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 | 508 | Finite.card_le_of_injective | Mathlib/Data/Finite/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>Fintype.ofFinite</a> β | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Finite β
f : α → β
hf : Function.Injective f
⊢ Nat.card α ≤ Nat.card β | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Finite β
f : α → β
hf : Function.Injective f
this : Fintype β
⊢ Nat.card α ≤ Nat.card β | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Nat.card) (:fv _uniq.2093)) ((:c Nat.card) (:fv _uniq.2096))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.2096))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.2093) (:fv _uniq.2096))"},{"name":"hf","sexp":"((:c Function.Injective) (:fv _uniq.2093) (:fv _uniq.... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV1))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"haveI","sourceEnd":4126,"sourceStart":4121,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4127,"sourceStart":4127,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4127,"sourceStart":4127,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"Fintype.ofFinite β","source_end":4149,"source_start":4130,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 28 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bb28628da5154a9180d853e09323ef85e6198c7af564862e90c6f24174f8c8f4 | 14525612dc19a30602b70c62dfca191abfcf49a0e52aa2d20a5b703b34081457 | 19a4e80af0dd7537501ef1d6f9d1e5f37b49f708cb16e89ad0ca2b3f9ab637d2 | 94605c0a2d882e7a731f378ff07ae0a32e76929f3c8786a56a1867a7cd7202c3 |
cat-searcher/leandojo-benchmark-4-random | test | 509 | Finite.card_le_of_injective | Mathlib/Data/Finite/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>Fintype.ofInjective</a> f hf | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Finite β
f : α → β
hf : Function.Injective f
this : Fintype β
⊢ Nat.card α ≤ Nat.card β | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Finite β
f : α → β
hf : Function.Injective f
this✝ : Fintype β
this : Fintype α
⊢ Nat.card α ≤ Nat.card β | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Nat.card) (:fv _uniq.2093)) ((:c Nat.card) (:fv _uniq.2096))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.2096))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.2093) (:fv _uniq.2096))"},{"name":"hf","sexp":"((:c Function.Injective) (:fv _uniq.2093) (:fv _uniq.... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV1))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"haveI","sourceEnd":4157,"sourceStart":4152,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":4158,"sourceStart":4158,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":4158,"sourceStart":4158,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"Fintype.ofInjective f hf","source_end":4185,"source_start":4161,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 28 | 5 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e633fb2fdffa3c095f868e7cd5f476ac5ffaacc977594a65191d3982821b06a6 | 94605c0a2d882e7a731f378ff07ae0a32e76929f3c8786a56a1867a7cd7202c3 | 7afb41e90bdb351d876f6989362f01f16731f01d31dae39ed9b13dee020e963c | de6e5d23e493cfa8528ee9d85c8acdafa6c3fea274bdc6b53275d9cc908c59c0 |
cat-searcher/leandojo-benchmark-4-random | test | 510 | Finite.card_le_of_injective | Mathlib/Data/Finite/Card.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>Nat.card_eq_fintype_card</a>, <a>ge_iff_le</a>] using <a>Fintype.card_le_of_injective</a> f hf | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝ : Finite β
f : α → β
hf : Function.Injective f
this✝ : Fintype β
this : Fintype α
⊢ Nat.card α ≤ Nat.card β | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Nat.card) (:fv _uniq.2093)) ((:c Nat.card) (:fv _uniq.2096))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝","sexp":"((:c Finite) (:fv _uniq.2096))"},{"name":"f","sexp":"(:forall _ (:fv _uniq.2093) (:fv _uniq.2096))"},{"name":"hf","sexp":"((:c Function.Injective) (:fv _uniq.2093) (:fv _uniq.... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 3 (:app (:c Nat.card) (:arg :explicit 0 (:fv FV1))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"simpa","sourceEnd":4193,"sourceStart":4188,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"chil... | [] | [{"source":"Nat.card_eq_fintype_card","source_end":4224,"source_start":4200,"syntax_kind":"ident"},{"source":"ge_iff_le","source_end":4235,"source_start":4226,"syntax_kind":"ident"},{"source":"Fintype.card_le_of_injective f hf","source_end":4276,"source_start":4243,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2093","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2096","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 28 | 6 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a95de5d8a6e0e34862cffaf44414c0424b8d36ab478d54683db36c8e728fe7f7 | de6e5d23e493cfa8528ee9d85c8acdafa6c3fea274bdc6b53275d9cc908c59c0 | ec1e0344bc377aa6b5250f3b3aefa878d69828bcc107baff45794494bcc68905 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 511 | EllipticCurve.ofJ1728_j | Mathlib/AlgebraicGeometry/EllipticCurve/Weierstrass.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | field_simp [<a>EllipticCurve.j</a>, <a>EllipticCurve.ofJ1728</a>, @<a>val_unitOfInvertible</a> _ _ _ <| <a>invertibleNeg</a> _, <a>WeierstrassCurve.ofJ1728_c₄</a>] | R : Type u
inst✝¹ : CommRing R
E : EllipticCurve R
inst✝ : Invertible 2
⊢ (ofJ1728 R).j = 1728 | R : Type u
inst✝¹ : CommRing R
E : EllipticCurve R
inst✝ : Invertible 2
⊢ -(1728 * 2 ^ 6) = (-48) ^ 3 | ((:c Eq) (:fv _uniq.319796) ((:c EllipticCurve.j) (:fv _uniq.319796) (:fv _uniq.319799) ((:c EllipticCurve.ofJ1728) (:fv _uniq.319796) (:fv _uniq.319799) (:fv _uniq.320587))) ((:c OfNat.ofNat) (:fv _uniq.319796) (:lit 1728) ((:c instOfNatAtLeastTwo) (:fv _uniq.319796) (:lit 1728) ((:c Semiring.toNatCast) (:fv _uniq.319... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.319796))"},{"name":"E","sexp":"((:c EllipticCurve) (:fv _uniq.319796) (:fv _uniq.319799))"},{"name":"inst✝","sexp":"((:c Invertible) (:fv _uniq.319796) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.319796) ((:c NonUnitalNonAssocCom... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c EllipticCurve.j) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c EllipticCurve.ofJ1728) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.319796","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.319799","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"field_simp","sourceEnd":29070,"sourceStart":29060,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":"[","sourceEnd":29072,"sourceSt... | [] | [{"source":"j","source_end":29073,"source_start":29072,"syntax_kind":"ident"},{"source":"ofJ1728","source_end":29082,"source_start":29075,"syntax_kind":"ident"},{"source":"@val_unitOfInvertible _ _ _ <| invertibleNeg _","source_end":29130,"source_start":29084,"syntax_kind":"«term_<|_»"},{"source":"WeierstrassCurve.ofJ1... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.319796","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.319799","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte... | 183 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77d4bb51c0140eaddb3ec7d1489b9ad40f08eb41c2a6a83fc76adca1e2265de0 | f8c4ea1307d4732df4ee55a3d24aa75584a86000ae9d5b72487864faa5d2c8e8 | d024022ca11f6816e46f72449eb8eb4bb2ddf955bf2be63374575feb2f614622 | fe4bc47cc0730683cbe4c274735c69bdcdc2b932111659889685ea515e34ec6d |
cat-searcher/leandojo-benchmark-4-random | test | 512 | EllipticCurve.ofJ1728_j | Mathlib/AlgebraicGeometry/EllipticCurve/Weierstrass.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num1 | R : Type u
inst✝¹ : CommRing R
E : EllipticCurve R
inst✝ : Invertible 2
⊢ -(1728 * 2 ^ 6) = (-48) ^ 3 | ((:c Eq) (:fv _uniq.319796) ((:c Neg.neg) (:fv _uniq.319796) ((:c InvolutiveNeg.toNeg) (:fv _uniq.319796) ((:c HasDistribNeg.toInvolutiveNeg) (:fv _uniq.319796) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.319796) ((:c NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing) (:fv _uniq.319796) ((:c NonUnitalCommRing.toNonUni... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹","sexp":"((:c CommRing) (:fv _uniq.319796))"},{"name":"E","sexp":"((:c EllipticCurve) (:fv _uniq.319796) (:fv _uniq.319799))"},{"name":"inst✝","sexp":"((:c Invertible) (:fv _uniq.319796) ((:c NonUnitalNonAssocRing.toMul) (:fv _uniq.319796) ((:c NonUnitalNonAssocCom... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c Neg.neg) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.319796","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.319799","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c CommRing) (:arg :expl... | {"children":[{"source":"norm_num1","sourceEnd":29178,"sourceStart":29169,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.normNum1","source":"norm_num1","sourceEnd":29178,"sourceStart":29169,"tag":"node"} | [] | [] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.319796","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.319799","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":explicit","context_index":2,"inte... | 183 | 5 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 298f11bcab3d8d49dc0cec8109500f0c2738dfb59203785a5daf995a152bd88c | fe4bc47cc0730683cbe4c274735c69bdcdc2b932111659889685ea515e34ec6d | 3942261cc642891fa68a99ae298a7dfb912321b05015e7d415bf5bff32a76a8d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 513 | LieModule.mem_weightSpace | Mathlib/Algebra/Lie/Weights/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>LieModule.weightSpace</a>, <a>LieModule.mem_weightSpaceOf</a>] | K : Type u_1
R : Type u_2
L : Type u_3
M : Type u_4
inst✝⁷ : CommRing R
inst✝⁶ : LieRing L
inst✝⁵ : LieAlgebra R L
inst✝⁴ : LieAlgebra.IsNilpotent R L
inst✝³ : AddCommGroup M
inst✝² : Module R M
inst✝¹ : LieRingModule L M
inst✝ : LieModule R L M
χ : L → R
m : M
⊢ m ∈ weightSpace M χ ↔ ∀ (x : L), ∃ k, (((toEnd R L M) x ... | ((:c Iff) ((:c Membership.mem) (:fv _uniq.91372) ((:c LieSubmodule) (:fv _uniq.91366) (:fv _uniq.91369) (:fv _uniq.91372) (:fv _uniq.91375) (:fv _uniq.91378) (:fv _uniq.91423) (:fv _uniq.92035) (:fv _uniq.92049)) ((:c SetLike.instMembership) ((:c LieSubmodule) (:fv _uniq.91366) (:fv _uniq.91369) (:fv _uniq.91372) (:fv ... | [{"name":"K","sexp":"(:sort (+ u_1 1))"},{"name":"R","sexp":"(:sort (+ u_2 1))"},{"name":"L","sexp":"(:sort (+ u_3 1))"},{"name":"M","sexp":"(:sort (+ u_4 1))"},{"name":"inst✝⁷","sexp":"((:c CommRing) (:fv _uniq.91366))"},{"name":"inst✝⁶","sexp":"((:c LieRing) (:fv _uniq.91369))"},{"name":"inst✝⁵","sexp":"((:c LieAlgeb... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV3)) (:arg :implicit-type 1 (:app (:c LieSubmodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (:fv FV3)) (:arg :instance 3 (:instance-of (:app (:c CommRing) (:arg :explicit 0 (:fv FV1))))) (:arg :in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91363","is_instance":false,"is_let":false,"name":"K","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91366","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8879,"sourceStart":8875,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"weightSpace","source_end":8892,"source_start":8881,"syntax_kind":"ident"},{"source":"mem_weightSpaceOf","source_end":8911,"source_start":8894,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.91363","is_instance":false,"is_let":false,"user_name":"K"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.91366","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 17 | 2 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6f6ca46bbd3f955a0cfc842d28c047dc79a8054aaa4cf2be80277bf69def6971 | 75ead468f0348fcf4942ed66055a2957a2fdb317e2cc37de5a48a4425193bdaf | bc976660835b4a365e6431f3e529c2717ed8e0895432be170707c1fceeadf826 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 514 | IsClosed.exists_closed_singleton | Mathlib/Topology/Separation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨V, Vsub, Vne, Vcls, hV⟩ := hS.exists_minimal_nonempty_closed_subset hne | X : Type u_1
Y : Type u_2
inst✝² : TopologicalSpace X
inst✝¹ : T0Space X
inst✝ : CompactSpace X
S : Set X
hS : IsClosed S
hne : S.Nonempty
⊢ ∃ x ∈ S, IsClosed {x} | case intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝² : TopologicalSpace X
inst✝¹ : T0Space X
inst✝ : CompactSpace X
S : Set X
hS : IsClosed S
hne : S.Nonempty
V : Set X
Vsub : V ⊆ S
Vne : V.Nonempty
Vcls : IsClosed V
hV : ∀ V' ⊆ V, V'.Nonempty → IsClosed V' → V' = V
⊢ ∃ x ∈ S, IsClosed {x} | ((:c Exists) (:fv _uniq.38164) (:lambda x (:fv _uniq.38164) ((:c And) ((:c Membership.mem) (:fv _uniq.38164) ((:c Set) (:fv _uniq.38164)) ((:c Set.instMembership) (:fv _uniq.38164)) 0 (:fv _uniq.38287)) ((:c IsClosed) (:fv _uniq.38164) (:fv _uniq.38170) ((:c Singleton.singleton) (:fv _uniq.38164) ((:c Set) (:fv _uniq.3... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.38164))"},{"name":"inst✝¹","sexp":"((:c T0Space) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"inst✝","sexp":"((:c CompactSpace) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"S... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":17992,"sourceStart":17986,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":17996,"sourceStart":17993,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"V","sourceEn... | [] | [{"source":"hS.exists_minimal_nonempty_closed_subset hne","source_end":18069,"source_start":18025,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨V, Vsub, Vne, Vcls, hV⟩","source_end":18021,"source_start":17993,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 77 | 4 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f7f56a29b56a93c165ce15be85c4fa7d6bb76200bf9f4eeaa49346f4d2cfd5cb | 2ac6baa63dc6aef909b88f04c842969b10c238686cdcedd4af7a7ad1e49c5538 | 7367dbefa3d2529081eefdf2b842291a070636b9011b2622ee371f9f355e0328 | 8a8b265882849e1a57d9c4eacfd9b055a2bdc28ec89266110907bb7e2322023e |
cat-searcher/leandojo-benchmark-4-random | test | 515 | IsClosed.exists_closed_singleton | Mathlib/Topology/Separation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>minimal_nonempty_closed_eq_singleton</a> Vcls Vne hV with ⟨x, rfl⟩ | case intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝² : TopologicalSpace X
inst✝¹ : T0Space X
inst✝ : CompactSpace X
S : Set X
hS : IsClosed S
hne : S.Nonempty
V : Set X
Vsub : V ⊆ S
Vne : V.Nonempty
Vcls : IsClosed V
hV : ∀ V' ⊆ V, V'.Nonempty → IsClosed V' → V' = V
