⋯)
⊢ normalize (normalize y) = normalize y | ((:c Eq) (:fv _uniq.140490) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) (:fv _uniq.140490) (:fv _uniq.140490) ((:c MonoidWithZero.toMulZeroOneClass) (:fv _uniq.140490) ((:c CommMonoidWithZero.toMonoidWithZero) (:fv _uniq.140490) ((:c CancelCommMonoidWithZero.toCommMonoidWithZero) (:fv _uniq.140490) (:fv _uniq.140493))))... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c MonoidWithZeroHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c MulZeroOneClass) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"source":"apply","sourceEnd":29512,"sourceStart":29507,"tag":"atom"},{"name":"normalize_idem","semanticRole":"global","source":"normalize_idem","sourceEnd":29527,"sourceStart":29513,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply normalize_idem","sourceEnd":29527,"sourceStart":29507... | [] | [{"source":"normalize_idem","source_end":29527,"source_start":29513,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 17 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e0770592d6c95ee3b4dc2804d5e01e1f6163a131741d9abcb41461956869376 | b5a435f4c8d121b827dde02d39f79a19060eb4e11c6733a5e2ee64e83ccbb484 | 699e2afe54d91dc2f19d0fa235c2273fd750aff062b62875aa034535f246ac86 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,244 | UniqueFactorizationMonoid.normalize_normalized_factor | Mathlib/RingTheory/UniqueFactorizationDomain.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case pos
α : Type u_1
inst✝² : CancelCommMonoidWithZero α
inst✝¹ : NormalizationMonoid α
inst✝ : UniqueFactorizationMonoid α
a : α
h : a = 0
⊢ ∀ x ∈ Multiset.map (fun x => normalize x) 0, normalize x = x | (:forall x (:fv _uniq.140490) (:forall _ ((:c Membership.mem) (:fv _uniq.140490) ((:c Multiset) (:fv _uniq.140490)) ((:c Multiset.instMembership) (:fv _uniq.140490)) 0 ((:c Multiset.map) (:fv _uniq.140490) (:fv _uniq.140490) (:lambda x (:fv _uniq.140490) ((:c DFunLike.coe) ((:c MonoidWithZeroHom) (:fv _uniq.140490) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c CancelCommMonoidWithZero) (:fv _uniq.140490))"},{"name":"inst✝¹","sexp":"((:c NormalizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"inst✝","sexp":"((:c UniqueFactorizationMonoid) (:fv _uniq.140490) (:fv _uniq.140493))"},{"name":"a",... | (:forall x :explicit (:fv FV0) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Multiset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Multiset) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140490","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c CancelCommMonoidWithZ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":29441,"sourceStart":29437,"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.140490","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.140493","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":instance-implicit","context_index... | 130 | 12 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7866cef44c13e31966d1572a5646aa56e729ed0999ab4bf939b5b14a7e8470ed | 53ed64ce4274ad0e64225e2f1e417da6f7e9f049b0ad040b33020d280ed3fb85 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,245 | Real.mul_le_sin | Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>inv_div</a>] | x : ℝ
hx : 0 ≤ x
hx' : x ≤ π / 2
⊢ 2 / π * x ≤ sin x | x : ℝ
hx : 0 ≤ x
hx' : x ≤ π / 2
⊢ (π / 2)⁻¹ * x ≤ sin x | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c in... | [{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.131565))"},{"name":"hx'","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.131565) ((:c HDiv.hDiv) (:c Real) (:c Real) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"name":"hx","sexp":"(:app (:c LE.le) (:arg :implicit-type 0 (:c Re... | {"children":[{"source":"rw","sourceEnd":13080,"sourceStart":13078,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13082,"sourceStart":13081,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13085,"sourceSt... | [] | [{"source":"inv_div","source_end":13093,"source_start":13086,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"user_name":"hx"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 79 | 4 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | caf9c68e3c7b8594348c3c2724b643dbbaafe6881baa86205e7c99b84d25ff83 | f6f97542321ce83babe493f22620461a1dda13a474e9392d88fa5e1dd4eaec15 | cfb6f4cddb7198cb1a60ec249679efca8e642a5c41d2aec953e7ffa9be6dc19f | 7084a67ca9be5b99303b72211a6c4c93a9a44f5281edcc63392b120c535f0a58 |
cat-searcher/leandojo-benchmark-4-random | test | 4,246 | Real.mul_le_sin | Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [-<a>inv_div</a>, <a>mul_inv_cancel_left₀</a> pi_div_two_pos.ne'] using @<a>Real.le_sin_mul</a> ((π / 2)⁻¹ * x) (<a>mul_nonneg</a> (<a>inv_nonneg</a>.2 pi_div_two_pos.le) hx) (by rwa [← <a>div_eq_inv_mul</a>, <a>div_le_one</a> <a>Real.pi_div_two_pos</a>]) | x : ℝ
hx : 0 ≤ x
hx' : x ≤ π / 2
⊢ (π / 2)⁻¹ * x ≤ sin x | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) ((:c DivInvMonoid.toInv) (:c Real) ((:c DivisionMonoid.toDivInvMonoid) (:c Real) ((:c DivisionCommMonoid.toDivisionMonoid) (:c Real) ((:c CommGroupWithZero.toDivisionC... | [{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.131565))"},{"name":"hx'","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.131565) ((:c HDiv.hDiv) (:c Real) (:c Real) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"name":"hx","sexp":"(:app (:c LE.le) (:arg :implicit-type 0 (:c Re... | {"children":[{"source":"simpa","sourceEnd":13102,"sourceStart":13097,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"inv_div","source_end":13112,"source_start":13105,"syntax_kind":"ident"},{"source":"mul_inv_cancel_left₀ pi_div_two_pos.ne'","source_end":13155,"source_start":13114,"syntax_kind":"Lean.Parser.Term.app"},{"source":"@le_sin_mul ((π / 2)⁻¹ * x)\n (mul_nonneg (inv_nonneg.2 pi_div_two_pos.le) hx)\n (by rwa ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"user_name":"hx"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 79 | 7 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4cbd4ed0c7bbd599a3ced6253d638bd6743ff29ec0bc9325fed95f731b8278b1 | 7084a67ca9be5b99303b72211a6c4c93a9a44f5281edcc63392b120c535f0a58 | ee3bee887170247b23a5dc20d0f31434254b8214621e6e12f345fa37a1665fff | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,247 | Real.mul_le_sin | Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>div_eq_inv_mul</a>, <a>div_le_one</a> <a>Real.pi_div_two_pos</a>] | x : ℝ
hx : 0 ≤ x
hx' : x ≤ π / 2
⊢ (π / 2)⁻¹ * x ≤ 1 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Real.instInv) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) (:... | [{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.131565))"},{"name":"hx'","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.131565) ((:c HDiv.hDiv) (:c Real) (:c Real) (... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"name":"x","sexp":"(:c Real)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"name":"hx","sexp":"(:app (:c LE.le) (:arg :implicit-type 0 (:c Re... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":13259,"sourceStart":13256,"tag":"atom"},{"children":[{"source":"[","sourceEnd":13261,"sourceStart":13260,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13264,"sourceStart":13261,"tag... | [] | [{"source":"div_eq_inv_mul","source_end":13279,"source_start":13265,"syntax_kind":"ident"},{"source":"div_le_one pi_div_two_pos","source_end":13306,"source_start":13281,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.131565","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.131566","is_instance":false,"is_let":false,"user_name":"hx"},{"binder_role":":explicit","context_index":3,"internal_name":"... | 79 | 10 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c5ae2ead7dc5eaf109041feb112f905c738dd5dd945b930a453c013c8f1f2546 | c97ed77c3d4d423d6759534028be34bc6004b232c6778ca3e99ec41a08d5273a | 4d50b5a89953f067b22fbcc033e6560b3a21fee9a05e7a4ff266bdbabe628ef6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,248 | Bornology.isVonNBounded_insert | Mathlib/Analysis/LocallyConvex/Bounded.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>Set.singleton_union</a>, <a>Bornology.isVonNBounded_union</a>, <a>Bornology.isVonNBounded_singleton</a>, <a>true_and</a>] | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝⁴ : NormedField 𝕜
inst✝³ : AddCommGroup E
inst✝² : Module 𝕜 E
inst✝¹ : TopologicalSpace E
inst✝ : ContinuousSMul 𝕜 E
x : E
s : Set E
⊢ IsVonNBounded 𝕜 (insert x s) ↔ IsVonNBounded 𝕜 s | ((:c Iff) ((:c Bornology.IsVonNBounded) (:fv _uniq.108441) (:fv _uniq.108447) ((:c SeminormedCommRing.toSeminormedRing) (:fv _uniq.108441) ((:c NormedCommRing.toSeminormedCommRing) (:fv _uniq.108441) ((:c NormedField.toNormedCommRing) (:fv _uniq.108441) (:fv _uniq.108459)))) ((:c SMulZeroClass.toSMul) (:fv _uniq.108441... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜'","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"E'","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝⁴","sexp":"((:c NormedField) (:fv _uniq.108441))"},{"name":"i... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Bornology.IsVonNBounded) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c SMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108441","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108444","is_instance":false,"is_let":false,"name":"𝕜'","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":11814,"sourceStart":11810,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11819,"sourceStart":11815,"tag":"atom"}],"kind"... | [] | [{"source":"singleton_union","source_end":11840,"source_start":11825,"syntax_kind":"ident"},{"source":"isVonNBounded_union","source_end":11861,"source_start":11842,"syntax_kind":"ident"},{"source":"isVonNBounded_singleton","source_end":11886,"source_start":11863,"syntax_kind":"ident"},{"source":"true_and","source_end":... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.108441","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.108444","is_instance":false,"is_let":false,"user_name":"𝕜'"},{"binder_role":":implicit","context_index":2,"internal_name"... | 72 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b125d46b12291a1d0037880d122c6c62791065b2df4508e0d69e7c819cda2832 | d43773b801feac2754e9cd7fc6f5b61c5d076dc729949d9f4de8e356f2f1b7b4 | 26f4393ac8b166392a2b2ed25b07e01e8d7645042934b0d0478b5940cf46e13a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,249 | monovary_inv₀ | Mathlib/Algebra/Order/Monovary.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>monovary_inv_left₀</a> hf, <a>antivary_inv_right₀</a> hg] | ι : Type u_1
α : Type u_2
β : Type u_3
inst✝¹ : LinearOrderedSemifield α
inst✝ : LinearOrderedSemifield β
s : Set ι
f f₁ f₂ : ι → α
g g₁ g₂ : ι → β
hf : StrongLT 0 f
hg : StrongLT 0 g
⊢ Monovary f⁻¹ g⁻¹ ↔ Monovary f g | ((:c Iff) ((:c Monovary) (:fv _uniq.147415) (:fv _uniq.147418) (:fv _uniq.147421) ((:c PartialOrder.toPreorder) (:fv _uniq.147418) ((:c StrictOrderedSemiring.toPartialOrder) (:fv _uniq.147418) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:fv _uniq.147418) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) ... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c LinearOrderedSemifield) (:fv _uniq.147418))"},{"name":"inst✝","sexp":"((:c LinearOrderedSemifield) (:fv _uniq.147421))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.147415)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Monovary) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 4 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV2)))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.147415","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147418","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13995,"sourceStart":13993,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13997,"sourceStart":13996,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"monovary_inv_left₀ hf","source_end":14020,"source_start":13997,"syntax_kind":"Lean.Parser.Term.app"},{"source":"antivary_inv_right₀ hg","source_end":14046,"source_start":14022,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.147415","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.147418","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 91 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f9e85323c346c30c97771a4b5d849f834b232a4e47f41367da9a00af34f299e | 99e114ffa263a40ea856702b548256920e5ae625e247841ff99596a9619c67c1 | 79caa17c72f8040f2cac3cb279e3b3af0a8b9089c5b37209370c52f441e06881 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,250 | smul_balancedCore_subset | Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro x ⟨y, hy, rfl⟩ | 𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
⊢ a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s | case intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
hy : y ∈ balancedCore 𝕜 s
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.2087)) ((:c Set.instHasSubset) (:fv _uniq.2087)) ((:c HSMul.hSMul) (:fv _uniq.2084) ((:c Set) (:fv _uniq.2087)) ((:c Set) (:fv _uniq.2087)) ((:c instHSMul) (:fv _uniq.2084) ((:c Set) (:fv _uniq.2087)) ((:c Set.smulSet) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2097))) (:fv... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedRing) (:fv _uniq.2084))"},{"name":"inst✝","sexp":"((:c SMul) (:fv _uniq.2084) (:fv _uniq.2087))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.2087))"},{"name":"... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"rintro","sourceEnd":2814,"sourceStart":2808,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2816,"sourceStart":2815,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":2816,"sourceStart":2815,"tag":"... | [{"role":"fresh_name","source":"y","source_end":2821,"source_start":2820,"syntax_kind":"ident"},{"role":"fresh_name","source":"hy","source_end":2825,"source_start":2823,"syntax_kind":"ident"}] | [{"source":"⟨y, hy, rfl⟩","source_end":2833,"source_start":2817,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 22 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11514638c5661b274a94d61fc0046ca72c5d4e78b5da3255a8ace6b7626edd69 | 13ff50259a87657a1f80c5e15151953d95f079eaa794d6b4d016c47da3b055d7 | c71aa7124de0f8932740567ee6ebb6fe7b0175333723be1bf4c9104933a076e3 | e6a5d3a4dcea316e356e438f2357e57e602344bdac0211675524edfc0e1da5d5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,251 | smul_balancedCore_subset | Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mem_balancedCore_iff</a>] at hy | case intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
hy : y ∈ balancedCore 𝕜 s
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | case intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
hy : ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ y ∈ t
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | ((:c Membership.mem) (:fv _uniq.2087) ((:c Set) (:fv _uniq.2087)) ((:c Set.instMembership) (:fv _uniq.2087)) ((:lambda _ (:fv _uniq.2087) ((:c HSMul.hSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2087) ((:c instHSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2097)) (:fv _uniq.2419) 0)) (:fv _uniq.2447)) ((:c b... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedRing) (:fv _uniq.2084))"},{"name":"inst✝","sexp":"((:c SMul) (:fv _uniq.2084) (:fv _uniq.2087))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.2087))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:lambda _ :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"rw","sourceEnd":2838,"sourceStart":2836,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2840,"sourceStart":2839,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mem_balancedCore_iff... | [] | [{"source":"mem_balancedCore_iff","source_end":2860,"source_start":2840,"syntax_kind":"ident"},{"source":"hy","source_end":2867,"source_start":2865,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 22 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f67410401b2e5ac0c84f927256e6e2a12f80febc5cecc92bbf382669c261f26 | e6a5d3a4dcea316e356e438f2357e57e602344bdac0211675524edfc0e1da5d5 | fe2a97e170fae11166a7bc38848caefc1986c2cdc377524bc64f318ac0a7fdbd | db40b3af4bc28915fbc159130bdc92f27ee84ce61c9f57913dc54715e6171719 |
cat-searcher/leandojo-benchmark-4-random | test | 4,252 | smul_balancedCore_subset | Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases hy with ⟨t, ht1, ht2, hy⟩ | case intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
hy : ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ y ∈ t
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | case intro.intro.intro.intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t✝ : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
t : Set E
ht1 : Balanced 𝕜 t
ht2 : t ⊆ s
hy : y ∈ t
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | ((:c Membership.mem) (:fv _uniq.2087) ((:c Set) (:fv _uniq.2087)) ((:c Set.instMembership) (:fv _uniq.2087)) ((:lambda _ (:fv _uniq.2087) ((:c HSMul.hSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2087) ((:c instHSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2097)) (:fv _uniq.2419) 0)) (:fv _uniq.2447)) ((:c b... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedRing) (:fv _uniq.2084))"},{"name":"inst✝","sexp":"((:c SMul) (:fv _uniq.2084) (:fv _uniq.2087))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.2087))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:lambda _ :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"rcases","sourceEnd":2876,"sourceStart":2870,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":13,"semanticRole":"local","source":"hy","sourceEnd":2879,"sourceStart":2877,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sou... | [] | [{"source":"hy","source_end":2879,"source_start":2877,"syntax_kind":"ident"},{"source":"⟨t, ht1, ht2, hy⟩","source_end":2906,"source_start":2885,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 22 | 8 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d56c94f028c27dcc4e61a98b1765a413d0698264147d9dbefcb889cf07488526 | db40b3af4bc28915fbc159130bdc92f27ee84ce61c9f57913dc54715e6171719 | ec88b738cfe9f6dbb23a175d23d64a82cef7599474cde1d17413ee2ea8dd1f5b | 256376a35b94dc21ebc2f4189997709b8fe12c8ed7dc97257f41db08760df14c |
cat-searcher/leandojo-benchmark-4-random | test | 4,253 | smul_balancedCore_subset | Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨t, ⟨ht1, ht2⟩, ht1 a ha (<a>Set.smul_mem_smul_set</a> hy)⟩ | case intro.intro.intro.intro.intro
𝕜 : Type u_1
E : Type u_2
ι : Type u_3
inst✝¹ : SeminormedRing 𝕜
inst✝ : SMul 𝕜 E
s✝ t✝ : Set E
x : E
s : Set E
a : 𝕜
ha : ‖a‖ ≤ 1
y : E
t : Set E
ht1 : Balanced 𝕜 t
ht2 : t ⊆ s
hy : y ∈ t
⊢ (fun x => a • x) y ∈ balancedCore 𝕜 s | ((:c Membership.mem) (:fv _uniq.2087) ((:c Set) (:fv _uniq.2087)) ((:c Set.instMembership) (:fv _uniq.2087)) ((:lambda _ (:fv _uniq.2087) ((:c HSMul.hSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2087) ((:c instHSMul) (:fv _uniq.2084) (:fv _uniq.2087) (:fv _uniq.2097)) (:fv _uniq.2419) 0)) (:fv _uniq.2447)) ((:c b... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"ι","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp":"((:c SeminormedRing) (:fv _uniq.2084))"},{"name":"inst✝","sexp":"((:c SMul) (:fv _uniq.2084) (:fv _uniq.2087))"},{"name":"s✝","sexp":"((:c Set) (:fv _uniq.2087))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:lambda _ :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","cont... | {"children":[{"source":"exact","sourceEnd":2914,"sourceStart":2909,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2918,"sourceStart":2915,"tag":"atom"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"t","sourceEnd":2919,"sourceStart":2918,"tag":"identifier"},{"source":",","sourceEnd":2920,"source... | [] | [{"source":"⟨t, ⟨ht1, ht2⟩, ht1 a ha (smul_mem_smul_set hy)⟩","source_end":2971,"source_start":2915,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2084","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2087","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_uni... | 22 | 9 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 51f9ed210f2fcfe19b4369214eef799aadb9570330b9e2b0f5d12c0caaec7a41 | 256376a35b94dc21ebc2f4189997709b8fe12c8ed7dc97257f41db08760df14c | 59cba0ba8d67c76335980f318324b311113d06a7ceafbff5176218e6c0f4110d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,254 | List.enumFrom_eq_nil | Mathlib/Data/List/Enum.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases l <;> simp | α : Type u_1
β : Type u_2
n : ℕ
l : List α
⊢ enumFrom n l = [] ↔ l = [] | ((:c Iff) ((:c Eq) ((:c List) ((:c Prod) (:c Nat) (:fv _uniq.14899))) ((:c List.enumFrom) (:fv _uniq.14899) (:fv _uniq.14975) (:fv _uniq.14976)) ((:c List.nil) ((:c Prod) (:c Nat) (:fv _uniq.14899)))) ((:c Eq) ((:c List) (:fv _uniq.14899)) (:fv _uniq.14976) ((:c List.nil) (:fv _uniq.14899)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:c Nat)"},{"name":"l","sexp":"((:c List) (:fv _uniq.14899))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:fv FV0)))))) (:arg :explicit 1 (:app (:c List.enumFrom) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:fv FV4)))) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14899","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14902","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":6789,"sourceStart":6784,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":4,"semanticRole":"local","source":"l","sourceEnd":6791,"sourceStart":6790,"tag":"identifie... | [] | [{"source":"l","source_end":6791,"source_start":6790,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14899","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14902","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 58 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3833216f3746b6bc719f7d09430cdef8003df0f49f294f92c80b4fd1d6c2cfa9 | 334b2cfc6c8b01dd9f5fd15c84192b715d10c0266404c9317569b9b2f69bdb29 | 4115d1e8703b0d845e78e8a6f9b9ab58f9dabeb2ff1bf7caf03dc596bed343df | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,257 | IsUnit.smul_sub_iff_sub_inv_smul | Mathlib/GroupTheory/GroupAction/Group.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>isUnit_smul_iff</a> r (1 - r⁻¹ • a), <a>smul_sub</a>, <a>smul_inv_smul</a>] | α : Type u
β : Type v
γ : Type w
inst✝⁵ : Group α
inst✝⁴ : Monoid β
inst✝³ : AddGroup β
inst✝² : DistribMulAction α β
inst✝¹ : IsScalarTower α β β
inst✝ : SMulCommClass α β β
r : α
a : β
⊢ IsUnit (r • 1 - a) ↔ IsUnit (1 - r⁻¹ • a) | ((:c Iff) ((:c IsUnit) (:fv _uniq.56244) (:fv _uniq.56252) ((:c HSub.hSub) (:fv _uniq.56244) (:fv _uniq.56244) (:fv _uniq.56244) ((:c instHSub) (:fv _uniq.56244) ((:c SubNegMonoid.toSub) (:fv _uniq.56244) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.56244) (:fv _uniq.57826)))) ((:c HSMul.hSMul) (:fv _uniq.56242) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"inst✝⁵","sexp":"((:c Group) (:fv _uniq.56242))"},{"name":"inst✝⁴","sexp":"((:c Monoid) (:fv _uniq.56244))"},{"name":"inst✝³","sexp":"((:c AddGroup) (:fv _uniq.56244))"},{"name":"inst✝²","sexp":"((... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsUnit) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56242","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56244","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":16075,"sourceStart":16073,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":16077,"sourceStart":16076,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"... | [] | [{"source":"isUnit_smul_iff r (1 - r⁻¹ • a)","source_end":16117,"source_start":16081,"syntax_kind":"Lean.Parser.Term.app"},{"source":"smul_sub","source_end":16127,"source_start":16119,"syntax_kind":"ident"},{"source":"smul_inv_smul","source_end":16142,"source_start":16129,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56242","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56244","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 167 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4d4ddd5fc04c8036082d0aaecb4d1ed55bf3dde1d9041c31d8f60a08e4a1140 | 960c66eccbb3e0177b42df244dc3c24bd3aa3721a6be3c2680949eb6f64f204e | 48e8f9d7c6ccf0dd1d0df1488d03650d8d01c34040d1a318abc0b697c7db35cb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,258 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":25410,"sourceStart":25406,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"h","source_end":25413,"source_start":25412,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 2 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d6e1a785f41a1489224973a826e96a4337aa32ede2b7d4aab58ca1add0fc52d3 | abc56d55988d6e719c0386f40958ed9cf05920311f049bed93bf1665f8118f42 | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,259 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have : f (x + y + z) = <a>FormalMultilinearSeries.sum</a> (<a>FormalMultilinearSeries.changeOrigin</a> p y) z := by rw [<a>mem_emetric_ball_zero_iff</a>, <a>lt_tsub_iff_right</a>, <a>add_comm</a>] at hz rw [p.changeOrigin_eval_of_finite hf.finite, <a>add_assoc</a>, hf.sum] refine <a>mem_emetric_ball_zero_iff</a>.2 (<a>... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c HasSum) (:fv _uniq.532882) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.532882) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.532882) (:fv _uniq.533002))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.532882) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.532882) ((:c SeminormedAddCommGroup.to... | [{"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c HasSum) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"have","sourceEnd":25507,"sourceStart":25503,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":25508,"sourceStart":25508,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":25508,"sourceStart":25508,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"f (x + y + z) =\n FormalMultilinearSeries.sum (FormalMultilinearSeries.changeOrigin p y) z","source_end":25606,"source_start":25510,"syntax_kind":"«term_=_»"},{"source":"mem_emetric_ball_zero_iff","source_end":25648,"source_start":25623,"syntax_kind":"ident"},{"source":"hz","source_end":25684,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 9 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2a4d325b56268de6ee70ec02424698ebda97be92182e85cda67ad6089fdb9a7b | 828c1554801a4a34bd22798460172061c451a8caba4356fdb2fa57aabc34c982 | f456164d78a93f31fd7184cc19d37489a1bd58df9997ce714cfd52752756f37b | eb558b79b87af69169d6c185d879ac0357799714108bfeb4f6adc7a0e85be2e9 |
cat-searcher/leandojo-benchmark-4-random | test | 4,260 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [this] | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c HasSum) (:fv _uniq.532882) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.532882) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.532882) (:fv _uniq.533002))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.532882) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.532882) ((:c SeminormedAddCommGroup.to... | [{"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c HasSum) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":25864,"sourceStart":25862,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25866,"sourceStart":25865,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":28,"seman... | [] | [{"source":"this","source_end":25870,"source_start":25866,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 23 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a4a8102418d501fdc152c890d121475051487c49e234801ec11f588ab169c392 | eb558b79b87af69169d6c185d879ac0357799714108bfeb4f6adc7a0e85be2e9 | 65e47f2d4a9bfabc21e1664a0b073b87e8fee657aeade999395c39aa954c5bad | c4eebf0fc6b9d89b9744cc2cd935bb410c0400cfde7d06313aa461e83d276077 |
cat-searcher/leandojo-benchmark-4-random | test | 4,261 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply (p.changeOrigin y).<a>FormalMultilinearSeries.hasSum_of_finite</a> fun _ => p.changeOrigin_finite_of_finite hf.finite | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c HasSum) (:fv _uniq.532882) (:c Nat) ((:c AddCommGroup.toAddCommMonoid) (:fv _uniq.532882) ((:c NormedAddCommGroup.toAddCommGroup) (:fv _uniq.532882) (:fv _uniq.533002))) ((:c UniformSpace.toTopologicalSpace) (:fv _uniq.532882) ((:c PseudoMetricSpace.toUniformSpace) (:fv _uniq.532882) ((:c SeminormedAddCommGroup.to... | [{"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c HasSum) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:c Nat)) (:arg :instance 2 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV2))))) (:arg :instance 3 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 4 (:lambda n :explicit (:c Nat) (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"apply","sourceEnd":25881,"sourceStart":25876,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":25883,"sourceStart":25882,"tag":"atom"},{"children":[{"source":"p.changeOrigin","sourceEnd":25897,"sourceStart":25883,"tag":"identifier"},{"children":[{"contextIndex":22,"s... | [] | [{"source":"(p.changeOrigin y).hasSum_of_finite fun _ => p.changeOrigin_finite_of_finite hf.finite","source_end":25968,"source_start":25882,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 26 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e5513437b81b659424bea9f6968dbd29c156368f54f1cee5409e9842af077924 | c4eebf0fc6b9d89b9744cc2cd935bb410c0400cfde7d06313aa461e83d276077 | 3f9de3517586e971b6f9409e8c2e7b4711d60401de7485aea9eb83365f03ae49 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,262 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mem_emetric_ball_zero_iff</a>, <a>lt_tsub_iff_right</a>, <a>add_comm</a>] at hz | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c Eq) (:fv _uniq.532882) ((:fv _uniq.533215) ((:c HAdd.hAdd) (:fv _uniq.532879) (:fv _uniq.532879) (:fv _uniq.532879) ((:c instHAdd) (:fv _uniq.532879) ((:c AddCommMagma.toAdd) (:fv _uniq.532879) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.532879) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.532879) ((:c A... | [{"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":25621,"sourceStart":25619,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25623,"sourceStart":25622,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mem_emetric_ball... | [] | [{"source":"mem_emetric_ball_zero_iff","source_end":25648,"source_start":25623,"syntax_kind":"ident"},{"source":"hz","source_end":25684,"source_start":25682,"syntax_kind":"ident"},{"source":"lt_tsub_iff_right","source_end":25667,"source_start":25650,"syntax_kind":"ident"},{"source":"add_comm","source_end":25677,"source... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 11 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 24a75f0f79ff99ebde4719615f9db93eae0e4c30afe8c92fda31bd9f1a65be90 | 02fd601b2c516cf8654cc9b7009aa66300cc7831f58901cc33f19b52cf311ee0 | f9038f35d67162c2d4697c3b40d36a2242ba1be5da9a2a708607d2bc62a038f8 | 947ef12fd05ce13fc19923929591c6ba7a0fa4b2114d81b7a3c4a3a21dca2011 |
cat-searcher/leandojo-benchmark-4-random | test | 4,263 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [p.changeOrigin_eval_of_finite hf.finite, <a>add_assoc</a>, hf.sum] | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c Eq) (:fv _uniq.532882) ((:fv _uniq.533215) ((:c HAdd.hAdd) (:fv _uniq.532879) (:fv _uniq.532879) (:fv _uniq.532879) ((:c instHAdd) (:fv _uniq.532879) ((:c AddCommMagma.toAdd) (:fv _uniq.532879) ((:c AddCommSemigroup.toAddCommMagma) (:fv _uniq.532879) ((:c AddCommMonoid.toAddCommSemigroup) (:fv _uniq.532879) ((:c A... | [{"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV2)) (:arg :explicit 1 (:app (:fv FV11) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV1)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"rw","sourceEnd":25693,"sourceStart":25691,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":25695,"sourceStart":25694,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"p... | [] | [{"source":"p.changeOrigin_eval_of_finite hf.finite","source_end":25734,"source_start":25695,"syntax_kind":"Lean.Parser.Term.app"},{"source":"add_assoc","source_end":25745,"source_start":25736,"syntax_kind":"ident"},{"source":"hf.sum","source_end":25753,"source_start":25747,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 16 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f6b4d3f28b882d5862663767887092758d520ccdd6f3778e42e47f6d5b31884c | 947ef12fd05ce13fc19923929591c6ba7a0fa4b2114d81b7a3c4a3a21dca2011 | 1472246b5032c06e365c48fc0a3b41ca30317822120a8f9cb196614862cd4eaf | 981373e5f26f2bb62aa42ef02bfa43b4fae0ba67f117623279ce4a4381c64280 |