⊢ ∃ x ∈ S, IsClosed {x} | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝² : TopologicalSpace X
inst✝¹ : T0Space X
inst✝ : CompactSpace X
S : Set X
hS : IsClosed S
hne : S.Nonempty
x : X
Vsub : {x} ⊆ S
Vne : {x}.Nonempty
Vcls : IsClosed {x}
hV : ∀ V' ⊆ {x}, V'.Nonempty → IsClosed V' → V' = {x}
⊢ ∃ x ∈ S, IsClosed {x} | ((:c Exists) (:fv _uniq.38164) (:lambda x (:fv _uniq.38164) ((:c And) ((:c Membership.mem) (:fv _uniq.38164) ((:c Set) (:fv _uniq.38164)) ((:c Set.instMembership) (:fv _uniq.38164)) 0 (:fv _uniq.38287)) ((:c IsClosed) (:fv _uniq.38164) (:fv _uniq.38170) ((:c Singleton.singleton) (:fv _uniq.38164) ((:c Set) (:fv _uniq.3... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.38164))"},{"name":"inst✝¹","sexp":"((:c T0Space) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"inst✝","sexp":"((:c CompactSpace) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"S... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rcases","sourceEnd":18078,"sourceStart":18072,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"minimal_nonempty_closed_eq_singleton","semanticRole":"global","source":"minimal_nonempty_closed_eq_singleton","sourceEnd":18115,"sour... | [] | [{"source":"minimal_nonempty_closed_eq_singleton Vcls Vne hV","source_end":18127,"source_start":18079,"syntax_kind":"Lean.Parser.Term.app"},{"source":"⟨x, rfl⟩","source_end":18145,"source_start":18133,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 77 | 5 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55c897658318c7adfe584ed5fd004bd14ec9dda44295d75335517ecace765932 | 8a8b265882849e1a57d9c4eacfd9b055a2bdc28ec89266110907bb7e2322023e | 641229cf9bcdb2e13f086b6fd93626094bd57af16b0798ae3501c738573d5d59 | ca7c9dc4d681e2aad4659b03059ea9207efa4e8d58d8391f03ae80b8673d81ee |
cat-searcher/leandojo-benchmark-4-random | test | 516 | IsClosed.exists_closed_singleton | Mathlib/Topology/Separation.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact ⟨x, Vsub (<a>Set.mem_singleton</a> x), Vcls⟩ | case intro.intro.intro.intro.intro
X : Type u_1
Y : Type u_2
inst✝² : TopologicalSpace X
inst✝¹ : T0Space X
inst✝ : CompactSpace X
S : Set X
hS : IsClosed S
hne : S.Nonempty
x : X
Vsub : {x} ⊆ S
Vne : {x}.Nonempty
Vcls : IsClosed {x}
hV : ∀ V' ⊆ {x}, V'.Nonempty → IsClosed V' → V' = {x}
⊢ ∃ x ∈ S, IsClosed {x} | ((:c Exists) (:fv _uniq.38164) (:lambda x (:fv _uniq.38164) ((:c And) ((:c Membership.mem) (:fv _uniq.38164) ((:c Set) (:fv _uniq.38164)) ((:c Set.instMembership) (:fv _uniq.38164)) 0 (:fv _uniq.38287)) ((:c IsClosed) (:fv _uniq.38164) (:fv _uniq.38170) ((:c Singleton.singleton) (:fv _uniq.38164) ((:c Set) (:fv _uniq.3... | [{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"Y","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.38164))"},{"name":"inst✝¹","sexp":"((:c T0Space) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"inst✝","sexp":"((:c CompactSpace) (:fv _uniq.38164) (:fv _uniq.38170))"},{"name":"S... | (:app (:c Exists) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c And) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":18153,"sourceStart":18148,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":18157,"sourceStart":18154,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"x","sourceEnd":18158,"sourceStart":18157,"tag":"identifier"},{"source":",","sourceEnd":18159,"... | [] | [{"source":"⟨x, Vsub (mem_singleton x), Vcls⟩","source_end":18191,"source_start":18154,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.38164","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.38167","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 77 | 6 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf78e5e72bd693d31034086940c0f73c6808e947e189fbd361cef6ddc7100602 | ca7c9dc4d681e2aad4659b03059ea9207efa4e8d58d8391f03ae80b8673d81ee | 9158f94036f18aa82f57bbc920c6ee962ac425593a566ba182aa055b487ec476 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 517 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>Nat.eq_zero_or_pos</a> n with (rfl | hnpos) | p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | case inl
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝ : CommRing R
hdiv : ¬p ∣ 0
⊢ (expand R p) (cyclotomic 0 R) = cyclotomic (0 * p) R * cyclotomic 0 R
case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | ((:c Eq) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq.457) (:fv _uniq.458)))) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.457) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Polyno... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rcases","sourceEnd":1693,"sourceStart":1687,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.eq_zero_or_pos","semanticRole":"global","source":"Nat.eq_zero_or_pos","sourceEnd":1712,"sourceStart":1694,"tag":"identifier"},{"chi... | [] | [{"source":"Nat.eq_zero_or_pos n","source_end":1714,"source_start":1694,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(rfl | hnpos)","source_end":1733,"source_start":1720,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 11bc78d4b8535d0bb9d9c2b47d8867e393eaed98342e709e74416f1d39a24c49 | a6e9b3fb221d752f2005b029097d21f3978e9f87487dfb235d6c3a541b8fa859 | 29e4a172f46706fdaf18580e43d464a6352431bf15dd2ad1effdef7f4c2cf328 | 84f5c711b0bdd9fb93c9732b191550e381accdbee9f2129720aed34f7c1f1940 |
cat-searcher/leandojo-benchmark-4-random | test | 518 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | haveI := <a>NeZero.of_pos</a> hnpos | case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | ((:c Eq) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq.457) (:fv _uniq.458)))) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.457) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Polyno... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"haveI","sourceEnd":1751,"sourceStart":1746,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":1752,"sourceStart":1752,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":1752,"sourceStart":1752,"tag":"node"}],"kind":"Lean.Parser.Term.haveId",... | [] | [{"source":"NeZero.of_pos hnpos","source_end":1774,"source_start":1755,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 10 | exact | true | 1 | 7 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9630ec30cce1aa81454e0fe2200eb2615378e4bb0e57d605097478f38a815df6 | 4b554222802b857aceebf630535edeb2ee07730324dbb3707798982b68db51d1 | 28e951fd705c27cc81e862e324858d143beaf9f58547f5532027429aa8711280 | 551494e871ca28d023011545b35f2e11d60bcc1a4c9a12bab9981c5e854649a9 |
cat-searcher/leandojo-benchmark-4-random | test | 519 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | suffices <a>Polynomial.expand</a> ℤ p (<a>Polynomial.cyclotomic</a> n ℤ) = <a>Polynomial.cyclotomic</a> (n * p) ℤ * <a>Polynomial.cyclotomic</a> n ℤ by rw [← <a>Polynomial.map_cyclotomic_int</a>, ← <a>Polynomial.map_expand</a>, this, <a>Polynomial.map_mul</a>, <a>Polynomial.map_cyclotomic_int</a>, <a>Polynomial.map_cyc... | case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ (expand ℤ p) (cyclotomic n ℤ) = cyclotomic (n * p) ℤ * cyclotomic n ℤ | ((:c Eq) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq.457) (:fv _uniq.458)))) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.457) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Polyno... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"suffices","sourceEnd":1785,"sourceStart":1777,"tag":"atom"},{"children":[{"children":[{"source":"","sourceEnd":1786,"sourceStart":1786,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":1786,"sourceStart":1786,"tag":"node"},{"children":[{"children":[{"name":"Polynomial.expand","se... | [] | [{"source":"expand ℤ p (cyclotomic n ℤ) = cyclotomic (n * p) ℤ * cyclotomic n ℤ","source_end":1861,"source_start":1786,"syntax_kind":"«term_=_»"},{"source":"map_cyclotomic_int","source_end":1895,"source_start":1877,"syntax_kind":"ident"},{"source":"map_expand","source_end":1911,"source_start":1901,"syntax_kind":"ident"... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 11 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b55e454ffbd08079464f82ef17cdbf00c6b0aba5c1127056f51c93a50b394c3 | 551494e871ca28d023011545b35f2e11d60bcc1a4c9a12bab9981c5e854649a9 | 7593314b69a96ff0c3e9656b771236d92084945df698a3d02ef2d94209144ff7 | bd2d5279a160301dc0d581fd549e347b55bb72a3c3d5888ef8e5e1c0769078c9 |
cat-searcher/leandojo-benchmark-4-random | test | 520 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>Polynomial.eq_of_monic_of_dvd_of_natDegree_le</a> ((<a>Polynomial.cyclotomic.monic</a> _ ℤ).<a>Polynomial.Monic.mul</a> (<a>Polynomial.cyclotomic.monic</a> _ ℤ)) ((<a>Polynomial.cyclotomic.monic</a> n ℤ).<a>Polynomial.Monic.expand</a> hp.pos) ?_ ?_ | case inr
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ (expand ℤ p) (cyclotomic n ℤ) = cyclotomic (n * p) ℤ * cyclotomic n ℤ | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℤ * cyclotomic n ℤ ∣ (expand ℤ p) (cyclotomic n ℤ)
case inr.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ ((expand... | ((:c Eq) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) (:c Int.instCommSemiring))) ((:c DFunLike.coe) ((:c AlgHom) (:c Int) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) (:c Int.instCommSemiring))) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) (:c Int.instCommSem... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Int))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:c Int)) (:arg :explicit 1 (:app (:c Polynomia... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"refine","sourceEnd":1989,"sourceStart":1983,"tag":"atom"},{"children":[{"name":"Polynomial.eq_of_monic_of_dvd_of_natDegree_le","semanticRole":"global","source":"eq_of_monic_of_dvd_of_natDegree_le","sourceEnd":2024,"sourceStart":1990,"tag":"identifier"},{"children":[{"children":[{"source":"(","so... | [] | [{"source":"eq_of_monic_of_dvd_of_natDegree_le ((cyclotomic.monic _ ℤ).mul (cyclotomic.monic _ ℤ))\n ((cyclotomic.monic n ℤ).expand hp.pos) ?_ ?_","source_end":2131,"source_start":1990,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 22 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c66aa28bd20f960d5633990b91d6cec700e9c4da57312ea7621cd0cf31be1a58 | bd2d5279a160301dc0d581fd549e347b55bb72a3c3d5888ef8e5e1c0769078c9 | aab677a810c18e470d363866aa76ff32a3acf0becfe13244f56c989888a32794 | 13002275f5cbc8e22e845f149544a704ef1dac00dea00128735860f7adfa51a0 |
cat-searcher/leandojo-benchmark-4-random | test | 521 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case inl
p : ℕ
hp : Nat.Prime p
R : Type u_1
inst✝ : CommRing R
hdiv : ¬p ∣ 0
⊢ (expand R p) (cyclotomic 0 R) = cyclotomic (0 * p) R * cyclotomic 0 R | ((:c Eq) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq.457) (:fv _uniq.458)))) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.457) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"p","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.457))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c inst... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV3)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV3))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV3)) (:arg :explicit 1 (:app (:c Polyno... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.455","is_instance":false,"is_let":false,"name":"hp","sexp":"(:app (:c Nat.Prime) (:arg :explicit 0 (:fv FV1)))"},... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":1743,"sourceStart":1739,"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":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.455","is_instance":false,"is_let":false,"user_name":"hp"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.... | 3 | 7 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2ef4e3fca2e171eb3fb98e342edf77ff5a823694ba69a56ddcacbce5e399252e | 068782c144f367da466c84439cb194c9820a3ed7d4fc885dd4c36ec145548058 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 522 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Polynomial.map_cyclotomic_int</a>, ← <a>Polynomial.map_expand</a>, this, <a>Polynomial.map_mul</a>, <a>Polynomial.map_cyclotomic_int</a>, <a>Polynomial.map_cyclotomic</a>] | p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this✝ : NeZero n
this : (expand ℤ p) (cyclotomic n ℤ) = cyclotomic (n * p) ℤ * cyclotomic n ℤ
⊢ (expand R p) (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R | ((:c Eq) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq.457) (:fv _uniq.458)))) ((:c DFunLike.coe) ((:c AlgHom) (:fv _uniq.457) ((:c Polynomial) (:fv _uniq.457) ((:c CommSemiring.toSemiring) (:fv _uniq.457) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:app (:c Polyno... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":1871,"sourceStart":1869,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":1873,"sourceStart":1872,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"sour... | [] | [{"source":"map_cyclotomic_int","source_end":1895,"source_start":1877,"syntax_kind":"ident"},{"source":"map_expand","source_end":1911,"source_start":1901,"syntax_kind":"ident"},{"source":"this","source_end":1917,"source_start":1913,"syntax_kind":"ident"},{"source":"Polynomial.map_mul","source_end":1937,"source_start":1... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 12 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 43d88fed09a98931fbae1d219a7d6e638e65e13f8c5fa8a1197d6b69989fbca1 | 6616bd2ebe0d988e98414ea65270511dabba7da9fbf57d79ca32c39f01edb82a | fdbcf3a612e600883f154e1d7229d43a2c89fadf6072e28d1138d16a41030697 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 523 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine (<a>Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast</a> _ _ (<a>Polynomial.IsPrimitive.mul</a> (<a>Polynomial.cyclotomic.isPrimitive</a> (n * p) ℤ) (<a>Polynomial.cyclotomic.isPrimitive</a> n ℤ)) ((<a>Polynomial.cyclotomic.monic</a> n ℤ).<a>Polynomial.Monic.expand</a> hp.pos).<a>Polynomial.Monic.isPrimi... | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℤ * cyclotomic n ℤ ∣ (expand ℤ p) (cyclotomic n ℤ) | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ map (Int.castRingHom ℚ) (cyclotomic (n * p) ℤ * cyclotomic n ℤ) ∣
map (Int.castRingHom ℚ) ((expand ℤ p) (cyclotomic n ℤ)) | ((:c Dvd.dvd) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) ((:c CommRing.toCommSemiring) (:c Int) (:c Int.instCommRing)))) ((:c semigroupDvd) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) ((:c CommRing.toCommSemiring) (:c Int) (:c Int.instCommRing)))) ((:c SemigroupWithZero.toSemi... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Int))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Int)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"refine","sourceEnd":2143,"sourceStart":2137,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"(","sourceEnd":2145,"sourceStart":2144,"tag":"atom"},{"children":[{"name":"Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast","semanticRole":"global","source":"IsPrimitive.Int.dvd_i... | [] | [{"source":"(IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast _ _\n (IsPrimitive.mul (cyclotomic.isPrimitive (n * p) ℤ) (cyclotomic.isPrimitive n ℤ))\n ((cyclotomic.monic n ℤ).expand hp.pos).isPrimitive).2 ?_","source_end":2351,"source_start":2144,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 27 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b4f2885bd217f5a53fa55f584fb342017c88acb9bd56011b2160502e965d4f5b | 9d234f273607abccad248bcd047d369c976a2b611fd0412ce53db44c3316a2f3 | 8ca4f38760dd7cdc103315dad9b7f1197c35438a36ed60e023fde5fb84c85ccb | 86048199b0cf1a24c9c14fd290d96385d503ffc93827a0194cf470711aa7196a |
cat-searcher/leandojo-benchmark-4-random | test | 524 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.map_mul</a>, <a>Polynomial.map_cyclotomic_int</a>, <a>Polynomial.map_cyclotomic_int</a>, <a>Polynomial.map_expand</a>, <a>Polynomial.map_cyclotomic_int</a>] | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ map (Int.castRingHom ℚ) (cyclotomic (n * p) ℤ * cyclotomic n ℤ) ∣
map (Int.castRingHom ℚ) ((expand ℤ p) (cyclotomic n ℤ)) | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℚ * cyclotomic n ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":2358,"sourceStart":2356,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2360,"sourceStart":2359,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.map_mul",... | [] | [{"source":"Polynomial.map_mul","source_end":2378,"source_start":2360,"syntax_kind":"ident"},{"source":"map_cyclotomic_int","source_end":2398,"source_start":2380,"syntax_kind":"ident"},{"source":"map_cyclotomic_int","source_end":2418,"source_start":2400,"syntax_kind":"ident"},{"source":"map_expand","source_end":2430,"s... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 28 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 19e6ed1a613509fe28be91dab1dfe36a79295652a5c92587afe6c5eb422fac83 | 86048199b0cf1a24c9c14fd290d96385d503ffc93827a0194cf470711aa7196a | b9f4abbb332fa1dea493b910b74cb922658406abf77ed84b93cf74b254663a05 | 0d257a84c9d9c80db83a46e171871db15157e311521e8348e646db5b5cac33d4 |
cat-searcher/leandojo-benchmark-4-random | test | 525 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>IsCoprime.mul_dvd</a> (<a>Polynomial.cyclotomic.isCoprime_rat</a> fun h => ?_) ?_ ?_ | case inr.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℚ * cyclotomic n ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
h : n * p = n
⊢ False
case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyc... | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"refine","sourceEnd":2462,"sourceStart":2456,"tag":"atom"},{"children":[{"name":"IsCoprime.mul_dvd","semanticRole":"global","source":"IsCoprime.mul_dvd","sourceEnd":2480,"sourceStart":2463,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":2482,"sourceStart":2481,"tag":"atom"... | [] | [{"source":"IsCoprime.mul_dvd (cyclotomic.isCoprime_rat fun h => ?_) ?_ ?_","source_end":2525,"source_start":2463,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 35 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b180ba34444a26aa9b2346cf8ba4e2355e308209cc21b4dce5c90fa834706bec | 0d257a84c9d9c80db83a46e171871db15157e311521e8348e646db5b5cac33d4 | 944e255dab365e6d16bfb26075568db5e8f2036cd8262170ba55aca2de4d6e88 | 22054510c608809071879b66cbeffb5d4fe1a48c7a016aac5ef085690ae92f04 |
cat-searcher/leandojo-benchmark-4-random | test | 526 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace h : n * p = n * 1 := by simp [h] | case inr.refine_1.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
h : n * p = n
⊢ False | case inr.refine_1.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
h : n * p = n * 1
⊢ False | (:c False) | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:c False) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"replace","sourceEnd":2540,"sourceStart":2533,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h","sourceEnd":2542,"sourceStart":2541,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h","sourceEnd":2542,"sourceStart":2541,"tag":"node"},{... | [] | [{"source":"n * p = n * 1","source_end":2558,"source_start":2545,"syntax_kind":"«term_=_»"},{"source":"h","source_end":2572,"source_start":2571,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 40 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | efc18a355a2e322c3537886f0f6928636f43a313741714d9c0d83d5d3ef681b0 | 3d50faa59c4a90f69baafdadeae684a38d1cea925e808cc44ece1fcc53be03c3 | a6c067c0ae76a8b86514c0b5996adc3b02655f669558713a0fbb10ddfbd86194 | 272842050ec8b1a119ed296ac22b259e7e2998a6c943599b52a8fe23d184df34 |
cat-searcher/leandojo-benchmark-4-random | test | 527 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Nat.Prime.ne_one</a> hp (<a>mul_left_cancel₀</a> hnpos.ne' h) | case inr.refine_1.refine_1
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
h : n * p = n * 1
⊢ False | (:c False) | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:c False) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"exact","sourceEnd":2585,"sourceStart":2580,"tag":"atom"},{"children":[{"name":"Nat.Prime.ne_one","semanticRole":"global","source":"Nat.Prime.ne_one","sourceEnd":2602,"sourceStart":2586,"tag":"identifier"},{"children":[{"contextIndex":3,"semanticRole":"local","source":"hp","sourceEnd":2605,"sourc... | [] | [{"source":"Nat.Prime.ne_one hp (mul_left_cancel₀ hnpos.ne' h)","source_end":2638,"source_start":2586,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 43 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3e048a15910ce56ee7ca2dee5eec88ade2d6dc48fa12add7282e2fe814874e33 | 272842050ec8b1a119ed296ac22b259e7e2998a6c943599b52a8fe23d184df34 | 8c3364e61fc4ca52e350babb29c9a8c16a83467c20f3d88ab075f6b7d771a097 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 528 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
h : n * p = n
⊢ n * p = n * 1 | ((:c Eq) (:c Nat) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.454) (:fv _uniq.453)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.454) ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1))))) | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c HMul.hMul) (: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 HMul) (:arg :explicit 0 (:c Nat)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Nat))))) ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"simp","sourceEnd":2569,"sourceStart":2565,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2571,"sourceStart":2570,"tag":"atom"... | [] | [{"source":"h","source_end":2572,"source_start":2571,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 42 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01725984345e35eab3e7538a6f129b5ed3782a4a07b19283bb499e195e83f436 | a5afd3e114402b2d45b4e5db895262360d74abc9ba350364ec694c7112543ac7 | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 529 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hpos : 0 < n * p := <a>mul_pos</a> hnpos hp.pos | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"have","sourceEnd":2650,"sourceStart":2646,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hpos","sourceEnd":2655,"sourceStart":2651,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hpos","sourceEnd":2655,"sourceStart":2651,"tag":"node"... | [] | [{"source":"0 < n * p","source_end":2667,"source_start":2658,"syntax_kind":"«term_<_»"},{"source":"mul_pos hnpos hp.pos","source_end":2691,"source_start":2671,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 48 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 935fef35a75d1d6773dca3dc43a5e1a552444894acb43a4c97e18508e61ab3c2 | ada245cbb1ba6dfcab5e34174e6fcefd5621e61d05d5e58198b63838c0052334 | 41cff1a8a8810a0c5bf19538b71a86775682a5b8ac38f1767ab92e9d9b58fc12 | 257068b9f5750d744100bdca398da3ac5fb939fcb549ac611aeeda2c570907e4 |
cat-searcher/leandojo-benchmark-4-random | test | 530 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hprim := <a>Complex.isPrimitiveRoot_exp</a> _ hpos.ne' | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"have","sourceEnd":2702,"sourceStart":2698,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hprim","sourceEnd":2708,"sourceStart":2703,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hprim","sourceEnd":2708,"sourceStart":2703,"tag":"nod... | [] | [{"source":"Complex.isPrimitiveRoot_exp _ hpos.ne'","source_end":2750,"source_start":2712,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 49 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0cc7fe02bdce24168415c59249028f87fbfe7fcca96798b84799e1b271d67efa | 257068b9f5750d744100bdca398da3ac5fb939fcb549ac611aeeda2c570907e4 | 4a94287a9d52d0b3b6aceabc7268b0c2e07b2e15885997d1d8083cf8889b7f3f | 6896d3c18bbaaffac089c1ed41e03603bc13b980ffdb88f4024f944634c7084a |
cat-searcher/leandojo-benchmark-4-random | test | 531 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.cyclotomic_eq_minpoly_rat</a> hprim hpos] | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ cyclotomic (n * p) ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ minpoly ℚ (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) ∣ (expand ℚ p) (cyclotomic ... | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":2759,"sourceStart":2757,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2761,"sourceStart":2760,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Polynom... | [] | [{"source":"cyclotomic_eq_minpoly_rat hprim hpos","source_end":2797,"source_start":2761,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 50 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7639f3bd6f87a3bd33c52474e90885fc3f169c7ebf97667cfccb61289216103b | 6896d3c18bbaaffac089c1ed41e03603bc13b980ffdb88f4024f944634c7084a | d4fb4e619199e5d968ea5e06e606659a262ff7ddd3b028e2700f594c1282f8bc | 3310a07a61baaa6bdd84c0f2a467a7320821c24144699da981f80c37f07a47f8 |
cat-searcher/leandojo-benchmark-4-random | test | 532 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>minpoly.dvd</a> ℚ _ ?_ | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ minpoly ℚ (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) ∣ (expand ℚ p) (cyclotomic ... | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ (aeval (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p)))) ((expand ℚ p) (cyclotomic n ℚ... | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"refine","sourceEnd":2811,"sourceStart":2805,"tag":"atom"},{"children":[{"name":"minpoly.dvd","semanticRole":"global","source":"minpoly.dvd","sourceEnd":2823,"sourceStart":2812,"tag":"identifier"},{"children":[{"children":[{"source":"ℚ","sourceEnd":2827,"sourceStart":2824,"tag":"atom"}],"kind":"t... | [] | [{"source":"minpoly.dvd ℚ _ ?_","source_end":2832,"source_start":2812,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 53 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 38c082b158420fd5e5efb3ddda4373cf1d48a242ea62aa948a15af2ee3148dea | 3310a07a61baaa6bdd84c0f2a467a7320821c24144699da981f80c37f07a47f8 | 6f524bb80a1fbed777cc13a969a8befc27e845b04d89ae82b6dd348ac8e1b4ab | 2907875150d1e436d8c9d514e782238415ccd131a7b9fa2f38dea585e703d05d |
cat-searcher/leandojo-benchmark-4-random | test | 533 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.aeval_def</a>, ← <a>Polynomial.eval_map</a>, <a>Polynomial.map_expand</a>, <a>Polynomial.map_cyclotomic</a>, <a>Polynomial.expand_eval</a>, ← <a>Polynomial.IsRoot.def</a>, @<a>Polynomial.isRoot_cyclotomic_iff</a>] | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ (aeval (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p)))) ((expand ℚ p) (cyclotomic n ℚ... | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p)) ^ p) n | ((:c Eq) (:c Complex) ((:c DFunLike.coe) ((:c AlgHom) (:c Rat) ((:c Polynomial) (:c Rat) ((:c CommSemiring.toSemiring) (:c Rat) ((:c Semifield.toCommSemiring) (:c Rat) ((:c Field.toSemifield) (:c Rat) (:c Rat.instField))))) (:c Complex) ((:c Semifield.toCommSemiring) (:c Rat) ((:c Field.toSemifield) (:c Rat) (:c Rat.in... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:c Rat)) (:arg :explicit 1 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":2841,"sourceStart":2839,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":2843,"sourceStart":2842,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.aeval_def... | [] | [{"source":"aeval_def","source_end":2852,"source_start":2843,"syntax_kind":"ident"},{"source":"eval_map","source_end":2866,"source_start":2858,"syntax_kind":"ident"},{"source":"map_expand","source_end":2878,"source_start":2868,"syntax_kind":"ident"},{"source":"map_cyclotomic","source_end":2894,"source_start":2880,"synt... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 54 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0e2299cf62e35548e78285d6c1bb45b8c70a5f34ec7c2e7dc89c41bd3fb84adb | 2907875150d1e436d8c9d514e782238415ccd131a7b9fa2f38dea585e703d05d | e6c44ffb5f3005293f24e54ce93e3e4f6fee0b33a1fe47475ca851f364e51aeb | 14c1b98324514991bbc9c16c25d0b1a1ad893501e4cd5cac3f45ac28b8bdef58 |
cat-searcher/leandojo-benchmark-4-random | test | 534 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>IsPrimitiveRoot.pow_of_dvd</a> hprim hp.ne_zero (<a>dvd_mul_left</a> p n) | case inr.refine_1.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p)) ^ p) n | case h.e'_4
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ n = n * p / p | ((:c IsPrimitiveRoot) (:c Complex) ((:c CommRing.toCommMonoid) (:c Complex) (:c Complex.commRing)) ((:c HPow.hPow) (:c Complex) (:c Nat) (:c Complex) ((:c instHPow) (:c Complex) (:c Nat) ((:c Monoid.toNatPow) (:c Complex) ((:c MonoidWithZero.toMonoid) (:c Complex) ((:c Semiring.toMonoidWithZero) (:c Complex) ((:c CommS... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c IsPrimitiveRoot) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:i... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"convert","sourceEnd":2970,"sourceStart":2963,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"IsPrimitiveRoot.pow_of_dvd","semanticRole":"global","source":"IsPrimitiveRoot.pow_of_dvd","sourceEnd":299... | [] | [{"source":"IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)","source_end":3033,"source_start":2971,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 63 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e759d8be4c1756ad0b890c792dfd3dc298835e4a35aca4ed6717aa8d2d4687f | 14c1b98324514991bbc9c16c25d0b1a1ad893501e4cd5cac3f45ac28b8bdef58 | e02be194530387abf608ee44dcb99588a8173ed8791f05c87a6cc9f318187071 | c624e6a0bcedfb3395af69393129bbabd2310134982a667863c8193de50082c6 |