cat-searcher/leandojo-benchmark-4-random | test | 4,264 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>mem_emetric_ball_zero_iff</a>.2 (<a>lt_of_le_of_lt</a> ?_ hz) | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c Membership.mem) (:fv _uniq.532879) ((:c Set) (:fv _uniq.532879)) ((:c Set.instMembership) (:fv _uniq.532879)) ((:c HAdd.hAdd) (:fv _uniq.532879) (:fv _uniq.532879) (:fv _uniq.532879) ((:c instHAdd) (:fv _uniq.532879) ((:c AddSemigroup.toAdd) (:fv _uniq.532879) ((:c AddMonoid.toAddSemigroup) (:fv _uniq.532879) ((: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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:c HAdd.hAdd) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"refine","sourceEnd":25767,"sourceStart":25761,"tag":"atom"},{"children":[{"children":[{"name":"mem_emetric_ball_zero_iff","semanticRole":"global","source":"mem_emetric_ball_zero_iff","sourceEnd":25793,"sourceStart":25768,"tag":"identifier"},{"source":".","sourceEnd":25794,"sourceStart":25793,"ta... | [] | [{"source":"mem_emetric_ball_zero_iff.2 (lt_of_le_of_lt ?_ hz)","source_end":25818,"source_start":25768,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 21 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2014312977f5800814e860b2a702d66c3c7e1201945cfa5eb5f7de5fde42ae3 | 981373e5f26f2bb62aa42ef02bfa43b4fae0ba67f117623279ce4a4381c64280 | 69b9afbb8141e024ac0b1459bad54eb381cf3e4f43314948aa4126c25f55840d | c71c31c7d148b1be8dc75e6c1c666c94fcb0ddb55f096274d1a564c983ae39e6 |
cat-searcher/leandojo-benchmark-4-random | test | 4,265 | HasFiniteFPowerSeriesOnBall.changeOrigin | Mathlib/Analysis/Analytic/CPolynomial.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact mod_cast <a>nnnorm_add_le</a> y z | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
f g : E → F
p pf pg : FormalMultilinearSeries 𝕜 E F
x✝ : E
r r'... | ((:c LE.le) (:c ENNReal) ((:c Preorder.toLE) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"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✝⁶","sexp":"((:c NontriviallyNormedField) (:fv _uniq.532876))"},{"name":"inst✝⁵","sexp":"((:c NormedAddCommGroup) (:fv _uniq.532879))"},{"name":"... | (:app (:c LE.le) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c ENNReal.ofNNReal) (:arg :explicit 0 (:app (:c NNNorm.nnnorm) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c NNNorm) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":25830,"sourceStart":25825,"tag":"atom"},{"children":[{"source":"mod_cast","sourceEnd":25839,"sourceStart":25831,"tag":"atom"},{"children":[{"name":"nnnorm_add_le","semanticRole":"global","source":"nnnorm_add_le","sourceEnd":25853,"sourceStart":25840,"tag":"identifier"},{"child... | [] | [{"source":"mod_cast nnnorm_add_le y z","source_end":25857,"source_start":25831,"syntax_kind":"Lean.modCast"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.532876","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.532879","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 84 | 22 | exact | true | 1 | 27 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a67906001bd98f00e15f2788a08a73760e1708d5b9b1917871bcf63902537c6d | c71c31c7d148b1be8dc75e6c1c666c94fcb0ddb55f096274d1a564c983ae39e6 | 0ae27911f4748556dea06b5f56bf8f7f371ce6744e2d255f197725834ebe73e0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,266 | Set.image_mono | Mathlib/Data/Set/Image.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro - ⟨a, ha, rfl⟩ | α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
f : α → β
s t : Set α
h : s ⊆ t
⊢ f '' s ⊆ f '' t | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
f : α → β
s t : Set α
h : s ⊆ t
a : α
ha : a ∈ s
⊢ f a ∈ f '' t | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.11394)) ((:c Set.instHasSubset) (:fv _uniq.11394)) ((:c Set.image) (:fv _uniq.11391) (:fv _uniq.11394) (:fv _uniq.11407) (:fv _uniq.11410)) ((:c Set.image) (:fv _uniq.11391) (:fv _uniq.11394) (:fv _uniq.11407) (:fv _uniq.11413))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.11391) (:fv _uniq.11394))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.11391))"},{"name":"... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11391","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11394","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rintro","sourceEnd":9279,"sourceStart":9273,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"-","sourceEnd":9281,"sourceStart":9280,"tag":"atom"}],"kind":"Lean.Parser.Tactic.rcasesPat.clear","source":"-","sourceEnd":9281,"sourceStart":9280,"tag":"node"}],"kind":"Lean.Parser.Tactic... | [{"role":"fresh_name","source":"a","source_end":9286,"source_start":9285,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":9290,"source_start":9288,"syntax_kind":"ident"}] | [{"source":"-","source_end":9281,"source_start":9280,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.clear"},{"source":"⟨a, ha, rfl⟩","source_end":9298,"source_start":9282,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11391","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11394","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59c5336a6b8f4a1b8b9ed17e2efb7542bbe3c04b9ad3f190fdf5decd0a3374c4 | 5ec223f2ff90b70bc8611e8c4daa9bd9e9518ff60f1241d04a66702de929d1b8 | 8456315df8ece4418b67dfd1e119a30128863d212f3a310d370f084de1efb4ee | 2333e0feb808ab65f16fcc9b2269b3d6bc7dce014c078a2f08333ee00bed0139 |
cat-searcher/leandojo-benchmark-4-random | test | 4,267 | Set.image_mono | Mathlib/Data/Set/Image.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.mem_image_of_mem</a> f (h ha) | case intro.intro
α : Type u_1
β : Type u_2
γ : Type u_3
ι : Sort u_4
ι' : Sort u_5
f : α → β
s t : Set α
h : s ⊆ t
a : α
ha : a ∈ s
⊢ f a ∈ f '' t | ((:c Membership.mem) (:fv _uniq.11394) ((:c Set) (:fv _uniq.11394)) ((:c Set.instMembership) (:fv _uniq.11394)) ((:fv _uniq.11407) (:fv _uniq.11498)) ((:c Set.image) (:fv _uniq.11391) (:fv _uniq.11394) (:fv _uniq.11407) (:fv _uniq.11413))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"ι","sexp":"(:sort u_4)"},{"name":"ι'","sexp":"(:sort u_5)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.11391) (:fv _uniq.11394))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.11391))"},{"name":"... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 3 (:app (:fv FV5) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11391","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11394","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":9305,"sourceStart":9300,"tag":"atom"},{"children":[{"name":"Set.mem_image_of_mem","semanticRole":"global","source":"mem_image_of_mem","sourceEnd":9322,"sourceStart":9306,"tag":"identifier"},{"children":[{"contextIndex":5,"semanticRole":"local","source":"f","sourceEnd":9324,"so... | [] | [{"source":"mem_image_of_mem f (h ha)","source_end":9331,"source_start":9306,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.11391","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.11394","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 91 | 6 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8dbd023a079d1ef1abd1159bc15fa613da56e15974eeceab4bf619c015d64c9c | 2333e0feb808ab65f16fcc9b2269b3d6bc7dce014c078a2f08333ee00bed0139 | 5b0759a7dfa5a6d6aa78dec58046a1b8ecefe159857be8c82514b50881f6bcd0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,268 | Filter.EventuallyEq.restrict | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hfg.filter_mono ?_ | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t : Set α
f g : α → δ
s : Set α
hfg : f =ᶠ[ae μ] g
⊢ f =ᶠ[ae (μ.restrict s)] g | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t : Set α
f g : α → δ
s : Set α
hfg : f =ᶠ[ae μ] g
⊢ ae (μ.restrict s) ≤ ae μ | ((:c Filter.EventuallyEq) (:fv _uniq.116115) (:fv _uniq.116121) ((:c MeasureTheory.ae) (:fv _uniq.116115) ((:c MeasureTheory.Measure) (:fv _uniq.116115) (:fv _uniq.116130)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.116115) (:fv _uniq.116130)) ((:c MeasureTheory.Measure.instOuterMeasureClass) (:fv _uniq.116115)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.116115))"},{"name":"inst✝... | (:app (:c Filter.EventuallyEq) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV3)) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c MeasureTheory.Measure) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpac... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"refine","sourceEnd":35945,"sourceStart":35939,"tag":"atom"},{"children":[{"source":"hfg.filter_mono","sourceEnd":35961,"sourceStart":35946,"tag":"identifier"},{"children":[{"children":[{"source":"?","sourceEnd":35963,"sourceStart":35962,"tag":"atom"},{"children":[{"source":"_","sourceEnd":35964,... | [] | [{"source":"hfg.filter_mono ?_","source_end":35964,"source_start":35946,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 198 | 4 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3227ec5f9f87536b587ffb97570ee36a155b03c326de4973a027a722f7ff65fb | 48cddbaffe2c4129492ca269653d677ca72a3441f72405473161bd1415bbcfcd | 87156e24515fc64606a6a3769cdae79f48ce00fed6aa3748d12422d5b9d05d99 | ca1f722d369df27ac33c3ee60e50e1ba3e7ec33587dd855a931b068c10a64ef2 |
cat-searcher/leandojo-benchmark-4-random | test | 4,269 | Filter.EventuallyEq.restrict | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MeasureTheory.Measure.ae_le_iff_absolutelyContinuous</a>] | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t : Set α
f g : α → δ
s : Set α
hfg : f =ᶠ[ae μ] g
⊢ ae (μ.restrict s) ≤ ae μ | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t : Set α
f g : α → δ
s : Set α
hfg : f =ᶠ[ae μ] g
⊢ μ.restrict s ≪ μ | ((:c LE.le) ((:c Filter) (:fv _uniq.116115)) ((:c Preorder.toLE) ((:c Filter) (:fv _uniq.116115)) ((:c PartialOrder.toPreorder) ((:c Filter) (:fv _uniq.116115)) ((:c Filter.instPartialOrder) (:fv _uniq.116115)))) ((:c MeasureTheory.ae) (:fv _uniq.116115) ((:c MeasureTheory.Measure) (:fv _uniq.116115) (:fv _uniq.116130)... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.116115))"},{"name":"inst✝... | (:app (:c LE.le) (:arg :implicit-type 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1)))) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:app (:c Filter) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 2 (:app (:c MeasureTheory.ae) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:app (:c Me... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"rw","sourceEnd":35969,"sourceStart":35967,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":35971,"sourceStart":35970,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheory.Me... | [] | [{"source":"Measure.ae_le_iff_absolutelyContinuous","source_end":36009,"source_start":35971,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 198 | 5 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bf2057ac20cd3c7495659a54a2f6e82246433ee5cd8d603aa824f56a1533f976 | ca1f722d369df27ac33c3ee60e50e1ba3e7ec33587dd855a931b068c10a64ef2 | d07618817c0088363c7c0d958ae227e3083957fef17f34910d690579ce8d732c | 7ccbac0cdc018f094de81a5dbfa604d93c36259bb075423bf115d85fda390b52 |
cat-searcher/leandojo-benchmark-4-random | test | 4,270 | Filter.EventuallyEq.restrict | Mathlib/MeasureTheory/Measure/Restrict.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>MeasureTheory.Measure.absolutelyContinuous_of_le</a> <a>MeasureTheory.Measure.restrict_le_self</a> | R : Type u_1
α : Type u_2
β : Type u_3
δ : Type u_4
γ : Type u_5
ι : Type u_6
m0 : MeasurableSpace α
inst✝¹ : MeasurableSpace β
inst✝ : MeasurableSpace γ
μ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α
s✝ s' t : Set α
f g : α → δ
s : Set α
hfg : f =ᶠ[ae μ] g
⊢ μ.restrict s ≪ μ | ((:c MeasureTheory.Measure.AbsolutelyContinuous) (:fv _uniq.116115) (:fv _uniq.116130) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.116115) (:fv _uniq.116130) (:fv _uniq.116144) (:fv _uniq.116608)) (:fv _uniq.116144)) | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"δ","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.116115))"},{"name":"inst✝... | (:app (:c MeasureTheory.Measure.AbsolutelyContinuous) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:app (:c MeasureTheory.Measure.restrict) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit 1) (:arg :explicit 2 (:fv FV9)) (:arg :explicit 3 (:fv FV23)))) (:arg :explicit 3 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"source":"exact","sourceEnd":36018,"sourceStart":36013,"tag":"atom"},{"children":[{"name":"MeasureTheory.Measure.absolutelyContinuous_of_le","semanticRole":"global","source":"Measure.absolutelyContinuous_of_le","sourceEnd":36053,"sourceStart":36019,"tag":"identifier"},{"children":[{"name":"MeasureTheory.M... | [] | [{"source":"Measure.absolutelyContinuous_of_le Measure.restrict_le_self","source_end":36078,"source_start":36019,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.116112","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.116115","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 198 | 8 | exact | true | 1 | 24 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37ecaafe3c08a243b8b37498b8ae26757126a4f0dbeec9393f1cacb09b0479ab | 7ccbac0cdc018f094de81a5dbfa604d93c36259bb075423bf115d85fda390b52 | ebafc1048a37f75fdfdfc5e8bfdd8d0112441e86e5f93029d19a99e2c7e4b2ae | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,271 | Fin.castAdd_inj | Mathlib/Data/Fin/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Fin.ext_iff</a>] | n m : ℕ
a b : Fin m
⊢ castAdd n a = castAdd n b ↔ a = b | ((:c Iff) ((:c Eq) ((:c Fin) ((:c HAdd.hAdd) (:c Nat) (:c Nat) (:c Nat) ((:c instHAdd) (:c Nat) (:c instAddNat)) (:fv _uniq.23614) (:fv _uniq.23612))) ((:c Fin.castAdd) (:fv _uniq.23614) (:fv _uniq.23612) (:fv _uniq.23628)) ((:c Fin.castAdd) (:fv _uniq.23614) (:fv _uniq.23612) (:fv _uniq.23629))) ((:c Eq) ((:c Fin) (:f... | [{"name":"n","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"a","sexp":"((:c Fin) (:fv _uniq.23614))"},{"name":"b","sexp":"((:c Fin) (:fv _uniq.23614))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Fin) (:arg :explicit 0 (:app (:c HAdd.hAdd) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HAdd) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23612","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"name":"m","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":24957,"sourceStart":24953,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"ext_iff","source_end":24966,"source_start":24959,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.23612","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.23614","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":3,"internal_name":"_un... | 273 | 2 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 17f074b9709ff566cb80b0e6cf541c9f844d7d1be3aa09b44eebf96798049a60 | 5368e003de04dbb2022ed28a780a45a5d904662800510570695aed2df4dbd36b | ddb07a9cc9d6065fe1a9dc637bd55ef264211c1f65d80a8717bc396cab1a6f0f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,272 | Matrix.conjTranspose_zpow | Mathlib/LinearAlgebra/Matrix/ZPow.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>zpow_natCast</a>, <a>zpow_natCast</a>, <a>Matrix.conjTranspose_pow</a>] | n' : Type u_1
inst✝³ : DecidableEq n'
inst✝² : Fintype n'
R : Type u_2
inst✝¹ : CommRing R
inst✝ : StarRing R
A : M
n : ℕ
⊢ (A ^ ↑n)ᴴ = Aᴴ ^ ↑n | ((:c Eq) ((:c Matrix) (:fv _uniq.139795) (:fv _uniq.139795) (:fv _uniq.139810)) ((:c Matrix.conjTranspose) (:fv _uniq.139795) (:fv _uniq.139795) (:fv _uniq.139810) ((:c InvolutiveStar.toStar) (:fv _uniq.139810) ((:c StarAddMonoid.toInvolutiveStar) (:fv _uniq.139810) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.139810)... | [{"name":"n'","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.139795))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.139795))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.139810))"},{"name":"inst✝","sexp":"((:c StarRing) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:app (:c Matrix.conjTranspose) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139795","is_instance":false,"is_let":false,"name":"n'","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.139802","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c DecidableEq) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":13950,"sourceStart":13948,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13952,"sourceStart":13951,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"zpow_natCast","source_end":13964,"source_start":13952,"syntax_kind":"ident"},{"source":"zpow_natCast","source_end":13978,"source_start":13966,"syntax_kind":"ident"},{"source":"conjTranspose_pow","source_end":13997,"source_start":13980,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139795","is_instance":false,"is_let":false,"user_name":"n'"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.139802","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_inde... | 95 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b8e6df8e10b3c2471b43c4efe3ace5915d57021382c5ed8266c5022f6f7acb0 | 435019dc5823715b869b87dbcca5816c44b9b6919d34637f2d5ab8345368e20e | fe8c8bcb8400ea19f7e98acc9959a7eef751badb02660b350ccd371ce2a25721 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,273 | Matrix.conjTranspose_zpow | Mathlib/LinearAlgebra/Matrix/ZPow.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>zpow_negSucc</a>, <a>zpow_negSucc</a>, <a>Matrix.conjTranspose_nonsing_inv</a>, <a>Matrix.conjTranspose_pow</a>] | n' : Type u_1
inst✝³ : DecidableEq n'
inst✝² : Fintype n'
R : Type u_2
inst✝¹ : CommRing R
inst✝ : StarRing R
A : M
n : ℕ
⊢ (A ^ -[n+1])ᴴ = Aᴴ ^ -[n+1] | ((:c Eq) ((:c Matrix) (:fv _uniq.139795) (:fv _uniq.139795) (:fv _uniq.139810)) ((:c Matrix.conjTranspose) (:fv _uniq.139795) (:fv _uniq.139795) (:fv _uniq.139810) ((:c InvolutiveStar.toStar) (:fv _uniq.139810) ((:c StarAddMonoid.toInvolutiveStar) (:fv _uniq.139810) ((:c AddMonoidWithOne.toAddMonoid) (:fv _uniq.139810)... | [{"name":"n'","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝³","sexp":"((:c DecidableEq) (:fv _uniq.139795))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.139795))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.139810))"},{"name":"inst✝","sexp":"((:c StarRing) (:fv _uniq.... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV3)))) (:arg :explicit 1 (:app (:c Matrix.conjTranspose) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV3)) (:arg :instance 3 (:inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139795","is_instance":false,"is_let":false,"name":"n'","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.139802","is_instance":true,"is_let":false,"name":"inst✝³","sexp":"(:app (:c DecidableEq) (:arg :... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":14018,"sourceStart":14016,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":14020,"sourceStart":14019,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"zpow_negSucc","source_end":14032,"source_start":14020,"syntax_kind":"ident"},{"source":"zpow_negSucc","source_end":14046,"source_start":14034,"syntax_kind":"ident"},{"source":"conjTranspose_nonsing_inv","source_end":14073,"source_start":14048,"syntax_kind":"ident"},{"source":"conjTranspose_pow","source_end"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.139795","is_instance":false,"is_let":false,"user_name":"n'"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.139802","is_instance":true,"is_let":false,"user_name":"inst✝³"},{"binder_role":":instance-implicit","context_inde... | 95 | 11 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | be8715d13153f14560e4edae52e84eab7c6aabd8425eb6186defb764ecbfbfa1 | b9c53fef46a337cfba0bf442ae58530f80fce2661be8dd0b7f24144297e30813 | 721afa810ee1db0490c15f1938760dd274bb803ea7970858faff2ad3564de082 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,274 | List.countP_join' | Mathlib/Data/List/Join.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>List.join</a>, <a>List.countP_append</a>, <a>List.map_cons</a>, <a>Nat.sum_cons</a>, countP_join' _ l] | α : Type u_1
β : Type u_2
p : α → Bool
a : List α
l : List (List α)
⊢ countP p (a :: l).join = Nat.sum (map (countP p) (a :: l)) | ((:c Eq) (:c Nat) ((:c List.countP) (:fv _uniq.2533) (:fv _uniq.2579) ((:c List.join) (:fv _uniq.2533) ((:c List.cons) ((:c List) (:fv _uniq.2533)) (:fv _uniq.2662) (:fv _uniq.2663)))) ((:c Nat.sum) ((:c List.map) ((:c List) (:fv _uniq.2533)) (:c Nat) ((:c List.countP) (:fv _uniq.2533) (:fv _uniq.2579)) ((:c List.cons)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"p","sexp":"(:forall _ (:fv _uniq.2533) (:c Bool))"},{"name":"a","sexp":"((:c List) (:fv _uniq.2533))"},{"name":"l","sexp":"((:c List) ((:c List) (:fv _uniq.2533)))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c List.countP) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV3)) (:arg :explicit 2 (:app (:c List.join) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List.cons) (:arg :implicit-type 0 (:app (:c List) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2533","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2536","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":explicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":2745,"sourceStart":2743,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2747,"sourceStart":2746,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"join","source_end":2751,"source_start":2747,"syntax_kind":"ident"},{"source":"countP_append","source_end":2766,"source_start":2753,"syntax_kind":"ident"},{"source":"map_cons","source_end":2776,"source_start":2768,"syntax_kind":"ident"},{"source":"Nat.sum_cons","source_end":2790,"source_start":2778,"syntax_k... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2533","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2536","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq... | 21 | 2 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d23618b58020fea8ffbc7f50708ca09fbf9855605a5b0737636282708d52594f | d379871a80c8de3d53b3dd43641281786c7820081740dbb99db5238ee5836e10 | bcd1c5a8c36f4c1528e6940d442933bc3f54e85bc6b4e4dd8481b2142ada2065 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,275 | NormedSpace.vonNBornology_eq | Mathlib/Analysis/LocallyConvex/Bounded.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Bornology.ext_iff_isBounded</a>] | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
⊢ Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.toBornology | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
⊢ ∀ (s : Set E), Bornology.IsBounded s ↔ Bornology.IsBounded s | ((:c Eq) ((:c Bornology) (:fv _uniq.247613)) ((:c Bornology.vonNBornology) (:fv _uniq.247607) (:fv _uniq.247613) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.247607) (:fv _uniq.247625)) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.247613) (:fv _uniq.247628)) ((:c NormedSpace.toModule) (:fv _uniq.247... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜'","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"E'","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.247607))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Bornology) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c Bornology.vonNBornology) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c NormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"name":"𝕜'","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"rw","sourceEnd":19977,"sourceStart":19975,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19979,"sourceStart":19978,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Bornology.ext_if... | [] | [{"source":"Bornology.ext_iff_isBounded","source_end":20006,"source_start":19979,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"user_name":"𝕜'"},{"binder_role":":implicit","context_index":2,"internal_name"... | 128 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 350bee190151989fdcb7a4fc4846b96110f7a7108cc2fd3530dc568b2bc95d6a | 4579f0327c3e321c6e140ecd832dfb95e90a4a6357ab2ef147e5c912f66a016b | 4e65e6852ab844cac43b75d66a92ecf8df5a6555910bc16829335cf52ce6b0ce | 11d34b613befd2392af018ec72669bbe69a56d01c0e11459962172cc99945f86 |
cat-searcher/leandojo-benchmark-4-random | test | 4,276 | NormedSpace.vonNBornology_eq | Mathlib/Analysis/LocallyConvex/Bounded.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro s | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
⊢ ∀ (s : Set E), Bornology.IsBounded s ↔ Bornology.IsBounded s | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
s : Set E
⊢ Bornology.IsBounded s ↔ Bornology.IsBounded s | (:forall s ((:c Set) (:fv _uniq.247613)) ((:c Iff) ((:c Bornology.IsBounded) (:fv _uniq.247613) ((:c Bornology.vonNBornology) (:fv _uniq.247607) (:fv _uniq.247613) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.247607) (:fv _uniq.247625)) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.247613) (:fv _uniq... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜'","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"E'","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.247607))"... | (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV2))) (:app (:c Iff) (:arg :explicit 0 (:app (:c Bornology.IsBounded) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Bornology) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 0))) (:arg :explicit 1 (:app (:c Bornology.IsBounded)... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"name":"𝕜'","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"intro","sourceEnd":20015,"sourceStart":20010,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":20017,"sourceStart":20016,"tag":"identifier"}],"kind":"null","source":"s","sourceEnd":20017,"sourceStart":20016,"tag":"node"}],"kind":"Lean.Parser.Tactic.intro","source... | [{"role":"fresh_name","source":"s","source_end":20017,"source_start":20016,"syntax_kind":"ident"}] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"user_name":"𝕜'"},{"binder_role":":implicit","context_index":2,"internal_name"... | 128 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 45df3d29dfd797f4a5e5a004c5430beee91be99408cb0812412e1247dedf8cce | 11d34b613befd2392af018ec72669bbe69a56d01c0e11459962172cc99945f86 | 0a51bbeea7c70886e909365c9565310e61329a03af1dc6cc3a9d3459a6b0303f | 9e0a5d76050c90b1d8274aed31ef16a15de6d6d800c6c1582c6d4b115a81fd76 |
cat-searcher/leandojo-benchmark-4-random | test | 4,277 | NormedSpace.vonNBornology_eq | Mathlib/Analysis/LocallyConvex/Bounded.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Bornology.isBounded_iff_isVonNBounded</a>] | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
s : Set E
⊢ Bornology.IsBounded s ↔ Bornology.IsBounded s | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
s : Set E
⊢ Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s | ((:c Iff) ((:c Bornology.IsBounded) (:fv _uniq.247613) ((:c Bornology.vonNBornology) (:fv _uniq.247607) (:fv _uniq.247613) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.247607) (:fv _uniq.247625)) ((:c SeminormedAddCommGroup.toAddCommGroup) (:fv _uniq.247613) (:fv _uniq.247628)) ((:c NormedSpace.toModule) (:fv... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜'","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"E'","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.247607))"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Bornology.IsBounded) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Bornology) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:fv FV10)))) (:arg :explicit 1 (:app (:c Bornology.IsBounded) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:in... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"name":"𝕜'","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"rw","sourceEnd":20022,"sourceStart":20020,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":20024,"sourceStart":20023,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Bornology.isBoun... | [] | [{"source":"Bornology.isBounded_iff_isVonNBounded","source_end":20061,"source_start":20024,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"user_name":"𝕜'"},{"binder_role":":implicit","context_index":2,"internal_name"... | 128 | 8 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a170a2ae75383fb0ad5a76320f2e6f8cf9618c927337cdfb1f4a8a986abbd0bf | 9e0a5d76050c90b1d8274aed31ef16a15de6d6d800c6c1582c6d4b115a81fd76 | 17afff8a8a84ebd42e94b0d0ce8d7971b847e7668d7d0177c0bb9df79b28b7b5 | e64295884e605ab77f5fcd05c388463eb6c4e73e8e5e419e5e7c4da58bdd910b |
cat-searcher/leandojo-benchmark-4-random | test | 4,278 | NormedSpace.vonNBornology_eq | Mathlib/Analysis/LocallyConvex/Bounded.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>NormedSpace.isVonNBounded_iff</a> _ | 𝕜 : Type u_1
𝕜' : Type u_2
E : Type u_3
E' : Type u_4
F : Type u_5
ι : Type u_6
inst✝² : NontriviallyNormedField 𝕜
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace 𝕜 E
s : Set E
⊢ Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s | ((:c Iff) ((:c Bornology.IsVonNBounded) (:fv _uniq.247607) (:fv _uniq.247613) ((:c SeminormedCommRing.toSeminormedRing) (:fv _uniq.247607) ((:c NormedCommRing.toSeminormedCommRing) (:fv _uniq.247607) ((:c NormedField.toNormedCommRing) (:fv _uniq.247607) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.247607) (:f... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"𝕜'","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"E'","sexp":"(:sort (+ u_4 1))"},{"name":"F","sexp":"(:sort (+ u_5 1))"},{"name":"ι","sexp":"(:sort (+ u_6 1))"},{"name":"inst✝²","sexp":"((:c NontriviallyNormedField) (:fv _uniq.247607))"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Bornology.IsVonNBounded) (:arg :explicit 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c SeminormedRing) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c SMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"name":"𝕜'","sexp":"(:sort Type)"},{"binder_role":":implicit"... | {"children":[{"source":"exact","sourceEnd":20070,"sourceStart":20065,"tag":"atom"},{"children":[{"name":"NormedSpace.isVonNBounded_iff","semanticRole":"global","source":"isVonNBounded_iff","sourceEnd":20088,"sourceStart":20071,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":20090,"sourceStart":2... | [] | [{"source":"isVonNBounded_iff _","source_end":20090,"source_start":20071,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.247607","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.247610","is_instance":false,"is_let":false,"user_name":"𝕜'"},{"binder_role":":implicit","context_index":2,"internal_name"... | 128 | 11 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54d76a5270e4e38fbadc5c5e612f1405e30412c6949a33b551e4465bb3ae89ff | e64295884e605ab77f5fcd05c388463eb6c4e73e8e5e419e5e7c4da58bdd910b | 0f1cb59e16d4bcc5fb0e0c54e54f81f274fcbdf458abf40cf1d248584779fd08 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,279 | Rat.mkRat_nonneg | Mathlib/Algebra/Order/Ring/Rat.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>Rat.divInt_nonneg</a> ha (<a>Int.natCast_nonneg</a> _) | a✝ b✝ c p q : ℚ
a : ℤ
ha : 0 ≤ a
b : ℕ
⊢ 0 ≤ mkRat a b | ((:c LE.le) (:c Rat) (:c Rat.instLE) ((:c OfNat.ofNat) (:c Rat) (:lit 0) ((:c Rat.instOfNat) (:lit 0))) ((:c mkRat) (:fv _uniq.1829) (:fv _uniq.1831))) | [{"name":"a✝","sexp":"(:c Rat)"},{"name":"b✝","sexp":"(:c Rat)"},{"name":"c","sexp":"(:c Rat)"},{"name":"p","sexp":"(:c Rat)"},{"name":"q","sexp":"(:c Rat)"},{"name":"a","sexp":"(:c Int)"},{"name":"ha","sexp":"((:c LE.le) (:c Int) (:c Int.instLEInt) ((:c OfNat.ofNat) (:c Int) (:lit 0) ((:c instOfNat) (:lit 0))) (:fv _u... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Rat))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Rat)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Rat)) (:arg :explici... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1744","is_instance":false,"is_let":false,"name":"a✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1746","is_instance":false,"is_let":false,"name":"b✝","sexp":"(:c Rat)"},{"binder_role":":implicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":1642,"sourceStart":1637,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"divInt_nonneg ha (Int.natCast_nonneg _)","source_end":1688,"source_start":1649,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1744","is_instance":false,"is_let":false,"user_name":"a✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1746","is_instance":false,"is_let":false,"user_name":"b✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 11 | 2 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e32ed6dffc878b7ef9e27b77cf625ce07b199167aefa5356f4045ef1f5c0e39 | f9b3219dacb977f1413d335f3dd345d0c3e3ed17b2c2b89e97ad21066d688ea1 | ee05d3050f960dc1ed726ba8b9f910b9f03ecaa2cb7ec0952b605a7eeab644ce | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,280 | dist_vadd_left | Mathlib/Analysis/Normed/Group/AddTorsor.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>dist_eq_norm_vsub</a> V _ x, <a>vadd_vsub</a>] | α : Type u_1
V : Type u_2