cat-searcher/leandojo-benchmark-4-random | test | 535 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.mul_div_cancel</a> _ (<a>Nat.Prime.pos</a> hp)] | case h.e'_4
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hpos : 0 < n * p
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑(n * p))) (n * p)
⊢ n = n * p / p | ((:c Eq) (:c Nat) (:fv _uniq.454) ((:c HDiv.hDiv) (:c Nat) (:c Nat) (:c Nat) ((:c instHDiv) (:c Nat) (:c Nat.instDiv)) ((:c HMul.hMul) (:c Nat) (:c Nat) (:c Nat) ((:c instHMul) (:c Nat) (:c instMulNat)) (:fv _uniq.454) (:fv _uniq.453)) (:fv _uniq.453))) | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:fv FV2)) (:arg :explicit 2 (: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":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":3042,"sourceStart":3040,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3044,"sourceStart":3043,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Nat.mul... | [] | [{"source":"Nat.mul_div_cancel _ (Nat.Prime.pos hp)","source_end":3083,"source_start":3044,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 64 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fadbfce23832d1a7194f30d6eae2be17be1a14f4e72d6ac4c5822b58b9f26ea3 | c624e6a0bcedfb3395af69393129bbabd2310134982a667863c8193de50082c6 | cdc74b3196e30557b01136fc2d9f1ee1148b751a61721e73370008449f096b1b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 536 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hprim := <a>Complex.isPrimitiveRoot_exp</a> _ hnpos.ne.symm | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ cyclotomic n ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ cyclotomic n ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"have","sourceEnd":3096,"sourceStart":3092,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hprim","sourceEnd":3102,"sourceStart":3097,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hprim","sourceEnd":3102,"sourceStart":3097,"tag":"nod... | [] | [{"source":"Complex.isPrimitiveRoot_exp _ hnpos.ne.symm","source_end":3149,"source_start":3106,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 71 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f925544ae0c346fbe9d89bf182e5061f153bd85fb94389dfc174efc29d8bf68a | b8642bd015ea90cad85cd2c572e979e2e685352b5e29da94e8f3f3aaaae114a7 | 13f5de1130a276ec3c4d7dacc4cd78c2b044e86697a7e52a059c8a032cdb6937 | b99ad596da876d7e94a916769cd42f073fc0a7316b5ad9c6ef0441935d4215d1 |
cat-searcher/leandojo-benchmark-4-random | test | 537 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.cyclotomic_eq_minpoly_rat</a> hprim hnpos] | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ cyclotomic n ℚ ∣ (expand ℚ p) (cyclotomic n ℚ) | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ minpoly ℚ (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) ∣
(expand ℚ p) (minpoly ℚ (Complex.exp (2 * ↑Real.pi * Com... | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":3158,"sourceStart":3156,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3160,"sourceStart":3159,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Polynom... | [] | [{"source":"cyclotomic_eq_minpoly_rat hprim hnpos","source_end":3197,"source_start":3160,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 72 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d8e7d84e4b014234a9a98695d77a13290cba277ccc6684047cf16317e5be20a9 | b99ad596da876d7e94a916769cd42f073fc0a7316b5ad9c6ef0441935d4215d1 | 98b51acd5040ec68098a9f1a83c490a97da6be48ca43693892c85b5aca3bf90e | cbf790da9d5c0d0e314c29a174f7d0e14abc08454cbcc9312859e02322bda285 |
cat-searcher/leandojo-benchmark-4-random | test | 538 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine <a>minpoly.dvd</a> ℚ _ ?_ | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ minpoly ℚ (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) ∣
(expand ℚ p) (minpoly ℚ (Complex.exp (2 * ↑Real.pi * Com... | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ (aeval (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)))
((expand ℚ p) (minpoly ℚ (Complex.exp (2 * ↑Real.pi * Comp... | ((:c Dvd.dvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c semigroupDvd) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c SemigroupWithZero.toSemigroup) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalSemiring.toSemigroupWithZero) ((:c Polynomial) (:c Rat) (:c Rat.semiring)) ((:c NonUnitalCommSemiring.... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Dvd.dvd) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg :instance 1 (:instance-of (:app (:c Dvd) (:arg :explicit 0 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"refine","sourceEnd":3211,"sourceStart":3205,"tag":"atom"},{"children":[{"name":"minpoly.dvd","semanticRole":"global","source":"minpoly.dvd","sourceEnd":3223,"sourceStart":3212,"tag":"identifier"},{"children":[{"children":[{"source":"ℚ","sourceEnd":3227,"sourceStart":3224,"tag":"atom"}],"kind":"t... | [] | [{"source":"minpoly.dvd ℚ _ ?_","source_end":3232,"source_start":3212,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 75 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2422aedd5627cb2ba4dbe83a3e9f2cf373e7d2df8991ec758cdee2523036efb | cbf790da9d5c0d0e314c29a174f7d0e14abc08454cbcc9312859e02322bda285 | 6f524bb80a1fbed777cc13a969a8befc27e845b04d89ae82b6dd348ac8e1b4ab | 0982c2a653c133d6832ff8aae6baa26b9e32e91d8afb7f8fa8d5ca7b1a83fd0d |
cat-searcher/leandojo-benchmark-4-random | test | 539 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.aeval_def</a>, ← <a>Polynomial.eval_map</a>, <a>Polynomial.map_expand</a>, <a>Polynomial.expand_eval</a>, ← <a>Polynomial.IsRoot.def</a>, ← <a>Polynomial.cyclotomic_eq_minpoly_rat</a> hprim hnpos, <a>Polynomial.map_cyclotomic</a>, @<a>Polynomial.isRoot_cyclotomic_iff</a>] | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ (aeval (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)))
((expand ℚ p) (minpoly ℚ (Complex.exp (2 * ↑Real.pi * Comp... | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n) ^ p) n | ((:c Eq) (:c Complex) ((:c DFunLike.coe) ((:c AlgHom) (:c Rat) ((:c Polynomial) (:c Rat) ((:c CommSemiring.toSemiring) (:c Rat) ((:c Semifield.toCommSemiring) (:c Rat) ((:c Field.toSemifield) (:c Rat) (:c Rat.instField))))) (:c Complex) ((:c Semifield.toCommSemiring) (:c Rat) ((:c Field.toSemifield) (:c Rat) (:c Rat.in... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c Eq) (:arg :implicit-type 0 (:c Complex)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c AlgHom) (:arg :explicit 0 (:c Rat)) (:arg :explicit 1 (:app (:c Polynomial) (:arg :explicit 0 (:c Rat)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Rat))))))) (:arg... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"rw","sourceEnd":3241,"sourceStart":3239,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3243,"sourceStart":3242,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.aeval_def... | [] | [{"source":"aeval_def","source_end":3252,"source_start":3243,"syntax_kind":"ident"},{"source":"eval_map","source_end":3266,"source_start":3258,"syntax_kind":"ident"},{"source":"map_expand","source_end":3278,"source_start":3268,"syntax_kind":"ident"},{"source":"expand_eval","source_end":3291,"source_start":3280,"syntax_... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 76 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f90fd142929eb48c2946fde9cfb8249aef70ff1fa148ec367df0ce4fc9eb7de | 0982c2a653c133d6832ff8aae6baa26b9e32e91d8afb7f8fa8d5ca7b1a83fd0d | de9e0a1e77e1327a1481d1c3bdf042c009c4058fc2f4459889b542d315eb4fa5 | f939966c676bb40a24260a4040198ff9ab00e3ebeb5848eb54954ad2d7494d91 |
cat-searcher/leandojo-benchmark-4-random | test | 540 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>IsPrimitiveRoot.pow_of_prime</a> hprim hp hdiv | case inr.refine_1.refine_3
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
hprim : IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)) n
⊢ IsPrimitiveRoot (Complex.exp (2 * ↑Real.pi * Complex.I / ↑n) ^ p) n | ((:c IsPrimitiveRoot) (:c Complex) ((:c CommRing.toCommMonoid) (:c Complex) (:c Complex.commRing)) ((:c HPow.hPow) (:c Complex) (:c Nat) (:c Complex) ((:c instHPow) (:c Complex) (:c Nat) ((:c Monoid.toNatPow) (:c Complex) ((:c MonoidWithZero.toMonoid) (:c Complex) ((:c Semiring.toMonoidWithZero) (:c Complex) ((:c CommS... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c IsPrimitiveRoot) (:arg :implicit-type 0 (:c Complex)) (:arg :instance 1 (:instance-of (:app (:c CommMonoid) (:arg :explicit 0 (:c Complex))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Complex)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Complex)) (:arg :instance 3 (:i... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"source":"exact","sourceEnd":3411,"sourceStart":3406,"tag":"atom"},{"children":[{"name":"IsPrimitiveRoot.pow_of_prime","semanticRole":"global","source":"IsPrimitiveRoot.pow_of_prime","sourceEnd":3440,"sourceStart":3412,"tag":"identifier"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"hpr... | [] | [{"source":"IsPrimitiveRoot.pow_of_prime hprim hp hdiv","source_end":3454,"source_start":3412,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 86 | exact | true | 1 | 9 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 296417923e29a547b93a00a24a397de2674a8b213fbf9dce41d20cb583544b19 | f939966c676bb40a24260a4040198ff9ab00e3ebeb5848eb54954ad2d7494d91 | ffb0d9215906a8b027d9d2ab38bbc43f6982a37e42db50a65e1d0946e80f0865 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 541 | Polynomial.cyclotomic_expand_eq_cyclotomic_mul | Mathlib/RingTheory/Polynomial/Cyclotomic/Expand.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Polynomial.natDegree_expand</a>, <a>Polynomial.natDegree_cyclotomic</a>, <a>Polynomial.natDegree_mul</a> (<a>Polynomial.cyclotomic_ne_zero</a> _ ℤ) (<a>Polynomial.cyclotomic_ne_zero</a> _ ℤ), <a>Polynomial.natDegree_cyclotomic</a>, <a>Polynomial.natDegree_cyclotomic</a>, <a>mul_comm</a> n, <a>Nat.totient_mul</a>... | case inr.refine_2
p n : ℕ
hp : Nat.Prime p
hdiv : ¬p ∣ n
R : Type u_1
inst✝ : CommRing R
hnpos : n > 0
this : NeZero n
⊢ ((expand ℤ p) (cyclotomic n ℤ)).natDegree ≤ (cyclotomic (n * p) ℤ * cyclotomic n ℤ).natDegree | ((:c LE.le) (:c Nat) (:c instLENat) ((:c Polynomial.natDegree) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) ((:c CommRing.toCommSemiring) (:c Int) (:c Int.instCommRing))) ((:c DFunLike.coe) ((:c AlgHom) (:c Int) ((:c Polynomial) (:c Int) ((:c CommSemiring.toSemiring) (:c Int) (:c Int.instCommSemiring))) ((:c Polynom... | [{"name":"p","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"hp","sexp":"((:c Nat.Prime) (:fv _uniq.453))"},{"name":"hdiv","sexp":"((:c Not) ((:c Dvd.dvd) (:c Nat) (:c Nat.instDvd) (:fv _uniq.453) (:fv _uniq.454)))"},{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c CommRing) (:fv _uniq.45... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:c Int)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:c Int))))) (:arg :explicit 2 (:app (:c... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"name":"p","sexp":"(:c Nat)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":3462,"sourceStart":3460,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":3464,"sourceStart":3463,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"natDegree_expand","source_end":3480,"source_start":3464,"syntax_kind":"ident"},{"source":"natDegree_cyclotomic","source_end":3502,"source_start":3482,"syntax_kind":"ident"},{"source":"natDegree_mul (cyclotomic_ne_zero _ ℤ) (cyclotomic_ne_zero _ ℤ)","source_end":3577,"source_start":3510,"syntax_kind":"Lean.P... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.453","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.454","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_uniq.4... | 3 | 89 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66790fa30b14762a5501b704370fd6b69ee53693b936b95adb4ebe3259ddeb01 | 09e70dea8e2ab2fc709f7fd171c485a654349dc5820870101f11d5564ea6241c | 866f349d2101f710fcdf0e88942514c96d989c27169e8b2dc4cda27fa2c41cf7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 542 | StrictAnti.prod_map | Mathlib/Order/Monotone/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Prod.lt_iff</a>] | ι : Type u_1
α : Type u
β : Type v
γ : Type w
δ : Type u_2
π : ι → Type u_3
r : α → α → Prop
inst✝³ : PartialOrder α
inst✝² : PartialOrder β
inst✝¹ : Preorder γ
inst✝ : Preorder δ
f : α → γ
g : β → δ
hf : StrictAnti f
hg : StrictAnti g
a b : α × β
⊢ a < b → Prod.map f g b < Prod.map f g a | ι : Type u_1
α : Type u
β : Type v
γ : Type w
δ : Type u_2
π : ι → Type u_3
r : α → α → Prop
inst✝³ : PartialOrder α
inst✝² : PartialOrder β
inst✝¹ : Preorder γ
inst✝ : Preorder δ
f : α → γ
g : β → δ
hf : StrictAnti f
hg : StrictAnti g
a b : α × β
⊢ a.1 < b.1 ∧ a.2 ≤ b.2 ∨ a.1 ≤ b.1 ∧ a.2 < b.2 →
(Prod.map f g b).1... | (:forall _ ((:c LT.lt) ((:c Prod) (:fv _uniq.48355) (:fv _uniq.48357)) ((:c Preorder.toLT) ((:c Prod) (:fv _uniq.48355) (:fv _uniq.48357)) ((:c Prod.instPreorder) (:fv _uniq.48355) (:fv _uniq.48357) ((:c PartialOrder.toPreorder) (:fv _uniq.48355) (:fv _uniq.48376)) ((:c PartialOrder.toPreorder) (:fv _uniq.48357) (:fv _... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.48353) (:sort (+ u_3 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.48355) (:fora... | (:forall _ :explicit (:app (:c LT.lt) (:arg :implicit-type 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2)))) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:app (:c Prod) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV2))))))) (:arg :explicit 2 (:fv FV16)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48353","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48355","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":52604,"sourceStart":52600,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":52609,"sourceStart":52605,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":526... | [] | [{"source":"Prod.lt_iff","source_end":52622,"source_start":52611,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48353","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48355","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 476 | 4 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 066594764ce2eb6c5b82c4af5a835f4dfd4d751ad605aa2c8e8d506c8d0a928b | 81e51d74cb897572e812c3aba54abfbcaf617d61b1234ed68ae08c481e585b8d | 387bd4fe175282164880fb72f6d3a443902a4dbc0d4a893a096d0b1bed5fd4a8 | f5cfb1fdd196fe45be38ea15d483a8186112b3fdfaef25a740977b66168d0a00 |
cat-searcher/leandojo-benchmark-4-random | test | 543 | StrictAnti.prod_map | Mathlib/Order/Monotone/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.imp</a> (<a>And.imp</a> hf.imp hg.antitone.imp) (<a>And.imp</a> hf.antitone.imp hg.imp) | ι : Type u_1
α : Type u
β : Type v
γ : Type w
δ : Type u_2
π : ι → Type u_3
r : α → α → Prop
inst✝³ : PartialOrder α
inst✝² : PartialOrder β
inst✝¹ : Preorder γ
inst✝ : Preorder δ
f : α → γ
g : β → δ
hf : StrictAnti f
hg : StrictAnti g
a b : α × β
⊢ a.1 < b.1 ∧ a.2 ≤ b.2 ∨ a.1 ≤ b.1 ∧ a.2 < b.2 →
(Prod.map f g b).1... | (:forall _ ((:c Or) ((:c And) ((:c LT.lt) (:fv _uniq.48355) ((:c Preorder.toLT) (:fv _uniq.48355) ((:c PartialOrder.toPreorder) (:fv _uniq.48355) (:fv _uniq.48376))) ((:c Prod.fst) (:fv _uniq.48355) (:fv _uniq.48357) (:fv _uniq.48571)) ((:c Prod.fst) (:fv _uniq.48355) (:fv _uniq.48357) (:fv _uniq.48574))) ((:c LE.le) (... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"γ","sexp":"(:sort (+ w 1))"},{"name":"δ","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.48353) (:sort (+ u_3 1)))"},{"name":"r","sexp":"(:forall _ (:fv _uniq.48355) (:fora... | (:forall _ :explicit (:app (:c Or) (:arg :explicit 0 (:app (:c And) (:arg :explicit 0 (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Prod.fst) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2))... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48353","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48355","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":52631,"sourceStart":52626,"tag":"atom"},{"children":[{"name":"Or.imp","semanticRole":"global","source":"Or.imp","sourceEnd":52638,"sourceStart":52632,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":52640,"sourceStart":52639,"tag":"atom"},{"children":[{"... | [] | [{"source":"Or.imp (And.imp hf.imp hg.antitone.imp) (And.imp hf.antitone.imp hg.imp)","source_end":52704,"source_start":52632,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.48353","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.48355","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 476 | 5 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e07e8cd236b3411a5b2c4b0484a1b8ae9da376c1b3902878d27cc73c21a41909 | f5cfb1fdd196fe45be38ea15d483a8186112b3fdfaef25a740977b66168d0a00 | fd4abef1ab8676681a55af33e270aa12ebef8649db6e9b59eb4282d51d54df84 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 544 | PiLp.norm_equiv_symm_const | Mathlib/Analysis/NormedSpace/PiLp.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | p : ℝ≥0∞
𝕜 : Type u_1
ι : Type u_2
α : ι → Type u_3
β✝ : ι → Type u_4
inst✝⁷ : Fact (1 ≤ p)
inst✝⁶ : Fintype ι
inst✝⁵ : Semiring 𝕜
inst✝⁴ : (i : ι) → SeminormedAddCommGroup (α i)
inst✝³ : (i : ι) → SeminormedAddCommGroup (β✝ i)
inst✝² : (i : ι) → Module 𝕜 (α i)
inst✝¹ : (i : ι) → Module 𝕜 (β✝ i)
c : 𝕜
β : Type u_5... | ((:c Eq) (:c Real) ((:c NNReal.toReal) ((:c HMul.hMul) (:c NNReal) (:c NNReal) (:c NNReal) ((:c instHMul) (:c NNReal) ((:c CanonicallyOrderedCommSemiring.toMul) (:c NNReal) (:c instNNRealCanonicallyOrderedCommSemiring))) ((:c HPow.hPow) (:c NNReal) (:c Real) (:c NNReal) ((:c instHPow) (:c NNReal) (:c Real) (:c NNReal.i... | [{"name":"p","sexp":"(:c ENNReal)"},{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"α","sexp":"(:forall _ (:fv _uniq.411360) (:sort (+ u_3 1)))"},{"name":"β✝","sexp":"(:forall _ (:fv _uniq.411360) (:sort (+ u_4 1)))"},{"name":"inst✝⁷","sexp":"((:c Fact) ((:c LE.le) (:c ENNReal)... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c NNReal.toReal) (:arg :explicit 0 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c NNReal)) (:arg :implicit-type 1 (:c NNReal)) (:arg :implicit-type 2 (:c NNReal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c NNReal)) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.411354","is_instance":false,"is_let":false,"name":"p","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.411357","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":implicit","... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":42801,"sourceStart":42797,"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.411354","is_instance":false,"is_let":false,"user_name":"p"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.411357","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":implicit","context_index":2,"internal_name":"... | 216 | 2 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fc9f48b01668063c890bb536126c638fc520b1eeb59e3fa174a9048deaf84a6 | 9a429e57913e661da5ebdc7d74a31b91086bcd69f0ac130c04f45572e40614c5 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 545 | Mathlib.Meta.NormNum.isInt_eq_false | Mathlib/Tactic/NormNum/Eq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | α : Type u_1
inst✝¹ : Ring α
inst✝ : CharZero α
n✝¹ n✝ : ℤ
h : decide (n✝¹ = n✝) = false
⊢ ¬↑n✝¹ = ↑n✝ | α : Type u_1
inst✝¹ : Ring α
inst✝ : CharZero α
n✝¹ n✝ : ℤ
h : decide (n✝¹ = n✝) = false
⊢ ¬n✝¹ = n✝ | ((:c Not) ((:c Eq) (:fv _uniq.842) ((:c Int.cast) (:fv _uniq.842) ((:c Ring.toIntCast) (:fv _uniq.842) (:fv _uniq.843)) (:fv _uniq.979)) ((:c Int.cast) (:fv _uniq.842) ((:c Ring.toIntCast) (:fv _uniq.842) (:fv _uniq.843)) (:fv _uniq.980)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.842))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.842) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.842) ((:c Ring.toAddGroupWithOne) (:fv _uniq.842) (:fv _uniq.843))))"},{"name":"n✝¹","sexp":"(:c Int)"},{"name":"n✝",... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c Int.cast) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c IntCast) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV4)))) (:arg :explicit 2 (:app (:c Int.cast) (:arg :implicit... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.842","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.843","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Ring) (:arg :explicit 0 (:f... | {"children":[{"source":"simp","sourceEnd":765,"sourceStart":761,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.842","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.843","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":3,"i... | 5 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4793147670cf6196f9791b704c320c8c5df3cd1e0908a5249c10e197a1d223d2 | 938279768450676266e64af5dd89dd8f429d5775502304e801b055e3b17c67f0 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | e25f4aa5ec80e1fa2466d7337157bd7bf352685c33e36913b6995907ca384dba |
cat-searcher/leandojo-benchmark-4-random | test | 546 | Mathlib.Meta.NormNum.isInt_eq_false | Mathlib/Tactic/NormNum/Eq.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>of_decide_eq_false</a> h | α : Type u_1
inst✝¹ : Ring α
inst✝ : CharZero α
n✝¹ n✝ : ℤ
h : decide (n✝¹ = n✝) = false
⊢ ¬n✝¹ = n✝ | ((:c Not) ((:c Eq) (:c Int) (:fv _uniq.979) (:fv _uniq.980))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Ring) (:fv _uniq.842))"},{"name":"inst✝","sexp":"((:c CharZero) (:fv _uniq.842) ((:c AddGroupWithOne.toAddMonoidWithOne) (:fv _uniq.842) ((:c Ring.toAddGroupWithOne) (:fv _uniq.842) (:fv _uniq.843))))"},{"name":"n✝¹","sexp":"(:c Int)"},{"name":"n✝",... | (:app (:c Not) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:fv FV4)) (:arg :explicit 2 (:fv FV5))))) | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.842","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.843","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Ring) (:arg :explicit 0 (:f... | {"children":[{"source":"exact","sourceEnd":772,"sourceStart":767,"tag":"atom"},{"children":[{"name":"of_decide_eq_false","semanticRole":"global","source":"of_decide_eq_false","sourceEnd":791,"sourceStart":773,"tag":"identifier"},{"children":[{"contextIndex":6,"semanticRole":"local","source":"h","sourceEnd":793,"sourceS... | [] | [{"source":"of_decide_eq_false h","source_end":793,"source_start":773,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.842","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":2,"internal_name":"_uniq.843","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index":3,"i... | 5 | 6 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d4594c7340ed5f6ce3934ed8f841ce94a3c7cb179761f951889802f97837edc | e25f4aa5ec80e1fa2466d7337157bd7bf352685c33e36913b6995907ca384dba | f2e0c815dcdab11a0c1bd6bd1417f488a40c37478b1e31c4a1627d481a1229a1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 547 | PosSMulReflectLT.of_pos | Mathlib/Algebra/Order/Module/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ha | ha := ha.eq_or_lt | α : Type u_1
β : Type u_2
a✝ a₁ a₂ : α
b b₁✝ b₂✝ : β
inst✝⁴ : Zero α
inst✝³ : Zero β
inst✝² : SMulWithZero α β
inst✝¹ : PartialOrder α
inst✝ : Preorder β
h₀ : ∀ (a : α), 0 < a → ∀ (b₁ b₂ : β), a • b₁ < a • b₂ → b₁ < b₂
a : α
ha : 0 ≤ a
b₁ b₂ : β
h : a • b₁ < a • b₂
⊢ b₁ < b₂ | case inl
α : Type u_1
β : Type u_2
a✝ a₁ a₂ : α
b b₁✝ b₂✝ : β
inst✝⁴ : Zero α
inst✝³ : Zero β
inst✝² : SMulWithZero α β
inst✝¹ : PartialOrder α
inst✝ : Preorder β
h₀ : ∀ (a : α), 0 < a → ∀ (b₁ b₂ : β), a • b₁ < a • b₂ → b₁ < b₂
a : α
ha✝ : 0 ≤ a
b₁ b₂ : β
h : a • b₁ < a • b₂
ha : 0 = a
⊢ b₁ < b₂
case inr
α : Type u_1
β... | ((:c LT.lt) (:fv _uniq.66865) ((:c Preorder.toLT) (:fv _uniq.66865) (:fv _uniq.66925)) (:fv _uniq.67304) (:fv _uniq.67307)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"a✝","sexp":"(:fv _uniq.66862)"},{"name":"a₁","sexp":"(:fv _uniq.66862)"},{"name":"a₂","sexp":"(:fv _uniq.66862)"},{"name":"b","sexp":"(:fv _uniq.66865)"},{"name":"b₁✝","sexp":"(:fv _uniq.66865)"},{"name":"b₂✝","sexp":"(:fv _uniq.6... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV17)) (:arg :explicit 3 (:fv FV18))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"obtain","sourceEnd":25610,"sourceStart":25604,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"ha","sourceEnd":25613,"sourceStart":25611,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"ha","sourceEnd":25613,"sourc... | [] | [{"source":"ha.eq_or_lt","source_end":25633,"source_start":25622,"syntax_kind":"ident"},{"source":"ha | ha","source_end":25618,"source_start":25611,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 157 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 26b0eafe04a2e53ed440a7db7d0c1cffd6c675c0599c22fb570480c11a5b81a0 | c17d4c27cdbcb91f954e18bf327de6d7b120bde9d394e1540a01d8460c398bc0 | 93c28276dd9dcbc9041cfff53f7cf21b68d30e4e6aaa16cbb13a80f9cffae219 | f1a8417ea5d007b2c10b4925b246d4e134c2a0ed6a06e404d3dc7f84dc203987 |
cat-searcher/leandojo-benchmark-4-random | test | 548 | PosSMulReflectLT.of_pos | Mathlib/Algebra/Order/Module/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [← ha] at h | case inl
α : Type u_1
β : Type u_2
a✝ a₁ a₂ : α
b b₁✝ b₂✝ : β
inst✝⁴ : Zero α
inst✝³ : Zero β
inst✝² : SMulWithZero α β
inst✝¹ : PartialOrder α
inst✝ : Preorder β
h₀ : ∀ (a : α), 0 < a → ∀ (b₁ b₂ : β), a • b₁ < a • b₂ → b₁ < b₂
a : α
ha✝ : 0 ≤ a
b₁ b₂ : β
h : a • b₁ < a • b₂
ha : 0 = a
⊢ b₁ < b₂ | ((:c LT.lt) (:fv _uniq.66865) ((:c Preorder.toLT) (:fv _uniq.66865) (:fv _uniq.66925)) (:fv _uniq.67304) (:fv _uniq.67307)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"a✝","sexp":"(:fv _uniq.66862)"},{"name":"a₁","sexp":"(:fv _uniq.66862)"},{"name":"a₂","sexp":"(:fv _uniq.66862)"},{"name":"b","sexp":"(:fv _uniq.66865)"},{"name":"b₁✝","sexp":"(:fv _uniq.66865)"},{"name":"b₂✝","sexp":"(:fv _uniq.6... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV17)) (:arg :explicit 3 (:fv FV18))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":25645,"sourceStart":25641,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"ha","source_end":25653,"source_start":25651,"syntax_kind":"ident"},{"source":"h","source_end":25659,"source_start":25658,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 157 | 7 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b4894ebc57f0031f9bca8aa7015c058837b943303d447e608c0d6bfb14cb627d | eb294b5c7db2d4b9da5f52d0ce59c6863403e2e5219f88433a84d4fba797119f | 025bcaed3e7e406e8a39d4890c0462d7194d1ecb33db4e3bcd3a124a62da011a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 549 | PosSMulReflectLT.of_pos | Mathlib/Algebra/Order/Module/Defs.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h₀ _ ha _ _ h | case inr
α : Type u_1
β : Type u_2
a✝ a₁ a₂ : α
b b₁✝ b₂✝ : β
inst✝⁴ : Zero α
inst✝³ : Zero β
inst✝² : SMulWithZero α β
inst✝¹ : PartialOrder α
inst✝ : Preorder β
h₀ : ∀ (a : α), 0 < a → ∀ (b₁ b₂ : β), a • b₁ < a • b₂ → b₁ < b₂
a : α
ha✝ : 0 ≤ a
b₁ b₂ : β
h : a • b₁ < a • b₂
ha : 0 < a
⊢ b₁ < b₂ | ((:c LT.lt) (:fv _uniq.66865) ((:c Preorder.toLT) (:fv _uniq.66865) (:fv _uniq.66925)) (:fv _uniq.67304) (:fv _uniq.67307)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"a✝","sexp":"(:fv _uniq.66862)"},{"name":"a₁","sexp":"(:fv _uniq.66862)"},{"name":"a₂","sexp":"(:fv _uniq.66862)"},{"name":"b","sexp":"(:fv _uniq.66865)"},{"name":"b₁✝","sexp":"(:fv _uniq.66865)"},{"name":"b₂✝","sexp":"(:fv _uniq.6... | (:app (:c LT.lt) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:fv FV17)) (:arg :explicit 3 (:fv FV18))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":25672,"sourceStart":25667,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"h₀","sourceEnd":25677,"sourceStart":25673,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":25679,"sourceStart"... | [] | [{"source":"h₀ _ ha _ _ h","source_end":25688,"source_start":25673,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.66862","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.66865","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 157 | 12 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fdff33c34d3a3f9d8ce5107d6f0e07b0d7b6435042fdd73fe16e7be18a09f831 | 7e3b746320fa470755862ae2472a57842f2c64e50244ec71699bd36d257a499b | 91b9b021c66a7a8903e334f1472823e8ae967a1de4dc7854851a45d62701feb2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 550 | toIcoDiv_add_left | Mathlib/Algebra/Order/ToIntervalMod.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>add_comm</a>, <a>toIcoDiv_add_right</a>] | α : Type u_1
inst✝ : LinearOrderedAddCommGroup α
hα : Archimedean α
p : α
hp : 0 < p