P : Type u_3
W : Type u_4
Q : Type u_5
inst✝⁵ : SeminormedAddCommGroup V
inst✝⁴ : PseudoMetricSpace P
inst✝³ : NormedAddTorsor V P
inst✝² : NormedAddCommGroup W
inst✝¹ : MetricSpace Q
inst✝ : NormedAddTorsor W Q
v : V
x : P
⊢ dist (v +ᵥ x) x = ‖v‖ | ((:c Eq) (:c Real) ((:c Dist.dist) (:fv _uniq.9549) ((:c PseudoMetricSpace.toDist) (:fv _uniq.9549) (:fv _uniq.9561)) ((:c HVAdd.hVAdd) (:fv _uniq.9546) (:fv _uniq.9549) (:fv _uniq.9549) ((:c instHVAdd) (:fv _uniq.9546) (:fv _uniq.9549) ((:c AddAction.toVAdd) (:fv _uniq.9546) (:fv _uniq.9549) ((:c SubNegMonoid.toAddMon... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"V","sexp":"(:sort (+ u_2 1))"},{"name":"P","sexp":"(:sort (+ u_3 1))"},{"name":"W","sexp":"(:sort (+ u_4 1))"},{"name":"Q","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝⁵","sexp":"((:c SeminormedAddCommGroup) (:fv _uniq.9546))"},{"name":"inst✝⁴","sexp":"((:c PseudoMetricSpa... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Dist.dist) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance 1 (:instance-of (:app (:c Dist) (:arg :explicit 0 (:fv FV2))))) (:arg :explicit 2 (:app (:c HVAdd.hVAdd) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :imp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9543","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9546","is_instance":false,"is_let":false,"name":"V","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":5066,"sourceStart":5064,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":5068,"sourceStart":5067,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"dist_eq_norm_vsub V _ x","source_end":5091,"source_start":5068,"syntax_kind":"Lean.Parser.Term.app"},{"source":"vadd_vsub","source_end":5102,"source_start":5093,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.9543","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.9546","is_instance":false,"is_let":false,"user_name":"V"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 34 | 2 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a7efa7e56f77d3c13014efb91e2c67468f48a0695d3809cac6e64c7158b0c84 | d13fa294c25b4042a2912dd00d28bb55cc943642a35583cfcde545484c88b413 | f34bd44354ac44430e86b31222e88280336ac6189f2c18ea8a5bc79768afca0c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,281 | ContDiffAt.dist | Mathlib/Analysis/InnerProductSpace/Calculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>dist_eq_norm</a>] | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁷ : _root_.RCLike 𝕜
inst✝⁶ : NormedAddCommGroup E
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
inst✝² : NormedSpace ℝ E
G : Type u_4
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
f g : G → E
f' g' : G →L[ℝ] E
s : Set G... | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁷ : _root_.RCLike 𝕜
inst✝⁶ : NormedAddCommGroup E
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
inst✝² : NormedSpace ℝ E
G : Type u_4
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
f g : G → E
f' g' : G →L[ℝ] E
s : Set G... | ((:c ContDiffAt) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.119428) (:fv _uniq.119431) (:fv _uniq.119540) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c RCLike) (:fv _uniq.119238))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119241))"},{"name":"inst✝⁵","sexp":"((:c InnerProductSpace) (:fv _uniq.119238... | (:app (:c ContDiffAt) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV9)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV9))))) (:arg :instance 4 (:instance-of (:app (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.119238","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119241","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"simp","sourceEnd":8489,"sourceStart":8485,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":8494,"sourceStart":8490,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":8494,"s... | [] | [{"source":"dist_eq_norm","source_end":8508,"source_start":8496,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.119238","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119241","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 4 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5f540e94b9496db491c27d3f6c03cd7f294e7843e1520c98b046ec3ebe53cfaa | a3b576abe2eb6fda511086ddc2b702462b682c68c08629473c8067ff2108d792 | 86fdcb37b2ebf051d17833a2a45ce1595879177ad70b67835951d58ba9165a2a | f37dee22af42958955f6fb99dfc256cabd59591753c5be3a9ff8cb05c8507168 |
cat-searcher/leandojo-benchmark-4-random | test | 4,282 | ContDiffAt.dist | Mathlib/Analysis/InnerProductSpace/Calculus.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hf.sub hg).<a>ContDiffAt.norm</a> 𝕜 (<a>sub_ne_zero</a>.2 hne) | 𝕜 : Type u_1
E : Type u_2
F : Type u_3
inst✝⁷ : _root_.RCLike 𝕜
inst✝⁶ : NormedAddCommGroup E
inst✝⁵ : InnerProductSpace 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : InnerProductSpace ℝ F
inst✝² : NormedSpace ℝ E
G : Type u_4
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
f g : G → E
f' g' : G →L[ℝ] E
s : Set G... | ((:c ContDiffAt) (:c Real) ((:c DenselyNormedField.toNontriviallyNormedField) (:c Real) (:c Real.denselyNormedField)) (:fv _uniq.119428) (:fv _uniq.119431) (:fv _uniq.119540) (:c Real) (:c Real.normedAddCommGroup) ((:c InnerProductSpace.toNormedSpace) (:c Real) (:c Real) (:c Real.RCLike) (:c Real.normedAddCommGroup) ((... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝⁷","sexp":"((:c RCLike) (:fv _uniq.119238))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.119241))"},{"name":"inst✝⁵","sexp":"((:c InnerProductSpace) (:fv _uniq.119238... | (:app (:c ContDiffAt) (:arg :explicit 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:c Real))))) (:arg :implicit-type 2 (:fv FV9)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV9))))) (:arg :instance 4 (:instance-of (:app (:c ... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.119238","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119241","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"source":"exact","sourceEnd":8517,"sourceStart":8512,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":8519,"sourceStart":8518,"tag":"atom"},{"children":[{"source":"hf.sub","sourceEnd":8525,"sourceStart":8519,"tag":"identifier"},{"children":[{"contextIndex":21,"semanticRole":"... | [] | [{"source":"(hf.sub hg).norm 𝕜 (sub_ne_zero.2 hne)","source_end":8559,"source_start":8518,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.119238","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.119241","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 66 | 5 | exact | true | 1 | 22 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7315ce9f48798e747bf68e7d9edbe6b809896123fc6e351371f64fe1e43ad2ec | f37dee22af42958955f6fb99dfc256cabd59591753c5be3a9ff8cb05c8507168 | 02a635ce99ac00c6b2c4391de85f5bedf874ec916d00e2ddbdf6ca4a97bb0e65 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,283 | Set.image_const_sub_uIcc | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := <a>Set.image_comp</a> (fun x => a + x) fun x => -x | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
a b c d : α
⊢ (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
a b c d : α
this : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)
⊢ (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] | ((:c Eq) ((:c Set) (:fv _uniq.321226)) ((:c Set.image) (:fv _uniq.321226) (:fv _uniq.321226) (:lambda x (:fv _uniq.321226) ((:c HSub.hSub) (:fv _uniq.321226) (:fv _uniq.321226) (:fv _uniq.321226) ((:c instHSub) (:fv _uniq.321226) ((:c SubNegMonoid.toSub) (:fv _uniq.321226) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.32122... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedAddCommGroup) (:fv _uniq.321226))"},{"name":"a","sexp":"(:fv _uniq.321226)"},{"name":"b","sexp":"(:fv _uniq.321226)"},{"name":"c","sexp":"(:fv _uniq.321226)"},{"name":"d","sexp":"(:fv _uniq.321226)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedAddCommGr... | {"children":[{"source":"have","sourceEnd":19621,"sourceStart":19617,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":19622,"sourceStart":19622,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":19622,"sourceStart":19622,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"image_comp (fun x => a + x) fun x => -x","source_end":19664,"source_start":19625,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"inter... | 195 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54fd33fd78a26626d5b14f05ee02cf3ec034183f77953b98f6d3a108a4c33fcf | 24de939f079d0b0e0d24d918baebc4ec744facbe8a8728c59d8d40f2a68f2c00 | 311e3b0be87290258bb569824a0ff1057542faa591b3cf142ab831824cf0004e | 34eb09fc29dfea00afdd630e0df786e9bb7bf8f35fe1162e99b80b292043d51a |
cat-searcher/leandojo-benchmark-4-random | test | 4,284 | Set.image_const_sub_uIcc | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp [<a>Function.comp_def</a>] at this | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
a b c d : α
this : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)
⊢ (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
a b c d : α
this : ∀ (a_1 : Set α), (fun x => a + -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)
⊢ (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] | ((:c Eq) ((:c Set) (:fv _uniq.321226)) ((:c Set.image) (:fv _uniq.321226) (:fv _uniq.321226) (:lambda x (:fv _uniq.321226) ((:c HSub.hSub) (:fv _uniq.321226) (:fv _uniq.321226) (:fv _uniq.321226) ((:c instHSub) (:fv _uniq.321226) ((:c SubNegMonoid.toSub) (:fv _uniq.321226) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.32122... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedAddCommGroup) (:fv _uniq.321226))"},{"name":"a","sexp":"(:fv _uniq.321226)"},{"name":"b","sexp":"(:fv _uniq.321226)"},{"name":"c","sexp":"(:fv _uniq.321226)"},{"name":"d","sexp":"(:fv _uniq.321226)"},{"name":"this","sexp":"(:forall a ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedAddCommGr... | {"children":[{"source":"dsimp","sourceEnd":19671,"sourceStart":19666,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19673,"sourceStart":19672,"tag":"... | [] | [{"source":"Function.comp_def","source_end":19690,"source_start":19673,"syntax_kind":"ident"},{"source":"this","source_end":19699,"source_start":19695,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"inter... | 195 | 6 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7b6d9af21c2633903be4c0bc475c09cad2264244d4c011daf476d1883a86e527 | 34eb09fc29dfea00afdd630e0df786e9bb7bf8f35fe1162e99b80b292043d51a | 1b2f44733ce2ab72bac64248ffd9e8a0caf94eb039bce005b83f5cd8beebe2bd | c812083b84dcf438eb416d271f2399079607d3e1a86690f9b01d36231373173f |
cat-searcher/leandojo-benchmark-4-random | test | 4,285 | Set.image_const_sub_uIcc | Mathlib/Data/Set/Pointwise/Interval.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>sub_eq_add_neg</a>, this, <a>add_comm</a>] | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
a b c d : α
this : ∀ (a_1 : Set α), (fun x => a + -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)
⊢ (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] | ((:c Eq) ((:c Set) (:fv _uniq.321226)) ((:c Set.image) (:fv _uniq.321226) (:fv _uniq.321226) (:lambda x (:fv _uniq.321226) ((:c HSub.hSub) (:fv _uniq.321226) (:fv _uniq.321226) (:fv _uniq.321226) ((:c instHSub) (:fv _uniq.321226) ((:c SubNegMonoid.toSub) (:fv _uniq.321226) ((:c AddGroup.toSubNegMonoid) (:fv _uniq.32122... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedAddCommGroup) (:fv _uniq.321226))"},{"name":"a","sexp":"(:fv _uniq.321226)"},{"name":"b","sexp":"(:fv _uniq.321226)"},{"name":"c","sexp":"(:fv _uniq.321226)"},{"name":"d","sexp":"(:fv _uniq.321226)"},{"name":"this","sexp":"(:forall a ((:... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Set.image) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :explicit 2 (:lambda x :explicit (:fv FV0) (:app (:c HSub.hSub) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:f... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedAddCommGr... | {"children":[{"source":"simp","sourceEnd":19706,"sourceStart":19702,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":19708,"sourceStart":19707,"tag":"a... | [] | [{"source":"sub_eq_add_neg","source_end":19722,"source_start":19708,"syntax_kind":"ident"},{"source":"this","source_end":19728,"source_start":19724,"syntax_kind":"ident"},{"source":"add_comm","source_end":19738,"source_start":19730,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.321226","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.321229","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":explicit","context_index":2,"inter... | 195 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6404f90be699344b7bb3a971a8da1e6d456b307738eb0804ccd8238273ef29f | c812083b84dcf438eb416d271f2399079607d3e1a86690f9b01d36231373173f | 7b71e44246776d97ed42b6b6b74118bd13c51fae310cabe1b08b8e4f25e46f87 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,286 | Nat.div_ne_zero_iff_of_dvd | Mathlib/Data/Nat/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain rfl | hb := <a>eq_or_ne</a> b 0 <;> simp [<a>Nat.div_ne_zero_iff</a>, <a>Nat.le_iff_ne_zero_of_dvd</a>, *] | a b c d m n k : ℕ
p q : ℕ → Prop
hba : b ∣ a
⊢ a / b ≠ 0 ↔ a ≠ 0 ∧ b ≠ 0 | ((:c Iff) ((:c Ne) (:c Nat) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) (:fv _uniq.90623) (:fv _uniq.90625)) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))) ((:c And) ((:c Ne) (:c Nat) (:fv _uniq.90623) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:... | [{"name":"a","sexp":"(:c Nat)"},{"name":"b","sexp":"(:c Nat)"},{"name":"c","sexp":"(:c Nat)"},{"name":"d","sexp":"(:c Nat)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"k","sexp":"(:c Nat)"},{"name":"p","sexp":"(:forall _ (:c Nat) (:sort 0))"},{"name":"q","sexp":"(:forall _ (:c Nat) (:sort 0)... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Ne) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Nat)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90623","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90625","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Nat)"},{"binder_role":":implicit","context_ind... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"obtain","sourceEnd":49891,"sourceStart":49885,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"rfl","sourceEnd":49895,"sourceStart":49892,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.... | [] | [{"source":"eq_or_ne b 0","source_end":49916,"source_start":49904,"syntax_kind":"Lean.Parser.Term.app"},{"source":"rfl | hb","source_end":49900,"source_start":49892,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"},{"source":"Nat.div_ne_zero_iff","source_end":49946,"source_start":49927,"syntax_kind":"ident"},{"source":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.90623","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.90625","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 424 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e1bfab6629ee0ebc9e10fce868db58103a0839b270ae262d92cc7a3881837e8 | bfd7399b2de8e77a37d0b32d59d5c9006db19c02604ca492c04dbecddb082364 | 9b2f7144a8ef1d5d45e5625ef9e1af2b24c0c738b4a54ade0c3af3be019e503e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,287 | isQuasiSeparated_univ_iff | Mathlib/Topology/QuasiSeparated.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>quasiSeparatedSpace_iff</a>] | α✝ : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α✝
inst✝¹ : TopologicalSpace β
f : α✝ → β
α : Type u_3
inst✝ : TopologicalSpace α
⊢ IsQuasiSeparated Set.univ ↔ QuasiSeparatedSpace α | α✝ : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α✝
inst✝¹ : TopologicalSpace β
f : α✝ → β
α : Type u_3
inst✝ : TopologicalSpace α
⊢ IsQuasiSeparated Set.univ ↔ ∀ (U V : Set α), IsOpen U → IsCompact U → IsOpen V → IsCompact V → IsCompact (U ∩ V) | ((:c Iff) ((:c IsQuasiSeparated) (:fv _uniq.639) (:fv _uniq.640) ((:c Set.univ) (:fv _uniq.639))) ((:c QuasiSeparatedSpace) (:fv _uniq.639) (:fv _uniq.640))) | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.602))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.605))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.602) (:fv _uniq.605))"},{"name":"α","sexp":"(:sort (+ u_3 1))"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsQuasiSeparated) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c Set.univ) (:arg :implicit-type 0 (:fv FV6)))))) (:arg :explicit 1 (:app (:c QuasiSeparatedSpace) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.602","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.605","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implicit... | {"children":[{"source":"rw","sourceEnd":2364,"sourceStart":2362,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2366,"sourceStart":2365,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"quasiSeparatedSpace_... | [] | [{"source":"quasiSeparatedSpace_iff","source_end":2389,"source_start":2366,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.602","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.605","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_name... | 8 | 4 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3c7f9c98e417e439b83e45430157dad65856174558ae1448c87bd1aef6d52082 | 82f69d30f124cdceec5d7afc1261672cf8cfcb2cc7f3c218774fd515f02b2e26 | 3765c2c344eb85e26171841a3b8f98eccb09b247d0f9175a1a6707084bf57da7 | 19d9babf1d6aa52963a289666c8c4b7ceaed81318dcea811d284bb71c4fbccf9 |
cat-searcher/leandojo-benchmark-4-random | test | 4,288 | isQuasiSeparated_univ_iff | Mathlib/Topology/QuasiSeparated.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>IsQuasiSeparated</a>] | α✝ : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α✝
inst✝¹ : TopologicalSpace β
f : α✝ → β
α : Type u_3
inst✝ : TopologicalSpace α
⊢ IsQuasiSeparated Set.univ ↔ ∀ (U V : Set α), IsOpen U → IsCompact U → IsOpen V → IsCompact V → IsCompact (U ∩ V) | ((:c Iff) ((:c IsQuasiSeparated) (:fv _uniq.639) (:fv _uniq.640) ((:c Set.univ) (:fv _uniq.639))) (:forall U ((:c Set) (:fv _uniq.639)) (:forall V ((:c Set) (:fv _uniq.639)) (:forall _ ((:c IsOpen) (:fv _uniq.639) (:fv _uniq.640) 1) (:forall _ ((:c IsCompact) (:fv _uniq.639) (:fv _uniq.640) 2) (:forall _ ((:c IsOpen) (... | [{"name":"α✝","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.602))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.605))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.602) (:fv _uniq.605))"},{"name":"α","sexp":"(:sort (+ u_3 1))"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsQuasiSeparated) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV6))))) (:arg :explicit 2 (:app (:c Set.univ) (:arg :implicit-type 0 (:fv FV6)))))) (:arg :explicit 1 (:forall U :explicit (:app (:c Set) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.602","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.605","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-implicit... | {"children":[{"source":"simp","sourceEnd":2397,"sourceStart":2393,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2399,"sourceStart":2398,"tag":"atom"... | [] | [{"source":"IsQuasiSeparated","source_end":2415,"source_start":2399,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.602","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.605","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_name... | 8 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d448ca63e586d4d45d51b5818be5669c5c00cdb8c435c12cecaf7d195759d2a | 19d9babf1d6aa52963a289666c8c4b7ceaed81318dcea811d284bb71c4fbccf9 | 2eb307113a1fe43a85ad340d04771332d329f4652643975cdbda719bb37b1659 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,289 | MeasureTheory.measure_le_average_pos | Mathlib/MeasureTheory/Integral/Average.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa using <a>MeasureTheory.measure_le_setAverage_pos</a> (<a>MeasureTheory.Measure.measure_univ_ne_zero</a>.2 hμ) (<a>MeasureTheory.measure_ne_top</a> _ _) hf.integrableOn | α : Type u_1
E : Type u_2
F : Type u_3
m0 : MeasurableSpace α
inst✝⁶ : NormedAddCommGroup E
inst✝⁵ : NormedSpace ℝ E
inst✝⁴ : CompleteSpace E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace ℝ F
inst✝¹ : CompleteSpace F
μ ν : Measure α
s t N : Set α
f : α → ℝ
inst✝ : IsFiniteMeasure μ
hμ : μ ≠ 0
hf : Integrable f μ
⊢... | ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialOrder.toPreorder) (:c ENNReal) ((:c OmegaCompletePartialOrder.toPartialOrder) (:c ENNReal) ((:c CompleteLattice.instOmegaCompletePartialOrder) (:c ENNReal) ((:c CompletelyDistribLattice.toCompleteLattice) (:c ENNReal) ((:c CompleteLinearOrder.toCompl... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.208438))"},{"name":"inst✝⁶","sexp":"((:c NormedAddCommGroup) (:fv _uniq.208441))"},{"name":"inst✝⁵","sexp":"((:c NormedSpace) (:c Real) (:fv _uni... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c ENNReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c ENNReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c ENNReal)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.208438","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208441","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":30223,"sourceStart":30218,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"measure_le_setAverage_pos (Measure.measure_univ_ne_zero.2 hμ) (measure_ne_top _ _)\n hf.integrableOn","source_end":30333,"source_start":30230,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.208438","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208441","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 153 | 2 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc6fff495b65050c49fbc7dd05432ee2263afd816fac08e222b3a3013b1b4f52 | d047b28d384d4b7a68e1daabb367f7b31849965b33bd5e0cfa82118cedb8a693 | 8b80f1d989434c85adc340114285b4c1dd9edc1f5a0d47c991ed54a25477c1dc | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,290 | Int.bitwise_bit | Mathlib/Data/Int/Bitwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' m with m m <;> cases' n with n n <;> simp [<a>Int.bitwise</a>, <a>Int.ofNat_eq_coe</a>, <a>Int.bit_coe_nat</a>, <a>Int.natBitwise</a>, <a>Bool.not_false</a>, <a>Bool.not_eq_false'</a>, <a>Int.bit_negSucc</a>] | f : Bool → Bool → Bool
a : Bool
m : ℤ
b : Bool
n : ℤ
⊢ bitwise f (bit a m) (bit b n) = bit (f a b) (bitwise f m n) | case ofNat.ofNat
f : Bool → Bool → Bool
a b : Bool
m n : ℕ
⊢ (bif f false false then -[Nat.bitwise (fun x y => !f x y) (Nat.bit a m) (Nat.bit b n)+1]
else ↑(Nat.bitwise f (Nat.bit a m) (Nat.bit b n))) =
bit (f a b) (bif f false false then -[Nat.bitwise (fun x y => !f x y) m n+1] else ↑(Nat.bitwise f m n))
case ... | ((:c Eq) (:c Int) ((:c Int.bitwise) (:fv _uniq.20041) ((:c Int.bit) (:fv _uniq.20042) (:fv _uniq.20043)) ((:c Int.bit) (:fv _uniq.20044) (:fv _uniq.20045))) ((:c Int.bit) ((:fv _uniq.20041) (:fv _uniq.20042) (:fv _uniq.20044)) ((:c Int.bitwise) (:fv _uniq.20041) (:fv _uniq.20043) (:fv _uniq.20045)))) | [{"name":"f","sexp":"(:forall _ (:c Bool) (:forall _ (:c Bool) (:c Bool)))"},{"name":"a","sexp":"(:c Bool)"},{"name":"m","sexp":"(:c Int)"},{"name":"b","sexp":"(:c Bool)"},{"name":"n","sexp":"(:c Int)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c Int.bitwise) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Int.bit) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:fv FV3)))) (:arg :explicit 2 (:app (:c Int.bit) (:arg :explicit 0 (:fv FV4)) (:arg :explicit 1 (:fv FV5)))))) (:arg :... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Bool) (:forall _ :explicit (:c Bool) (:c Bool)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"nam... | {"children":[{"children":[{"children":[{"source":"cases'","sourceEnd":13432,"sourceStart":13426,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":3,"semanticRole":"local","source":"m","sourceEnd":13434,"sourceStart":13433,"tag":"identifier"}],"kind":"Lean.Par... | [] | [{"source":"m","source_end":13434,"source_start":13433,"syntax_kind":"ident"},{"source":"n","source_end":13456,"source_start":13455,"syntax_kind":"ident"},{"source":"bitwise","source_end":13485,"source_start":13478,"syntax_kind":"ident"},{"source":"ofNat_eq_coe","source_end":13499,"source_start":13487,"syntax_kind":"id... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 96 | 4 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95be3552f0acccd013ceaa2474b4769d6c7c7953b1ceb693039add1076e6ee88 | 1074a6b4037c7bc1fde46804caaff08df9e484d58fa23e1babe25f12e60508a4 | 47ddca48bb48fbd348414ef6d205cf5e40bc0b36a1aff04d94f6dce275afa2b2 | 353b35bd5cded4276b7d91979db58062d639461e1657dfb325c78ce0915320cc |
cat-searcher/leandojo-benchmark-4-random | test | 4,291 | Int.bitwise_bit | Mathlib/Data/Int/Bitwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : f <a>Bool.false</a> <a>Bool.false</a> <;> simp (config := {decide := <a>Bool.true</a>}) [h] | case ofNat.ofNat
f : Bool → Bool → Bool
a b : Bool
m n : ℕ
⊢ (bif f false false then -[Nat.bitwise (fun x y => !f x y) (Nat.bit a m) (Nat.bit b n)+1]
else ↑(Nat.bitwise f (Nat.bit a m) (Nat.bit b n))) =
bit (f a b) (bif f false false then -[Nat.bitwise (fun x y => !f x y) m n+1] else ↑(Nat.bitwise f m n)) | ((:c Eq) (:c Int) ((:c cond) (:c Int) ((:fv _uniq.20041) (:c Bool.false) (:c Bool.false)) ((:c Int.negSucc) ((:c Nat.bitwise) (:lambda x (:c Bool) (:lambda y (:c Bool) ((:c not) ((:fv _uniq.20041) 1 0)))) ((:c Nat.bit) (:fv _uniq.20042) (:fv _uniq.20068)) ((:c Nat.bit) (:fv _uniq.20044) (:fv _uniq.20118)))) ((:c Nat.ca... | [{"name":"f","sexp":"(:forall _ (:c Bool) (:forall _ (:c Bool) (:c Bool)))"},{"name":"a","sexp":"(:c Bool)"},{"name":"b","sexp":"(:c Bool)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c cond) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:c Bool.false)) (:arg :explicit 1 (:c Bool.false)))) (:arg :explicit 2 (:app (:c Int.negSucc) (:arg :explicit 0 (:app (:c Nat.bitwise) (:arg :explicit 0 ... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Bool) (:forall _ :explicit (:c Bool) (:c Bool)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"nam... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":13592,"sourceStart":13584,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13594,"sourceStart":13593,"tag":"identifier"},{"source":":","sourceEnd":13596,"sourceStart":13595,"tag":"atom"}],... | [] | [{"source":"f false false","source_end":13610,"source_start":13597,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{decide := true}","source_end":13647,"source_start":13631,"syntax_kind":"Lean.Parser.Term.structInst"},{"source":"h","source_end":13651,"source_start":13650,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 96 | 17 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9fe964d4aed1ed5dc5492ee7d132a7296e328c79c3a97fc60f0a08e97aa1a82c | dcb4c950555652d16bd02e6203bd8d225b0551fbd6c4fb71d494d93f823a4ce1 | 12fd6d183a0220d9e47ea7066408357a94b5cad3d7ed42a70062a24e2a55b292 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,292 | Int.bitwise_bit | Mathlib/Data/Int/Bitwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : f <a>Bool.false</a> <a>Bool.true</a> <;> simp (config := {decide := <a>Bool.true</a>}) [h] | case ofNat.negSucc
f : Bool → Bool → Bool
a b : Bool
m n : ℕ
⊢ (bif f false true then -[Nat.bitwise (fun x y => !f x !y) (Nat.bit a m) (Nat.bit (!b) n)+1]
else ↑(Nat.bitwise (fun x y => f x !y) (Nat.bit a m) (Nat.bit (!b) n))) =
bit (f a b)
(bif f false true then -[Nat.bitwise (fun x y => !f x !y) m n+1] ... | ((:c Eq) (:c Int) ((:c cond) (:c Int) ((:fv _uniq.20041) (:c Bool.false) (:c Bool.true)) ((:c Int.negSucc) ((:c Nat.bitwise) (:lambda x (:c Bool) (:lambda y (:c Bool) ((:c not) ((:fv _uniq.20041) 1 ((:c not) 0))))) ((:c Nat.bit) (:fv _uniq.20042) (:fv _uniq.20068)) ((:c Nat.bit) ((:c not) (:fv _uniq.20044)) (:fv _uniq.... | [{"name":"f","sexp":"(:forall _ (:c Bool) (:forall _ (:c Bool) (:c Bool)))"},{"name":"a","sexp":"(:c Bool)"},{"name":"b","sexp":"(:c Bool)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c cond) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:c Bool.false)) (:arg :explicit 1 (:c Bool.true)))) (:arg :explicit 2 (:app (:c Int.negSucc) (:arg :explicit 0 (:app (:c Nat.bitwise) (:arg :explicit 0 (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Bool) (:forall _ :explicit (:c Bool) (:c Bool)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"nam... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":13666,"sourceStart":13658,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13668,"sourceStart":13667,"tag":"identifier"},{"source":":","sourceEnd":13670,"sourceStart":13669,"tag":"atom"}],... | [] | [{"source":"f false true","source_end":13683,"source_start":13671,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{decide := true}","source_end":13720,"source_start":13704,"syntax_kind":"Lean.Parser.Term.structInst"},{"source":"h","source_end":13724,"source_start":13723,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 96 | 26 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f307fb15fefb2eb8a892861494f082a02f5de5dd22f447b8ba870193dc494d6a | 0c446fa7ad6e013477addea89be94e1e17b9761059d904f2db6f86ca11b701b6 | 9779780b317ee29393104755f82e4e8e6e26e61cced01af1ee3a4acacea38f20 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,293 | Int.bitwise_bit | Mathlib/Data/Int/Bitwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : f <a>Bool.true</a> <a>Bool.false</a> <;> simp (config := {decide := <a>Bool.true</a>}) [h] | case negSucc.ofNat
f : Bool → Bool → Bool
a b : Bool
m n : ℕ
⊢ (bif f true false then -[Nat.bitwise (fun x y => !f (!x) y) (Nat.bit (!a) m) (Nat.bit b n)+1]
else ↑(Nat.bitwise (fun x y => f (!x) y) (Nat.bit (!a) m) (Nat.bit b n))) =
bit (f a b)
(bif f true false then -[Nat.bitwise (fun x y => !f (!x) y) m... | ((:c Eq) (:c Int) ((:c cond) (:c Int) ((:fv _uniq.20041) (:c Bool.true) (:c Bool.false)) ((:c Int.negSucc) ((:c Nat.bitwise) (:lambda x (:c Bool) (:lambda y (:c Bool) ((:c not) ((:fv _uniq.20041) ((:c not) 1) 0)))) ((:c Nat.bit) ((:c not) (:fv _uniq.20042)) (:fv _uniq.20083)) ((:c Nat.bit) (:fv _uniq.20044) (:fv _uniq.... | [{"name":"f","sexp":"(:forall _ (:c Bool) (:forall _ (:c Bool) (:c Bool)))"},{"name":"a","sexp":"(:c Bool)"},{"name":"b","sexp":"(:c Bool)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c cond) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:c Bool.true)) (:arg :explicit 1 (:c Bool.false)))) (:arg :explicit 2 (:app (:c Int.negSucc) (:arg :explicit 0 (:app (:c Nat.bitwise) (:arg :explicit 0 (... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Bool) (:forall _ :explicit (:c Bool) (:c Bool)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"nam... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":13739,"sourceStart":13731,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13741,"sourceStart":13740,"tag":"identifier"},{"source":":","sourceEnd":13743,"sourceStart":13742,"tag":"atom"}],... | [] | [{"source":"f true false","source_end":13756,"source_start":13744,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{decide := true}","source_end":13793,"source_start":13777,"syntax_kind":"Lean.Parser.Term.structInst"},{"source":"h","source_end":13797,"source_start":13796,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 96 | 35 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 703ebfd72c71b70c82cf74c709d00ed49e208aa127c411712afa7adeb2064fc0 | dea098c9567cd3fe3a0c637e3be6919beb76ffb253779c5d1b51fb6e2a5093bf | 794112632a6e23c23c73fce4edb3933bd66d80cc33ba6819814064f73ddce16d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,294 | Int.bitwise_bit | Mathlib/Data/Int/Bitwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | by_cases h : f <a>Bool.true</a> <a>Bool.true</a> <;> simp (config := {decide := <a>Bool.true</a>}) [h] | case negSucc.negSucc
f : Bool → Bool → Bool
a b : Bool
m n : ℕ
⊢ (bif f true true then -[Nat.bitwise (fun x y => !f (!x) !y) (Nat.bit (!a) m) (Nat.bit (!b) n)+1]
else ↑(Nat.bitwise (fun x y => f (!x) !y) (Nat.bit (!a) m) (Nat.bit (!b) n))) =
bit (f a b)