a✝ b✝ c : α
n : ℤ
a b : α
⊢ toIcoDiv hp a (p + b) = toIcoDiv hp a b + 1 | ((:c Eq) (:c Int) ((:c toIcoDiv) (:fv _uniq.134526) (:fv _uniq.134529) (:fv _uniq.134696) (:fv _uniq.134698) (:fv _uniq.135346) (:fv _uniq.136167) ((:c HAdd.hAdd) (:fv _uniq.134526) (:fv _uniq.134526) (:fv _uniq.134526) ((:c instHAdd) (:fv _uniq.134526) ((:c AddCommMagma.toAdd) (:fv _uniq.134526) ((:c AddCommSemigroup.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝","sexp":"((:c LinearOrderedAddCommGroup) (:fv _uniq.134526))"},{"name":"hα","sexp":"((:c Archimedean) (:fv _uniq.134526) ((:c LinearOrderedAddCommMonoid.toOrderedAddCommMonoid) (:fv _uniq.134526) ((:c LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Int)) (:arg :explicit 1 (:app (:c toIcoDiv) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LinearOrderedAddCommGroup) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c Archimedean) (:arg :explicit 0 (:fv FV0)) (:arg :instance ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.134526","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134529","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c LinearOrderedAddCommGr... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":12630,"sourceStart":12628,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":12632,"sourceStart":12631,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"add_comm","source_end":12640,"source_start":12632,"syntax_kind":"ident"},{"source":"toIcoDiv_add_right","source_end":12660,"source_start":12642,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.134526","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.134529","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":instance-implicit","context_index"... | 109 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 99c5077cd3587f0e44f3ca1b484dc624e6cde680f2e8f5fb49d5e94cf4a4dcb0 | ecfd3c5a30926a9cbd494c2053a053d9cf0557f1776bd59d7ce685ecb67eb5ca | c9ae7a73dd681003ca79adc377c511bf7784eba2e0eae5e8fd736bc4dca9437c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 551 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro b hb | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
⊢ GrowsPolynomially f | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | ((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437916)) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c AkraBazziRecurrence.GrowsPolynomially) (:arg :explicit 0 (:fv FV2))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"intro","sourceEnd":29926,"sourceStart":29921,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"b","sourceEnd":29928,"sourceStart":29927,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hb","sourceEnd":29931,"sourceStart":29929,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"b","source_end":29928,"source_start":29927,"syntax_kind":"ident"},{"role":"fresh_name","source":"hb","source_end":29931,"source_start":29929,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 4 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e386ef239fa84c52cd6a1b4bd3940fb21353f1c587003fcf5c691a9786f8f984 | a6a6fd8a037e49577c80e0a09da9bd1d25689354c00263c133c513556d68c1e5 | 2da7d8a2d234f34d6eefcdb206321e10a59f20aa70d4e73cedddb133aa95b27d | 8db30ff052661a9ac7498817c549b70c1d8bfa9946591781b89f44ebc8a309ca |
cat-searcher/leandojo-benchmark-4-random | test | 552 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hb_pos := hb.1 | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":29938,"sourceStart":29934,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hb_pos","sourceEnd":29945,"sourceStart":29939,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hb_pos","sourceEnd":29945,"sourceStart":29939,"t... | [] | [{"source":"hb.1","source_end":29953,"source_start":29949,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 5 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c544e6669ae839deab7c579857466942861bc913c52675255e7f7cbf4186876f | 8db30ff052661a9ac7498817c549b70c1d8bfa9946591781b89f44ebc8a309ca | 116496fe005752f52d17b428bfedd54c1f1e9bedc2709aba6ac8212c7ab78063 | 21ff7fac8d65092a68037b500665e1cd264a41f5b645ac03fb5f73db740a1788 |
cat-searcher/leandojo-benchmark-4-random | test | 553 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hf_lb := isBigO_iff''.mp hf.isBigO_symm | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_lb : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, c * ‖g x‖ ≤ ‖f x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":29960,"sourceStart":29956,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf_lb","sourceEnd":29966,"sourceStart":29961,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf_lb","sourceEnd":29966,"sourceStart":29961,"tag... | [] | [{"source":"isBigO_iff''.mp hf.isBigO_symm","source_end":30000,"source_start":29970,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 6 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db74b63de4742883cdcb1373a8ac96ee8f132b0568e76358a46aba87cc52d343 | 21ff7fac8d65092a68037b500665e1cd264a41f5b645ac03fb5f73db740a1788 | 8335fe49c7bca79a94d3aca18e51ec9096ec6d518779b4dd12178f510f0fa0f7 | 5d7741314824bfc68bc1ad419b88fde4c0abf98ac643f2b8988eb67965ba0d82 |
cat-searcher/leandojo-benchmark-4-random | test | 554 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hf_ub := isBigO_iff'.mp hf.isBigO | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_lb : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, c * ‖g x‖ ≤ ‖f x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x) | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_lb : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, c * ‖g x‖ ≤ ‖f x‖
hf_ub : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c * ‖g x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30007,"sourceStart":30003,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hf_ub","sourceEnd":30013,"sourceStart":30008,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hf_ub","sourceEnd":30013,"sourceStart":30008,"tag... | [] | [{"source":"isBigO_iff'.mp hf.isBigO","source_end":30041,"source_start":30017,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 7 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 37e626bd5b396eeab999ae3206e4f78b04d40e5dbafd67559713e47e63c56373 | 5d7741314824bfc68bc1ad419b88fde4c0abf98ac643f2b8988eb67965ba0d82 | 4f611304b860aa213bbe086631aa3943afbbc4f9ac74d75e80519aba3586f9d6 | 8756f245988b653b13a7a38be2864bb7320b4494cf0bfe53d3b46fe9909fd7ae |
cat-searcher/leandojo-benchmark-4-random | test | 555 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₁, hc₁_pos : 0 < c₁, hf_lb⟩ := hf_lb | f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_lb : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, c * ‖g x‖ ≤ ‖f x‖
hf_ub : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c * ‖g x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ... | case intro.intro
f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_ub : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c * ‖g x‖
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atT... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"obtain","sourceEnd":30050,"sourceStart":30044,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":30054,"sourceStart":30051,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₁","sourceE... | [] | [{"source":"hf_lb","source_end":30099,"source_start":30094,"syntax_kind":"ident"},{"source":"⟨c₁, hc₁_pos : 0 < c₁, hf_lb⟩","source_end":30090,"source_start":30051,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 8 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8079fc546c569bdea1d592682d68417408cf9eb41f126d76787277680c5d091a | 8756f245988b653b13a7a38be2864bb7320b4494cf0bfe53d3b46fe9909fd7ae | accfcb6d8485ad1aaa08712c9f3426b2f1e11f86238a10d19c3ba23cdb70da1b | d0a5067318a9ef4a50af350ddb1fedb71e92880d9a2bbfd1507dddb15b0409e8 |
cat-searcher/leandojo-benchmark-4-random | test | 556 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₂, hc₂_pos : 0 < c₂, hf_ub⟩ := hf_ub | case intro.intro
f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
hf_ub : ∃ c > 0, ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c * ‖g x‖
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
⊢ ∃ c₁ > 0, ∃ c₂ > 0, ∀ᶠ (x : ℝ) in atT... | case intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
⊢ ∃ c₁ > 0,... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"obtain","sourceEnd":30108,"sourceStart":30102,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":30112,"sourceStart":30109,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₂","sourceE... | [] | [{"source":"hf_ub","source_end":30157,"source_start":30152,"syntax_kind":"ident"},{"source":"⟨c₂, hc₂_pos : 0 < c₂, hf_ub⟩","source_end":30148,"source_start":30109,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 9 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7738de13b6f183f52706660a06442d5d0f4892d43f5b0f682eebed8c996485b0 | d0a5067318a9ef4a50af350ddb1fedb71e92880d9a2bbfd1507dddb15b0409e8 | 62e6c0fda6cc71b408e561b4b8da2a752e5ae4b3349a1edf2d18bac58992b88c | 94146f8eecd24b1aa7a18dd6be92746d1ba325c0596ebfe49a0f619b1559f689 |
cat-searcher/leandojo-benchmark-4-random | test | 557 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hg := hg.norm b hb | case intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
⊢ ∃ c₁ > 0,... | case intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
hg :
∃ c... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (:... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30164,"sourceStart":30160,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hg","sourceEnd":30167,"sourceStart":30165,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hg","sourceEnd":30167,"sourceStart":30165,"tag":"nod... | [] | [{"source":"hg.norm b hb","source_end":30183,"source_start":30171,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 10 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 95188d18293ebe0407a9ec694b870994aa2a5279ff4cedb74b39fc6108cbe5e5 | 94146f8eecd24b1aa7a18dd6be92746d1ba325c0596ebfe49a0f619b1559f689 | 7f55cf270537ef71094805b2ca3830a15fb187f78fad3d425f1b279e9fb8f12a | aba61506299229cf34f779e63bbe72c719d049e445f4b7df8fcbe838a5f99f72 |
cat-searcher/leandojo-benchmark-4-random | test | 558 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₃, hc₃_pos : 0 < c₃, hg⟩ := hg | case intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
hg :
∃ c... | case intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"obtain","sourceEnd":30192,"sourceStart":30186,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":30196,"sourceStart":30193,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₃","sourceE... | [] | [{"source":"hg","source_end":30235,"source_start":30233,"syntax_kind":"ident"},{"source":"⟨c₃, hc₃_pos : 0 < c₃, hg⟩","source_end":30229,"source_start":30193,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 11 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff162a8b8ed8b9197ae10a0e3453b17efc612555b0993ccb26eddf079f0c3a80 | aba61506299229cf34f779e63bbe72c719d049e445f4b7df8fcbe838a5f99f72 | b2c9319215fd6c6091ca358121de8a0d2c5ebd5c98fe58ed47ade9dbe146b27f | 1a5b057495e3d6c9846dfe92d1439a11370baff64bb7a6b92dd215791255ae68 |
cat-searcher/leandojo-benchmark-4-random | test | 559 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨c₄, hc₄_pos : 0 < c₄, hg⟩ := hg | case intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"obtain","sourceEnd":30244,"sourceStart":30238,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":30248,"sourceStart":30245,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₄","sourceE... | [] | [{"source":"hg","source_end":30287,"source_start":30285,"syntax_kind":"ident"},{"source":"⟨c₄, hc₄_pos : 0 < c₄, hg⟩","source_end":30281,"source_start":30245,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 12 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3caa4643b6cc693df2ac673294099ed600080e2c404a9807c1aca2869e2e58c3 | 1a5b057495e3d6c9846dfe92d1439a11370baff64bb7a6b92dd215791255ae68 | ffea9732e8a59c52146407b7849819244727831b81cb2bc1e7a48e66b10381e1 | 99a91250302289b44bda4364c8818dea3d0307f1253efb0affc6974627f31c33 |
cat-searcher/leandojo-benchmark-4-random | test | 560 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_lb_pos : 0 < c₁ * c₂⁻¹ * c₃ := by positivity | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30294,"sourceStart":30290,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_lb_pos","sourceEnd":30303,"sourceStart":30295,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_lb_pos","sourceEnd":30303,"sourceStart":3029... | [] | [{"source":"0 < c₁ * c₂⁻¹ * c₃","source_end":30333,"source_start":30306,"syntax_kind":"«term_<_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 13 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0916df5842dee3f43441ca150610070e5cf11a545f2fd0c04488f474892718b3 | 99a91250302289b44bda4364c8818dea3d0307f1253efb0affc6974627f31c33 | 7706ff3b18521bc7b7b4d269218ceb779d649a197706070d99536819f0cb0149 | 9428cf32b20862df564a654aeff5a7426d4d665c0bd752ca1621c9651b7f0524 |
cat-searcher/leandojo-benchmark-4-random | test | 561 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h_ub_pos : 0 < c₂ * c₄ * c₁⁻¹ := by positivity | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30357,"sourceStart":30353,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h_ub_pos","sourceEnd":30366,"sourceStart":30358,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h_ub_pos","sourceEnd":30366,"sourceStart":3035... | [] | [{"source":"0 < c₂ * c₄ * c₁⁻¹","source_end":30396,"source_start":30369,"syntax_kind":"«term_<_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 16 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5e63733240058b5f10071791f9438c4b63c3354d465f6f9a1ce3ed32e5f0c84f | 9428cf32b20862df564a654aeff5a7426d4d665c0bd752ca1621c9651b7f0524 | c6b35cd308ba311e754861e8f34d02335362dbd7e20d1d28c096dfae9a03e0a3 | ec9073718f90a6138cf26b5da53256608dad31cf9e4d9d34d2b8f88f2cbe5107 |