(bif f true true then -[Nat.bitwise (fun x y => !f (... | ((:c Eq) (:c Int) ((:c cond) (:c Int) ((:fv _uniq.20041) (:c Bool.true) (:c Bool.true)) ((:c Int.negSucc) ((:c Nat.bitwise) (:lambda x (:c Bool) (:lambda y (:c Bool) ((:c not) ((:fv _uniq.20041) ((:c not) 1) ((:c not) 0))))) ((:c Nat.bit) ((:c not) (:fv _uniq.20042)) (:fv _uniq.20083)) ((:c Nat.bit) ((:c not) (:fv _uni... | [{"name":"f","sexp":"(:forall _ (:c Bool) (:forall _ (:c Bool) (:c Bool)))"},{"name":"a","sexp":"(:c Bool)"},{"name":"b","sexp":"(:c Bool)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c cond) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:fv FV1) (:arg :explicit 0 (:c Bool.true)) (:arg :explicit 1 (:c Bool.true)))) (:arg :explicit 2 (:app (:c Int.negSucc) (:arg :explicit 0 (:app (:c Nat.bitwise) (:arg :explicit 0 (:... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Bool) (:forall _ :explicit (:c Bool) (:c Bool)))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"nam... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"by_cases","sourceEnd":13812,"sourceStart":13804,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13814,"sourceStart":13813,"tag":"identifier"},{"source":":","sourceEnd":13816,"sourceStart":13815,"tag":"atom"}],... | [] | [{"source":"f true true","source_end":13828,"source_start":13817,"syntax_kind":"Lean.Parser.Term.app"},{"source":"{decide := true}","source_end":13865,"source_start":13849,"syntax_kind":"Lean.Parser.Term.structInst"},{"source":"h","source_end":13869,"source_start":13868,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.20041","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.20042","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 96 | 44 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 118692f122eb2b8c82e25d8136763e7488e2569586ad906293203b071d42b7b6 | 5c4e39d0cc88b85f5df886a10c367525557b9d38121cb5b53a84dec9075f746f | 67452b74d81d0ec1af5a3e0482a0d616b1e2f11df807cf43cd12bb43a7f63006 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,295 | Real.log_sqrt | Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>eq_div_iff</a>, <a>mul_comm</a>, ← <a>Nat.cast_two</a>, ← <a>Real.log_pow</a>, <a>Real.sq_sqrt</a> hx] | x✝ y x : ℝ
hx : 0 ≤ x
⊢ log √x = log x / 2 | x✝ y x : ℝ
hx : 0 ≤ x
⊢ 2 ≠ 0 | ((:c Eq) (:c Real) ((:c Real.log) ((:c Real.sqrt) (:fv _uniq.30222))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Real.log) (:fv _uniq.30222)) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Re... | [{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30222))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Real.log) (:arg :explicit 0 (:app (:c Real.sqrt) (:arg :explicit 0 (:fv FV3)))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30058","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30060","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":implicit","context_... | {"children":[{"source":"rw","sourceEnd":11493,"sourceStart":11491,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11495,"sourceStart":11494,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"eq_div_iff","sem... | [] | [{"source":"eq_div_iff","source_end":11505,"source_start":11495,"syntax_kind":"ident"},{"source":"mul_comm","source_end":11515,"source_start":11507,"syntax_kind":"ident"},{"source":"Nat.cast_two","source_end":11533,"source_start":11521,"syntax_kind":"ident"},{"source":"log_pow","source_end":11546,"source_start":11539,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30058","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30060","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 110 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33a26316daa4483c69ce2b5f9dd7dd36b7f49154e07d9bcc32b36a710bc28311 | 36edb303f9c2d9b5e96e30167e292c83b381f8c8b161ff22bd1c946df2348339 | e64b3f7311ae15f9a01fe664f502513522deb840a00a8f17009445271e4147fd | cbd9100a2123b3a402399d09321cddcac717c66602cfdcf55d9e81dbcbe9a1af |
cat-searcher/leandojo-benchmark-4-random | test | 4,296 | Real.log_sqrt | Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>two_ne_zero</a> | x✝ y x : ℝ
hx : 0 ≤ x
⊢ 2 ≠ 0 | ((:c Ne) (:c Real) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MonoidWithZero.toZero) (:c Real)... | [{"name":"x✝","sexp":"(:c Real)"},{"name":"y","sexp":"(:c Real)"},{"name":"x","sexp":"(:c Real)"},{"name":"hx","sexp":"((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.30222))"}] | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 2)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:lit 2))))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-t... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30058","is_instance":false,"is_let":false,"name":"x✝","sexp":"(:c Real)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30060","is_instance":false,"is_let":false,"name":"y","sexp":"(:c Real)"},{"binder_role":":implicit","context_... | {"children":[{"source":"exact","sourceEnd":11567,"sourceStart":11562,"tag":"atom"},{"name":"two_ne_zero","semanticRole":"global","source":"two_ne_zero","sourceEnd":11579,"sourceStart":11568,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.exact","source":"exact two_ne_zero","sourceEnd":11579,"sourceStart":11562,"tag":"n... | [] | [{"source":"two_ne_zero","source_end":11579,"source_start":11568,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.30058","is_instance":false,"is_let":false,"user_name":"x✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.30060","is_instance":false,"is_let":false,"user_name":"y"},{"binder_role":":implicit","context_index":3,"internal_name":"_u... | 110 | 11 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4f6491f70bf088054c0c6e8615e25132f50ebe78f4af52ee167bbe820aced020 | cbd9100a2123b3a402399d09321cddcac717c66602cfdcf55d9e81dbcbe9a1af | 2662c4232446e487a789225de8be0c2082cc227c0e2cb9eb26e876189d892049 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,297 | openEmbedding_sigma_map | Mathlib/Topology/Constructions.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>openEmbedding_iff_embedding_open</a>, <a>isOpenMap_sigma_map</a>, <a>embedding_sigma_map</a> h, <a>forall_and</a>] | X : Type u
Y : Type v
Z : Type u_1
W : Type u_2
ε : Type u_3
ζ : Type u_4
ι : Type u_5
κ : Type u_6
σ : ι → Type u_7
τ : κ → Type u_8
inst✝² : (i : ι) → TopologicalSpace (σ i)
inst✝¹ : (k : κ) → TopologicalSpace (τ k)
inst✝ : TopologicalSpace X
f₁ : ι → κ
f₂ : (i : ι) → σ i → τ (f₁ i)
h : Injective f₁
⊢ OpenEmbedding (... | ((:c Iff) ((:c OpenEmbedding) ((:c Sigma) (:fv _uniq.184713) (:fv _uniq.184721)) ((:c Sigma) (:fv _uniq.184716) (:fv _uniq.184726)) ((:c instTopologicalSpaceSigma) (:fv _uniq.184713) (:fv _uniq.184721) (:fv _uniq.184734)) ((:c instTopologicalSpaceSigma) (:fv _uniq.184716) (:fv _uniq.184726) (:fv _uniq.184742)) ((:c Sig... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"Z","sexp":"(:sort (+ u_1 1))"},{"name":"W","sexp":"(:sort (+ u_2 1))"},{"name":"ε","sexp":"(:sort (+ u_3 1))"},{"name":"ζ","sexp":"(:sort (+ u_4 1))"},{"name":"ι","sexp":"(:sort (+ u_5 1))"},{"name":"κ","sexp":"(:sort (+ u_6 1))"},{"n... | (:app (:c Iff) (:arg :explicit 0 (:app (:c OpenEmbedding) (:arg :implicit-type 0 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV6)) (:arg :explicit 1 (:fv FV8)))) (:arg :implicit-type 1 (:app (:c Sigma) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:fv FV9)))) (:arg :instance 2 (:instance-of (:app (:c Topologica... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184696","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.184698","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":79188,"sourceStart":79184,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":79193,"sourceStart":79189,"tag":"atom"}],"kind"... | [] | [{"source":"openEmbedding_iff_embedding_open","source_end":79227,"source_start":79195,"syntax_kind":"ident"},{"source":"isOpenMap_sigma_map","source_end":79248,"source_start":79229,"syntax_kind":"ident"},{"source":"embedding_sigma_map h","source_end":79271,"source_start":79250,"syntax_kind":"Lean.Parser.Term.app"},{"so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.184696","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.184698","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 578 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2c63ab47c6bc029db1a58636e8d673fb178e437927724ec107098465ebdf095 | 7d81ca59dbdd53b7b326831065852419a9e2e10477df0a4fe91aa2e9d078d5a8 | 2bad299436f75489ce3dde7f5ef326564e394edaff483e918602e81b1dfd9927 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,298 | WithTop.map₂_coe_right | Mathlib/Order/WithBot.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases a <;> rfl | α : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
a✝ b✝ : α
f : α → β → γ
a : WithTop α
b : β
⊢ map₂ f a ↑b = map (fun x => f x b) a | ((:c Eq) ((:c WithTop) (:fv _uniq.69666)) ((:c WithTop.map₂) (:fv _uniq.69660) (:fv _uniq.69663) (:fv _uniq.69666) (:fv _uniq.69791) (:fv _uniq.69792) ((:c WithTop.some) (:fv _uniq.69663) (:fv _uniq.69793))) ((:c WithTop.map) (:fv _uniq.69660) (:fv _uniq.69666) (:lambda _ (:fv _uniq.69660) ((:fv _uniq.69791) 0 (:fv _un... | [{"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":"a✝","sexp":"(:fv _uniq.69660)"},{"name":"b✝","sexp":"(:fv _uniq.69660)"},{"name":"f","sexp":"(:forall _ (:fv _uniq.69660) (:forall _ (:fv _uniq.69663)... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithTop) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c WithTop.map₂) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :implicit-type 2 (:fv FV2)) (:arg :explicit 3 (:fv FV7)) (:arg :explicit 4 (:fv FV8)) (:arg :explicit 5 (:app (:c Wit... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69660","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69663","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"children":[{"source":"cases","sourceEnd":30087,"sourceStart":30082,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":8,"semanticRole":"local","source":"a","sourceEnd":30089,"sourceStart":30088,"tag":"ident... | [] | [{"source":"a","source_end":30089,"source_start":30088,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.69660","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.69663","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 267 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19e5e10a531dc65c7744924062355f8e6b3805e5182df2fcf2950ffc708d7dee | 3aaf751525d656fe0c931fe58d495f87402a17809d3c2f30b92dd7e00f4f72e1 | b3a40cf9567e285a349c24133d705e1dd422023556f3f85526f5e056d54641c5 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,299 | Matrix.isUnit_fromBlocks_zero₁₂ | Mathlib/LinearAlgebra/Matrix/SchurComplement.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [← <a>nonempty_invertible_iff_isUnit</a>, ← <a>nonempty_prod</a>, (<a>Matrix.fromBlocksZero₁₂InvertibleEquiv</a> _ _ _).<a>Equiv.nonempty_congr</a>] | l : Type u_1
m : Type u_2
n : Type u_3
α : Type u_4
inst✝⁶ : Fintype l
inst✝⁵ : Fintype m
inst✝⁴ : Fintype n
inst✝³ : DecidableEq l
inst✝² : DecidableEq m
inst✝¹ : DecidableEq n
inst✝ : CommRing α
A : Matrix m m α
C : Matrix n m α
D : Matrix n n α
⊢ IsUnit (fromBlocks A 0 C D) ↔ IsUnit A ∧ IsUnit D | ((:c Iff) ((:c IsUnit) ((:c Matrix) ((:c Sum) (:fv _uniq.103019) (:fv _uniq.103022)) ((:c Sum) (:fv _uniq.103019) (:fv _uniq.103022)) (:fv _uniq.103025)) ((:c MonoidWithZero.toMonoid) ((:c Matrix) ((:c Sum) (:fv _uniq.103019) (:fv _uniq.103022)) ((:c Sum) (:fv _uniq.103019) (:fv _uniq.103022)) (:fv _uniq.103025)) ((:c ... | [{"name":"l","sexp":"(:sort (+ u_1 1))"},{"name":"m","sexp":"(:sort (+ u_2 1))"},{"name":"n","sexp":"(:sort (+ u_3 1))"},{"name":"α","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁶","sexp":"((:c Fintype) (:fv _uniq.103016))"},{"name":"inst✝⁵","sexp":"((:c Fintype) (:fv _uniq.103019))"},{"name":"inst✝⁴","sexp":"((:c Fintype... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsUnit) (:arg :implicit-type 0 (:app (:c Matrix) (:arg :explicit 0 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 1 (:app (:c Sum) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :explicit 2 (:fv FV3)))) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103016","is_instance":false,"is_let":false,"name":"l","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103019","is_instance":false,"is_let":false,"name":"m","sexp":"(:sort Type)"},{"binder_role":":implicit","c... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":10374,"sourceStart":10370,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":10379,"sourceStart":10375,"tag":"atom"}],"kind"... | [] | [{"source":"nonempty_invertible_iff_isUnit","source_end":10415,"source_start":10385,"syntax_kind":"ident"},{"source":"nonempty_prod","source_end":10434,"source_start":10421,"syntax_kind":"ident"},{"source":"(fromBlocksZero₁₂InvertibleEquiv _ _ _).nonempty_congr","source_end":10498,"source_start":10440,"syntax_kind":"Le... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.103016","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.103019","is_instance":false,"is_let":false,"user_name":"m"},{"binder_role":":implicit","context_index":2,"internal_name":"_... | 33 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6aac81f40ec71da79fc2cc6fd53e281c6758fe1b359964ed0804abbaf0e6b08c | d810f09545bbc7cf42fd6e3f27751b405c768008acaf05227f03ecba0eab1656 | 3c2b89840222aa29556914ab6f63861a833f3eaf64987edc7cc824c45d19a1fb | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,300 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h : ∀ s, <a>MeasurableSet</a> s → c • μ s = ∞ → μ s = ∞ := by intro s _ hcμs simp only [hc_ne_top, <a>Algebra.id.smul_eq_mul</a>, <a>ENNReal.mul_eq_top</a>, <a>or_false_iff</a>, <a>Ne</a>, <a>false_and_iff</a>] at hcμs exact hcμs.2 | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c MeasureTheory.DominatedFinMeasAdditive) (:fv _uniq.74524) (:fv _uniq.74881) (:fv _uniq.74884) (:fv _uniq.74869) (:fv _uniq.74878) (:fv _uniq.74889) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c ENNReal.toReal) (:fv _uniq.75616)) (:fv _uniq.74896))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c MeasureTheory.DominatedFinMeasAdditive) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV16)) (:arg :instance 2 (:instance-of (:app (:c SeminormedAddCommGroup) (:arg :explicit 0 (:fv FV16))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV15)) (:arg :explicit 5 (:fv FV18)) (:arg :explicit 6 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13591,"sourceStart":13587,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":13593,"sourceStart":13592,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":13593,"sourceStart":13592,"tag":"node"... | [] | [{"source":"∀ s, MeasurableSet s → c • μ s = ∞ → μ s = ∞","source_end":13654,"source_start":13596,"syntax_kind":"Lean.Parser.Term.forall"},{"source":"hc_ne_top","source_end":13705,"source_start":13696,"syntax_kind":"ident"},{"source":"Algebra.id.smul_eq_mul","source_end":13729,"source_start":13707,"syntax_kind":"ident"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 4 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 60fa4c432840526ab27afe0760561e18361e24bbfbd20b7ac6890e529e84f4d0 | 592c12d9330c1d9f055eaa1d43b8c74c09a21ae9077d37594b26f0752fbb3afe | 7d4ca257644479cdd096225d5fb0e37df8519f419994adc44797bdde52e19cec | 6589de95df37d6a147e8109ebdd34d8f8f702428166b39701828fd65fe434ae2 |
cat-searcher/leandojo-benchmark-4-random | test | 4,301 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨hT.1.<a>MeasureTheory.FinMeasAdditive.of_eq_top_imp_eq_top</a> (μ := c • μ) h, fun s hs hμs => ?_⟩ | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c MeasureTheory.DominatedFinMeasAdditive) (:fv _uniq.74524) (:fv _uniq.74881) (:fv _uniq.74884) (:fv _uniq.74869) (:fv _uniq.74878) (:fv _uniq.74889) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c ENNReal.toReal) (:fv _uniq.75616)) (:fv _uniq.74896))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c MeasureTheory.DominatedFinMeasAdditive) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV16)) (:arg :instance 2 (:instance-of (:app (:c SeminormedAddCommGroup) (:arg :explicit 0 (:fv FV16))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV15)) (:arg :explicit 5 (:fv FV18)) (:arg :explicit 6 (:app... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13825,"sourceStart":13819,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13829,"sourceStart":13826,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":25,"semanticRole":"local","source":"hT","sourceEnd":13831,"sourceStart":13829,"tag":"iden... | [] | [{"source":"⟨hT.1.of_eq_top_imp_eq_top (μ := c • μ) h, fun s hs hμs => ?_⟩","source_end":13897,"source_start":13826,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 9 | exact | true | 1 | 26 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 630bb2a31ce3a3d06836dabcabdfdcebf5065a7fe9cab3d368cee817cbf974d8 | 6589de95df37d6a147e8109ebdd34d8f8f702428166b39701828fd65fe434ae2 | a0d8a96290ed8eee8599b131cd5388c4e84e1607cb8dc828dabe3be23a516a12 | bf6d100c586b5a66a325b529dd29640169c3af9b0f3030f7bda9ab72c363cd67 |
cat-searcher/leandojo-benchmark-4-random | test | 4,302 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hcμs : c • μ s ≠ ∞ := <a>mt</a> (h s hs) hμs.ne | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.74881) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.74881) (:fv _uniq.74884)) ((:fv _uniq.74889) (:fv _uniq.78264))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV16))))) (:arg :explicit 2 (:app (:fv FV18) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13904,"sourceStart":13900,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hcμs","sourceEnd":13910,"sourceStart":13905,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hcμs","sourceEnd":13910,"sourceStart":13905,"tag":... | [] | [{"source":"c • μ s ≠ ∞","source_end":13931,"source_start":13913,"syntax_kind":"«term_≠_»"},{"source":"mt (h s hs) hμs.ne","source_end":13954,"source_start":13935,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 10 | exact | true | 1 | 29 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ca9c0c9c4635503a88a2dbc5d0bfdfa7ef8e3a5aa19525c819199df5e689d45c | bf6d100c586b5a66a325b529dd29640169c3af9b0f3030f7bda9ab72c363cd67 | 9f4b3b996a14553c06e276416874e3b1715d7221b6ae1b8a35e238e3ce45486b | 3a960a7bc78a85d736555bdde2d0d0a9466782a44765373f43d2b5b4f2e067c5 |
cat-searcher/leandojo-benchmark-4-random | test | 4,303 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>smul_eq_mul</a>] at hcμs | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.74881) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.74881) (:fv _uniq.74884)) ((:fv _uniq.74889) (:fv _uniq.78264))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV16))))) (:arg :explicit 2 (:app (:fv FV18) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13959,"sourceStart":13957,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13961,"sourceStart":13960,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"smul_eq_mul","se... | [] | [{"source":"smul_eq_mul","source_end":13972,"source_start":13961,"syntax_kind":"ident"},{"source":"hcμs","source_end":13982,"source_start":13977,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 11 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce6f99cb1769e62798a39dc1aaee00f2710d107853562dd1dbe16a3bef97f99e | 3a960a7bc78a85d736555bdde2d0d0a9466782a44765373f43d2b5b4f2e067c5 | 2bde5e03110e99eec61d5dcd96257951385deecf7b84bb8dd00b9d369776af05 | 042a1d04b9b253fe552ed74877745da72f965516122789ba8c80236a19f31a75 |
cat-searcher/leandojo-benchmark-4-random | test | 4,304 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>MeasureTheory.DominatedFinMeasAdditive</a>, <a>MeasureTheory.Measure.smul_apply</a>, <a>smul_eq_mul</a>, <a>ENNReal.toReal_mul</a>] at hT | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.74881) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.74881) (:fv _uniq.74884)) ((:fv _uniq.74889) (:fv _uniq.78264))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV16))))) (:arg :explicit 2 (:app (:fv FV18) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":13992,"sourceStart":13985,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13994,"sourceStart":13993,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"MeasureTheo... | [] | [{"source":"hT","source_end":14070,"source_start":14068,"syntax_kind":"ident"},{"source":"DominatedFinMeasAdditive","source_end":14018,"source_start":13994,"syntax_kind":"ident"},{"source":"Measure.smul_apply","source_end":14038,"source_start":14020,"syntax_kind":"ident"},{"source":"smul_eq_mul","source_end":14051,"sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 14 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26d5ac47572158fadfc62dfe1a4e9f85299008f27ac4d644d05e80fc51c28433 | 042a1d04b9b253fe552ed74877745da72f965516122789ba8c80236a19f31a75 | 077517ef3ed82670acb2a0789d0f047b7898a3c872410c02165b8da1df3c615d | 0e94d808748491cafb67243583130949c4c67e74605736ac9ded9dd62514ec2f |
cat-searcher/leandojo-benchmark-4-random | test | 4,305 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (hT.2 s hs hcμs.lt_top).<a>LE.le.trans</a> (<a>le_of_eq</a> ?_) | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:fv _uniq.74881) ((:c SeminormedAddCommGroup.toNorm) (:fv _uniq.74881) (:fv _uniq.74884)) ((:fv _uniq.74889) (:fv _uniq.78264))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Norm.norm) (:arg :implicit-type 0 (:fv FV16)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:fv FV16))))) (:arg :explicit 2 (:app (:fv FV18) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":14079,"sourceStart":14073,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":14081,"sourceStart":14080,"tag":"atom"},{"children":[{"children":[{"contextIndex":30,"semanticRole":"local","source":"hT","sourceEnd":14083,"sourceStart":14081,"tag":"iden... | [] | [{"source":"(hT.2 s hs hcμs.lt_top).trans (le_of_eq ?_)","source_end":14124,"source_start":14080,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 20 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 263f31a6a80e8cbd440d86289062648683daeaef5db5fc24a50d388361739ea7 | 0e94d808748491cafb67243583130949c4c67e74605736ac9ded9dd62514ec2f | 04cbbb7f2d47ff4b3820ac0bb3b44dd97dbe3223aa645516f4d3b8444a1ae4ec | 4d761a2bfaca3bb70ba4760349efaa10e6d10ed697519ba8242b5d79cbe13e7f |
cat-searcher/leandojo-benchmark-4-random | test | 4,306 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.74896) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c ENNReal.toReal) (:fv _uniq.75616)) ((:c ENNReal.toReal) ((:c DFunLike.coe) ((:c MeasureTheory.Meas... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"ring","sourceEnd":14131,"sourceStart":14127,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":14131,"sourceStart":14127,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 21 | exact | true | 1 | 30 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f61882ee48f32c8763e429fc2096ae9929d568d3b98e168a0e017e9a9e6323d | 4d761a2bfaca3bb70ba4760349efaa10e6d10ed697519ba8242b5d79cbe13e7f | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,307 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro s _ hcμs | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | (:forall s ((:c Set) (:fv _uniq.74524)) (:forall _ ((:c MeasurableSet) (:fv _uniq.74524) (:fv _uniq.74869) 0) (:forall _ ((:c Eq) (:c ENNReal) ((:c HSMul.hSMul) (:c ENNReal) (:c ENNReal) (:c ENNReal) ((:c instHSMul) (:c ENNReal) (:c ENNReal) ((:c Algebra.toSMul) (:c ENNReal) (:c ENNReal) ((:c CanonicallyOrderedCommSemi... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (:forall s :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:forall _ :explicit (:app (:c MeasurableSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 0)) (:forall _ :explicit (:app (:c Eq) (:arg :implicit-type 0 (:c... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":13670,"sourceStart":13665,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"s","sourceEnd":13672,"sourceStart":13671,"tag":"identifier"},{"children":[{"source":"_","sourceEnd":13674,"sourceStart":13673,"tag":"atom"}],"kind":"Lean.Parser.Term.hole","source":"_... | [{"role":"fresh_name","source":"s","source_end":13672,"source_start":13671,"syntax_kind":"ident"},{"role":"fresh_name","source":"hcμs","source_end":13680,"source_start":13675,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 6 | exact | true | 1 | 25 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1009c39495157c41402e0dfbbf348adccafd1ba932a501f95c3ac964787bde85 | 2b17d6aded84b2b1d1ca44f2b4a75f30d2ef3e523b82305ff17ac97e46217867 | ba08556eb02cbe1cf5dbf497e9539fda700e009028b6cf59bc0f112389508676 | 4cde055f16829709ad6d68b0324d80e91fa3cd7f533a4bdc2300c5a6caf764a0 |
cat-searcher/leandojo-benchmark-4-random | test | 4,308 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [hc_ne_top, <a>Algebra.id.smul_eq_mul</a>, <a>ENNReal.mul_eq_top</a>, <a>or_false_iff</a>, <a>Ne</a>, <a>false_and_iff</a>] at hcμs | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.74524) (:fv _uniq.74869)) ((:c Set) (:fv _uniq.74524)) (:lambda _ ((:c Set) (:fv _uniq.74524)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.74524) (:fv _uniq.74869)) (:fv _uniq.74878) (:fv _uniq.76079)) ((:c Top.top) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (: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.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":13689,"sourceStart":13685,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13694,"sourceStart":13690,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":136... | [] | [{"source":"hc_ne_top","source_end":13705,"source_start":13696,"syntax_kind":"ident"},{"source":"Algebra.id.smul_eq_mul","source_end":13729,"source_start":13707,"syntax_kind":"ident"},{"source":"ENNReal.mul_eq_top","source_end":13749,"source_start":13731,"syntax_kind":"ident"},{"source":"or_false_iff","source_end":1376... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 7 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d9737bf9f61a3bf0572bac62565064546d927671a03561fefa35666a9e21344 | 4cde055f16829709ad6d68b0324d80e91fa3cd7f533a4bdc2300c5a6caf764a0 | 3c9e99ec47d258410b4ea32d8e01f93d0095a89cb3b56661a79dbf113febcdbc | f41de104d2298b2e19e1d145ee937414b3ec3a65259e96ef0b473cabab677b7f |
cat-searcher/leandojo-benchmark-4-random | test | 4,309 | MeasureTheory.DominatedFinMeasAdditive.of_smul_measure | Mathlib/MeasureTheory/Integral/SetToL1.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hcμs.2 | α : Type u_1
E : Type u_2
F : Type u_3
F' : Type u_4
G : Type u_5
𝕜 : Type u_6
p : ℝ≥0∞
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace ℝ E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℝ F
inst✝³ : NormedAddCommGroup F'
inst✝² : NormedSpace ℝ F'
inst✝¹ : NormedAddCommGroup G
m : MeasurableSpace α
μ : Measure ... | ((:c Eq) (:c ENNReal) ((:c DFunLike.coe) ((:c MeasureTheory.Measure) (:fv _uniq.74524) (:fv _uniq.74869)) ((:c Set) (:fv _uniq.74524)) (:lambda _ ((:c Set) (:fv _uniq.74524)) (:c ENNReal)) ((:c MeasureTheory.Measure.instFunLike) (:fv _uniq.74524) (:fv _uniq.74869)) (:fv _uniq.74878) (:fv _uniq.76079)) ((:c Top.top) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"F","sexp":"(:sort (+ u_3 1))"},{"name":"F'","sexp":"(:sort (+ u_4 1))"},{"name":"G","sexp":"(:sort (+ u_5 1))"},{"name":"𝕜","sexp":"(:sort (+ u_6 1))"},{"name":"p","sexp":"(:c ENNReal)"},{"name":"inst✝⁷","sexp":"((:c NormedAddCom... | (: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.74524","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"name":"E","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":13808,"sourceStart":13803,"tag":"atom"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"hcμs","sourceEnd":13814,"sourceStart":13809,"tag":"identifier"},{"source":".","sourceEnd":13815,"sourceStart":13814,"tag":"atom"},{"children":[{"source":"2","sourceEnd":138... | [] | [{"source":"hcμs.2","source_end":13816,"source_start":13809,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.74524","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.74527","is_instance":false,"is_let":false,"user_name":"E"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 53 | 8 | exact | true | 1 | 28 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | efb5f10de3c57356c3df4368728f06c4f80fed884c3274329430ababb5338f66 | f41de104d2298b2e19e1d145ee937414b3ec3a65259e96ef0b473cabab677b7f | a9d43fb783cdb2b48c7b0adcada5b52fd7bd183437a301e050dd74822efea2be | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 4,310 | MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff | Mathlib/Probability/Kernel/Disintegration/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← ρ.compProd_fst_condKernel] at hf | α : Type u_1
Ω : Type u_2
E : Type u_3
F : Type u_4
mα : MeasurableSpace α
inst✝⁶ : MeasurableSpace Ω
inst✝⁵ : StandardBorelSpace Ω
inst✝⁴ : Nonempty Ω
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : NormedAddCommGroup F
ρ : Measure (α × Ω)
inst✝ : IsFiniteMeasure ρ
f : α × Ω → F
hf : AEStronglyMeasurab... | α : Type u_1
Ω : Type u_2
E : Type u_3
F : Type u_4
mα : MeasurableSpace α
inst✝⁶ : MeasurableSpace Ω
inst✝⁵ : StandardBorelSpace Ω
inst✝⁴ : Nonempty Ω
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : NormedAddCommGroup F
ρ : Measure (α × Ω)
inst✝ : IsFiniteMeasure ρ
f : α × Ω → F
hf : AEStronglyMeasurab... | ((:c Iff) ((:c And) ((:c Filter.Eventually) (:fv _uniq.56916) (:lambda a (:fv _uniq.56916) ((:c MeasureTheory.Integrable) (:fv _uniq.56925) (:fv _uniq.57060) (:fv _uniq.56919) (:fv _uniq.56931) (:lambda ω (:fv _uniq.56919) ((:fv _uniq.58381) ((:c Prod.mk) (:fv _uniq.56916) (:fv _uniq.56919) 1 0))) ((:c DFunLike.coe) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.56916))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.56919))"},{"name":"inst✝⁵","sexp":"((... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rw","sourceEnd":13318,"sourceStart":13316,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13320,"sourceStart":13319,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13323,"sourceSt... | [] | [{"source":"ρ.compProd_fst_condKernel","source_end":13350,"source_start":13324,"syntax_kind":"ident"},{"source":"hf","source_end":13357,"source_start":13355,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 4 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | acd5b383473f07c72b9303488ab161ec7e11516034200100e6bb52e3af426342 | 0dee6d4f59c435e4cc15c94f22dc433e181f77e6f4b6011b66a4a6fac601a1ab | d2656dd7c804832498bd928631764fabfba7966ae869328b0f6b51f28f9ce4dc | bafe73359c889208d1aa91fa9670c936cdce2a09f820ba3acf51fb86e9eee779 |
cat-searcher/leandojo-benchmark-4-random | test | 4,311 | MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff | Mathlib/Probability/Kernel/Disintegration/Integral.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | conv_rhs => rw [← ρ.compProd_fst_condKernel] | α : Type u_1
Ω : Type u_2
E : Type u_3
F : Type u_4
mα : MeasurableSpace α
inst✝⁶ : MeasurableSpace Ω
inst✝⁵ : StandardBorelSpace Ω
inst✝⁴ : Nonempty Ω
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : NormedAddCommGroup F
ρ : Measure (α × Ω)
inst✝ : IsFiniteMeasure ρ
f : α × Ω → F
hf : AEStronglyMeasurab... | α : Type u_1
Ω : Type u_2
E : Type u_3
F : Type u_4
mα : MeasurableSpace α
inst✝⁶ : MeasurableSpace Ω
inst✝⁵ : StandardBorelSpace Ω
inst✝⁴ : Nonempty Ω
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
inst✝¹ : NormedAddCommGroup F
ρ : Measure (α × Ω)
inst✝ : IsFiniteMeasure ρ
f : α × Ω → F
hf : AEStronglyMeasurab... | ((:c Iff) ((:c And) ((:c Filter.Eventually) (:fv _uniq.56916) (:lambda a (:fv _uniq.56916) ((:c MeasureTheory.Integrable) (:fv _uniq.56925) (:fv _uniq.57060) (:fv _uniq.56919) (:fv _uniq.56931) (:lambda ω (:fv _uniq.56919) ((:fv _uniq.58381) ((:c Prod.mk) (:fv _uniq.56916) (:fv _uniq.56919) 1 0))) ((:c DFunLike.coe) ((... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"Ω","sexp":"(:sort (+ u_2 1))"},{"name":"E","sexp":"(:sort (+ u_3 1))"},{"name":"F","sexp":"(:sort (+ u_4 1))"},{"name":"mα","sexp":"((:c MeasurableSpace) (:fv _uniq.56916))"},{"name":"inst✝⁶","sexp":"((:c MeasurableSpace) (:fv _uniq.56919))"},{"name":"inst✝⁵","sexp":"((... | (:app (:c Iff) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda a :explicit (:fv FV0) (:app (:c MeasureTheory.Integrable) (:arg :implicit-type 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c NormedAddCommGroup) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"name":"Ω","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"conv_rhs","sourceEnd":13368,"sourceStart":13360,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"source":"=>","sourceEnd":13371,"sourceStart":13369,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"sou... | [] | [{"source":"ρ.compProd_fst_condKernel","source_end":13406,"source_start":13380,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.56916","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.56919","is_instance":false,"is_let":false,"user_name":"Ω"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 72 | 7 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 130b0942bdd3d0e5253856a0b3ca2abe403565aab93314cc0549499663dc6dd6 | bafe73359c889208d1aa91fa9670c936cdce2a09f820ba3acf51fb86e9eee779 | a9a9846ea611e342c831ed3037634f9a4a3d82d00a90b1951b5e6e3f8a0a60d0 | 565d78ff9744394427e3142ae8e8437cfaa554d2aa6e2ffff88eba0fb048288e |
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