cat-searcher/leandojo-benchmark-4-random | test | 562 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨c₁ * c₂⁻¹ * c₃, h_lb_pos, ?_⟩ | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Exists) (:c Real) (:lambda c₁ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₁ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"refine","sourceEnd":30422,"sourceStart":30416,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":30426,"sourceStart":30423,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"c₁","sourceEnd":30430,"sourceStart":30426,"tag":"identifier"},{"so... | [] | [{"source":"⟨c₁ * c₂⁻¹ * c₃, h_lb_pos, ?_⟩","source_end":30466,"source_start":30423,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 19 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d7641d05a7b550c5fb252d35fbda4b4be59543e0cc54736af72d36faaff8f050 | ec9073718f90a6138cf26b5da53256608dad31cf9e4d9d34d2b8f88f2cbe5107 | 0a9e3219846b92eb81beda39fc1adffbb3c458d3ac3d684e96460a8963a70552 | f2ef351e141466eb8fd0aca5aca836737e9ac451130374bc61943b71a6b31618 |
cat-searcher/leandojo-benchmark-4-random | test | 563 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨c₂ * c₄ * c₁⁻¹, h_ub_pos, ?_⟩ | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Exists) (:c Real) (:lambda c₂ (:c Real) ((:c And) ((:c GT.gt) (:c Real) (:c Real.instLT) 0 ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) (:forall u (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Rea... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Exists) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda c₂ :explicit (:c Real) (:app (:c And) (:arg :explicit 0 (:app (:c GT.gt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"refine","sourceEnd":30475,"sourceStart":30469,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":30479,"sourceStart":30476,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":13,"semanticRole":"local","source":"c₂","sourceEnd":30483,"sourceStart":30479,"tag":"identifier"},{"so... | [] | [{"source":"⟨c₂ * c₄ * c₁⁻¹, h_ub_pos, ?_⟩","source_end":30519,"source_start":30476,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 20 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd341d099de2e01d23b32c663cc5168f35f017d9027d637826ab229dd9d25403 | f2ef351e141466eb8fd0aca5aca836737e9ac451130374bc61943b71a6b31618 | 940b449eb7c0f6dc141c1c29e0c4a4100501ac55a141ee68eae92c3e378733a9 | 4129095d4f0827dd0fcb7e4acd4b79c5e5e8a258c71d22642be69b3a03cd73ca |
cat-searcher/leandojo-benchmark-4-random | test | 564 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have c₂_cancel : c₂⁻¹ * c₂ = 1 := <a>inv_mul_cancel</a> (by positivity) | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) (:forall u (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:forall u :explicit (:c Real) (:forall _ :explicit (: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 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30526,"sourceStart":30522,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₂_cancel","sourceEnd":30538,"sourceStart":30527,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"c₂_cancel","sourceEnd":30538,"sourceStart":30... | [] | [{"source":"c₂⁻¹ * c₂ = 1","source_end":30561,"source_start":30541,"syntax_kind":"«term_=_»"},{"source":"inv_mul_cancel (by positivity)","source_end":30595,"source_start":30565,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 21 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f97a6d0c893fd4bdbdc44b1e9a52f87745a491c112d60fef1dc19568ec87dd06 | 4129095d4f0827dd0fcb7e4acd4b79c5e5e8a258c71d22642be69b3a03cd73ca | 877999cf9b613110e2e8416f2986ed459081b590e2a3469e4d557817260ed7cd | ce4d8772a21c9e50aa8c9a83ad7628a32fdd6c749fd68ff2f9230474c8c8f4c9 |
cat-searcher/leandojo-benchmark-4-random | test | 565 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have c₁_cancel : c₁⁻¹ * c₁ = 1 := <a>inv_mul_cancel</a> (by positivity) | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) (:forall u (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:forall u :explicit (:c Real) (:forall _ :explicit (: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 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":30602,"sourceStart":30598,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"c₁_cancel","sourceEnd":30614,"sourceStart":30603,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"c₁_cancel","sourceEnd":30614,"sourceStart":30... | [] | [{"source":"c₁⁻¹ * c₁ = 1","source_end":30637,"source_start":30617,"syntax_kind":"«term_=_»"},{"source":"inv_mul_cancel (by positivity)","source_end":30671,"source_start":30641,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 27 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 05167179912288465430dc926e7e0182df10a2ab196fee4665d3c12d0f881dad | ce4d8772a21c9e50aa8c9a83ad7628a32fdd6c749fd68ff2f9230474c8c8f4c9 | 7859c13fff1b4c1d2520f1be3dc9bf66e34af86ee4bf0e998c924d558c9d851c | 4d062916d369c0e5c2dcd5a7bd8fdb6c9ef25512e5eaac9d170e016772a8ed0f |
cat-searcher/leandojo-benchmark-4-random | test | 566 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [(tendsto_id.const_mul_atTop hb_pos).<a>Filter.Tendsto.eventually_forall_ge_atTop</a> hf', (tendsto_id.const_mul_atTop hb_pos).<a>Filter.Tendsto.eventually_forall_ge_atTop</a> hf_lb, (tendsto_id.const_mul_atTop hb_pos).<a>Filter.Tendsto.eventually_forall_ge_atTop</a> hf_ub, (tendsto_id.const_mul_atTop hb... | case intro.intro.intro.intro.intro.intro.intro.intro
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) (:forall u (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:forall u :explicit (:c Real) (:forall _ :explicit (: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 (:instanc... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"filter_upwards","sourceEnd":30688,"sourceStart":30674,"tag":"atom"},{"children":[{"source":"[","sourceEnd":30690,"sourceStart":30689,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":30691,"sourceStart":30690,"tag":"atom"},{"children":[{"source":"tendsto... | [] | [{"source":"eventually_ge_atTop 0","source_end":31058,"source_start":31037,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(tendsto_id.const_mul_atTop hb_pos).eventually_forall_ge_atTop hg","source_end":31017,"source_start":30952,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(tendsto_id.const_mul_atTop hb_pos).even... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 33 | exact | true | 1 | 24 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9cbc89e131d809951d553f528befb45be7d0bd3f1629b1ca3953988e452c6c2c | 4d062916d369c0e5c2dcd5a7bd8fdb6c9ef25512e5eaac9d170e016772a8ed0f | be3dad3a91b5c678cfe8e6956a88a1c7213a77a5d6deefdf1b40acb850adf0eb | 2ed537e660b1682d212dbf515e164f81079309c4cd51fb734647f0c910256d69 |
cat-searcher/leandojo-benchmark-4-random | test | 567 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro u hu | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | (:forall u (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.437922) (:fv _uniq.453578)) (:fv _uniq.453578))) (... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:forall u :explicit (:c Real) (:forall _ :explicit (: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 R... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"intro","sourceEnd":31111,"sourceStart":31106,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":31113,"sourceStart":31112,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hu","sourceEnd":31116,"sourceStart":31114,"tag":"identifier"}],"kind":"null","sou... | [{"role":"fresh_name","source":"u","source_end":31113,"source_start":31112,"syntax_kind":"ident"},{"role":"fresh_name","source":"hu","source_end":31116,"source_start":31114,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 34 | exact | true | 1 | 30 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 79383b6272454310a9e64d8a183756f8f34c332409c2f7819b8dd46f3d4fd038 | 2ed537e660b1682d212dbf515e164f81079309c4cd51fb734647f0c910256d69 | b8632d84cb3204281b54ed03e19e0fb16735bff44caee18112f30d2377109c86 | 921523cfb40901a317d1418b214e865afbd9723213487e59c66a7e83e71b4b15 |
cat-searcher/leandojo-benchmark-4-random | test | 568 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hbx : b * x ≤ x := calc b * x ≤ 1 * x := by gcongr; exact <a>le_of_lt</a> hb.2 _ = x := by rw [<a>one_mul</a>] | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:fv _uniq.437916) (:fv _uniq.453606)) ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((: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) ((:c inst... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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 (:fv FV2) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":31123,"sourceStart":31119,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hbx","sourceEnd":31127,"sourceStart":31124,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hbx","sourceEnd":31127,"sourceStart":31124,"tag":"n... | [] | [{"source":"b * x ≤ x","source_end":31141,"source_start":31130,"syntax_kind":"«term_≤_»"},{"source":"calc b * x ≤ 1 * x := by gcongr; exact le_of_lt hb.2\n _ = x := by rw [one_mul]","source_end":31251,"source_start":31149,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 35 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0ec038e608452c7c8fa9fdfb7c3d9dd6d29974d1e7d6fb2a24601888baf5fcab | 921523cfb40901a317d1418b214e865afbd9723213487e59c66a7e83e71b4b15 | 1fea12fee0bcd5c0cbfc843d4a7f208ca03a47bb0f767d2c0082e30b94baf3de | 70c3d72e1ea2d7acb345496487bd9988af50c1f251622b17799fc95c75333bc4 |
cat-searcher/leandojo-benchmark-4-random | test | 569 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hg_bound := hg_bound x hbx | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:fv _uniq.437916) (:fv _uniq.453606)) ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((: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) ((:c inst... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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 (:fv FV2) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"have","sourceEnd":31258,"sourceStart":31254,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hg_bound","sourceEnd":31267,"sourceStart":31259,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hg_bound","sourceEnd":31267,"sourceStart":3125... | [] | [{"source":"hg_bound x hbx","source_end":31285,"source_start":31271,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 50 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4afb53ab462ce1b764eea191c76ce73a0fe791ffdc5da33b0ae62697ba2aadc3 | 70c3d72e1ea2d7acb345496487bd9988af50c1f251622b17799fc95c75333bc4 | 4f3ce02dff3f99747567393218b223c53cc155692193a4a3e33166ff3fd0b981 | 21cad95dd1aa12334c159f49698f7f621caef7fe104048217efe54f1d3b3c97e |
cat-searcher/leandojo-benchmark-4-random | test | 570 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?lb, ?ub⟩ | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | case lb
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:fv _uniq.437916) (:fv _uniq.453606)) ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((: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) ((:c inst... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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 (:fv FV2) (:arg :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"refine","sourceEnd":31294,"sourceStart":31288,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":31298,"sourceStart":31295,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":31299,"sourceStart":31298,"tag":"atom"},{"source":"lb","sourceEnd":31301,"sourceStart":31299,"tag":"ident... | [] | [{"source":"⟨?lb, ?ub⟩","source_end":31309,"source_start":31295,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 51 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0b662c449f6901635c1ede640e48c729235ec53f4701d8fd89fd31590147deea | 21cad95dd1aa12334c159f49698f7f621caef7fe104048217efe54f1d3b3c97e | 00a7985cb2f9fea5872be9f4b660a4950d2a11c3977b014086e1bbab97881969 | 8d82b21e8d80e743ea149f724583f1b4ed1d79491e5c162bef6bbcab0471af6e |
cat-searcher/leandojo-benchmark-4-random | test | 572 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | case ub => calc f u ≤ c₂ * ‖g u‖ := by rw [← <a>Real.norm_of_nonneg</a> (hf_pos u hu.1)]; exact h_ub u hu.1 _ ≤ c₂ * (c₄ * ‖g x‖) := by gcongr; exact (hg_bound u hu).2 _ = c₂ * c₄ * (c₁⁻¹ * c₁) * ‖g x‖ := by simp [c₁_cancel]; ring _ = c₂ * c₄ * c₁⁻¹ * (c₁ * ‖g x‖) := by ring _ ≤ c₂ * c₄ * c₁⁻¹ * f x := by gcongr rw [← ... | case ub
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:fv _uniq.437916) (:fv _uniq.453606)) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 (:fv FV2) (:arg :explicit 0 (:fv FV31)))) (:arg :explicit 3 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"case","sourceEnd":31804,"sourceStart":31800,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"ub","sourceEnd":31807,"sourceStart":31805,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"ub","sourceEnd":31807,"sourceStart":31805,"tag":"node"},{"children":[],"kind":"null","sou... | [] | [{"source":"f u ≤ c₂ * ‖g u‖","source_end":31844,"source_start":31820,"syntax_kind":"«term_≤_»"},{"source":"Real.norm_of_nonneg (hf_pos u hu.1)","source_end":31894,"source_start":31859,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h_ub u hu.1","source_end":31914,"source_start":31903,"syntax_kind":"Lean.Parser.Term.a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 93 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77ab584754a710830a026c9c856e1d44f7e60a46ce03d47a0f7278ed1d8525ed | d04f3415ceb21905437ea221b54a3946e62cf8f2863edfd6fef786b411755f0e | 64c72bb170f3ffd73d7af1dbfb616f989a99c36d08e9fe8477a5b6ea304ad96a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 573 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.43... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"positivity","sourceEnd":30350,"sourceStart":30340,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":30350,"sourceStart":30340,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 15 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42956d82b234f42add285e3c288cf107fa3b812597e611195a2291daad9fde71 | 0cd49fa15fb4311be3b86bf0ca7c68e1c81f1d8e9fa15e6935c1881cdc50f92b | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 574 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.43... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"positivity","sourceEnd":30413,"sourceStart":30403,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":30413,"sourceStart":30403,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 18 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc4055cda69618e1277953d3ca2a4d8d906b2219bfb76e436729a4990fe6caad | 4ee4271fabf2883a0c4e4f26525de69a123c096ef87bb84ca2cbcc89a10bc588 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 575 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Ne) (:c Real) (:fv _uniq.438336) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MonoidWithZero.toZero) (:c Real) ((:c GroupWithZero.toMonoidWithZero) (:c Real) ((:c DivisionSemiring.toGroupWithZero) (:c Real) ((:c Semifield.toDivisionSemiring) (:c Real) ((:c LinearOrderedSemifield.toSemifi... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:fv FV13)) (: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 :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":30594,"sourceStart":30584,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":30594,"sourceStart":30584,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":30594,"sourceStart":305... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 24 | exact | true | 1 | 22 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b3c99e36588194cb41b51e304afe2e354791a6ab374c71379b7fea6502fce7c8 | 36790a303e69f220f7528ba328d3fdd7d6d5fc9b48fe6bf82c6ccef7ab4afde5 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 576 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Ne) (:c Real) (:fv _uniq.438254) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MonoidWithZero.toZero) (:c Real) ((:c GroupWithZero.toMonoidWithZero) (:c Real) ((:c DivisionSemiring.toGroupWithZero) (:c Real) ((:c Semifield.toDivisionSemiring) (:c Real) ((:c LinearOrderedSemifield.toSemifi... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:fv FV10)) (: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 :explicit 1 (:lit 0)))))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":30670,"sourceStart":30660,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":30670,"sourceStart":30660,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":30670,"sourceStart":306... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 30 | exact | true | 1 | 23 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72be95c68c247a2e2d9fd709a0376f8ccd32a011a7b2b2a8a10c6edf8fd51f55 | b8bc14691c79982543751899592a46381d2b56d458914b97850e202d196d3d52 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 577 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.437922) (:fv _uniq.453578)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Re... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"gcongr","sourceEnd":31185,"sourceStart":31179,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":31185,"sourceStart":31179,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 40 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6e6f58430b15abc10db231cbb032d4c825c1524460d53987e3f0c105e8636642 | 3107812fe2781a02dd22b828d5c4e773f5f3b457b1a92c77e94c65d7d1fb09cd | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 082bdbe4f86bbcdb9f2ee816d1e6e52e89a2494f5ed24eda607b49d2f6796ffe |
cat-searcher/leandojo-benchmark-4-random | test | 578 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_of_lt</a> hb.2 | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) (:fv _uniq.437922) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne)))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 (:fv FV7)) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31192,"sourceStart":31187,"tag":"atom"},{"children":[{"name":"le_of_lt","semanticRole":"global","source":"le_of_lt","sourceEnd":31201,"sourceStart":31193,"tag":"identifier"},{"children":[{"children":[{"contextIndex":8,"semanticRole":"local","source":"hb","sourceEnd":31204,"sou... | [] | [{"source":"le_of_lt hb.2","source_end":31206,"source_start":31193,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 42 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 415636fa3e37d31028037fa408b381b82755fc16c9f0ced3546ea25e3448e9dc | 082bdbe4f86bbcdb9f2ee816d1e6e52e89a2494f5ed24eda607b49d2f6796ffe | 1a8bce131443e4284a4e18be28532b1697ac89aac74930a10414ddf083cc707e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 579 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>one_mul</a>] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) (:fv _uniq.453578)) (:fv _uniq.453578)) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":31241,"sourceStart":31239,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31243,"sourceStart":31242,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"one_mul","source_end":31250,"source_start":31243,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 45 | exact | true | 1 | 32 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 459cccb84faa8cdbaf1582b6b634681ddee19ac8328c6bac1ba4362192a08739 | aede9bdafb29a282b16969435853e9eea01c3feff9b49645574ff0328fb5054d | 18c3e98597a318bf9015f3d59a8918a79a527e2a3d6bbc4d287bd6db906f596d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 580 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc c₁ * c₂⁻¹ * c₃ * f x ≤ c₁ * c₂⁻¹ * c₃ * (c₂ * ‖g x‖) := by rw [← <a>Real.norm_of_nonneg</a> (hf_pos x hbx)]; gcongr; exact h_ub x hbx _ = (c₂⁻¹ * c₂) * c₁ * (c₃ * ‖g x‖) := by ring _ = c₁ * (c₃ * ‖g x‖) := by simp [c₂_cancel] _ ≤ c₁ * ‖g u‖ := by gcongr; exact (hg_bound u hu).1 _ ≤ f u := by rw [← <a>Real.norm_of_... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"calc","sourceEnd":31327,"sourceStart":31323,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"c₁","sourceEnd":31336,"sourceStart":31332,"tag":"identifier"},{"sourc... | [] | [{"source":"c₁ * c₂⁻¹ * c₃ * f x ≤ c₁ * c₂⁻¹ * c₃ * (c₂ * ‖g x‖)","source_end":31410,"source_start":31332,"syntax_kind":"«term_≤_»"},{"source":"Real.norm_of_nonneg (hf_pos x hbx)","source_end":31469,"source_start":31435,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h_ub x hbx","source_end":31496,"source_start":31486... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 54 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0924a705ce42a5b8f8716d28d971d57784f9cbc28fed44a4dcf248d637917488 | 1a1e98c34b6e4dd3ca750fb9eec283614adfa3d566e2fdc49fb5fee0c59d369c | a7df1880dbaff93185412d9311efc77093dc954766f1b98924795d82a5b256ca | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 581 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.norm_of_nonneg</a> (hf_pos x hbx)] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((: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 HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"rw","sourceEnd":31429,"sourceStart":31427,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31431,"sourceStart":31430,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31434,"sourceSt... | [] | [{"source":"Real.norm_of_nonneg (hf_pos x hbx)","source_end":31469,"source_start":31435,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 61 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5447847279c559f8d614884a2d960812eb88898c99a3848e9c237f0045e60fe | 07e23621da6622e56b5cae3cefaedbc57d171499102049e47491ef448fbfc3fe | 3238a17fcb0211871666238e8dec83ac6808365be8dc275bf2ed69590f6991d1 | 6e20c290c1e044c5596463963d65e5d875851ff292644323d79c8d6a621403a8 |
cat-searcher/leandojo-benchmark-4-random | test | 582 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((: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 HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"gcongr","sourceEnd":31478,"sourceStart":31472,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":31478,"sourceStart":31472,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 65 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6a847563058f4840a3592a2c8aaed9f4155bd8dbe68e424b9c2128d57d4393fb | 6e20c290c1e044c5596463963d65e5d875851ff292644323d79c8d6a621403a8 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 9d2096165d4f166a7eddca0da8ce96455d6fe8266ef22e7d16b146917092ff73 |
cat-searcher/leandojo-benchmark-4-random | test | 583 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h_ub x hbx | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437916) (:fv _uniq.453578))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV2) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31485,"sourceStart":31480,"tag":"atom"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"h_ub","sourceEnd":31490,"sourceStart":31486,"tag":"identifier"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"x","sourceEnd":31492,"sourceStart":31491,"t... | [] | [{"source":"h_ub x hbx","source_end":31496,"source_start":31486,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 67 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e382a581a5e12f1b8e29cf37f36526c3e92f0160f48519e4a0d8cf58285f891f | 9d2096165d4f166a7eddca0da8ce96455d6fe8266ef22e7d16b146917092ff73 | d2d53e516016f5dfb589f8c3b5063d412b116ff1b0ee0ac0161d9edbf1d6be9a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 584 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c Inv.inv... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":31564,"sourceStart":31560,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":31564,"sourceStart":31560,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":31564,"sourceStart":31560,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 70 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72ad6a5cbb39eb39ac40a9748675455a8a550c18659c1e7706babd1fdf050034 | 57a7bdc10a141196fd913026a9474abae64d6a9e188f499a2b8765225c78d2f5 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 585 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [c₂_cancel] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c Inv.inv) (:c Real) (:c Rea... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":31611,"sourceStart":31607,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"c₂_cancel","source_end":31624,"source_start":31613,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 75 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc03bb2ac61890a6757c6a15e5b27c660a6fe6684e390a344edb33d12bc851c3 | 590d9452446b83fc62b47bff957550b04b78cf988b28414fbe079edd71611450 | 657da709c57106a4675a4dd0a388b57453194995c469d4c9804040fb4f3ddc42 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 586 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438426) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"gcongr","sourceEnd":31667,"sourceStart":31661,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":31667,"sourceStart":31661,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 82 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c14c50afa171507824835e1134960fb2785344c07afd49ad7726a55a3488f77 | 38e7f462ec48deb4bfc59d7cb8d3a16d7889999ee7197e82b48684d85b080d10 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | b4de7b43342cf5304d5105bc83612d295eb2fdecfcd500d79ebd74398b02c468 |
cat-searcher/leandojo-benchmark-4-random | test | 587 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hg_bound u hu).1 | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438426) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453578)))) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31674,"sourceStart":31669,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":31676,"sourceStart":31675,"tag":"atom"},{"children":[{"contextIndex":34,"semanticRole":"local","source":"hg_bound","sourceEnd":31684,"sourceStart":31676,"tag":"identifier"},{"children":... | [] | [{"source":"(hg_bound u hu).1","source_end":31692,"source_start":31675,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 84 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 537b1bc851c941f55f820c65e82213b0bde26fc17a78e7999b7476d1694a669f | b4de7b43342cf5304d5105bc83612d295eb2fdecfcd500d79ebd74398b02c468 | 512d9e336642bdde408c28b4884c5043a537b149eb37e6e9f2c2362c34fd8cf9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 588 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.norm_of_nonneg</a> (hf_pos u hu.1)] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606)))) ((:fv _uniq.437916) (:fv _uniq.453606))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"rw","sourceEnd":31727,"sourceStart":31725,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31729,"sourceStart":31728,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31732,"sourceSt... | [] | [{"source":"Real.norm_of_nonneg (hf_pos u hu.1)","source_end":31768,"source_start":31733,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 89 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0f6eab25ea30f639ebe384f4f3ba03ecb21298dee1a5ad09d1b7ecd0a827fa7b | 918151d7269910c3df5ae958d727ba7f44e3567936e0701f278d0bc735f3567f | f870d82afa8484f4f28767a4004d16770f79e3036babac0b1ec02eaf300e8c55 | 4a808b9e12babca2a1ae781d969c6b43630079715c70a09f63273ea3c04500b7 |
cat-searcher/leandojo-benchmark-4-random | test | 589 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h_lb u hu.1 | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606)))) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437916) (:fv _uniq.453606)))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31785,"sourceStart":31780,"tag":"atom"},{"children":[{"contextIndex":27,"semanticRole":"local","source":"h_lb","sourceEnd":31790,"sourceStart":31786,"tag":"identifier"},{"children":[{"contextIndex":31,"semanticRole":"local","source":"u","sourceEnd":31792,"sourceStart":31791,"t... | [] | [{"source":"h_lb u hu.1","source_end":31797,"source_start":31786,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 92 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f592d46600c79f876b28d0f9af47c1c0793cd45f2fef166f5e9395711e28431 | 4a808b9e12babca2a1ae781d969c6b43630079715c70a09f63273ea3c04500b7 | bc2111f3bdda1264c2804378aab47532bca579f13183fa4aa7417f7328d3c894 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 590 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc f u ≤ c₂ * ‖g u‖ := by rw [← <a>Real.norm_of_nonneg</a> (hf_pos u hu.1)]; exact h_ub u hu.1 _ ≤ c₂ * (c₄ * ‖g x‖) := by gcongr; exact (hg_bound u hu).2 _ = c₂ * c₄ * (c₁⁻¹ * c₁) * ‖g x‖ := by simp [c₁_cancel]; ring _ = c₂ * c₄ * c₁⁻¹ * (c₁ * ‖g x‖) := by ring _ ≤ c₂ * c₄ * c₁⁻¹ * f x := by gcongr rw [← <a>Real.nor... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:fv _uniq.437916) (:fv _uniq.453606)) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 (:fv FV2) (:arg :explicit 0 (:fv FV31)))) (:arg :explicit 3 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"calc","sourceEnd":31815,"sourceStart":31811,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":2,"semanticRole":"local","source":"f","sourceEnd":31821,"sourceStart":31820,"tag":"identifier"},{"children":[{"contextIndex":31,"se... | [] | [{"source":"f u ≤ c₂ * ‖g u‖","source_end":31844,"source_start":31820,"syntax_kind":"«term_≤_»"},{"source":"Real.norm_of_nonneg (hf_pos u hu.1)","source_end":31894,"source_start":31859,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h_ub u hu.1","source_end":31914,"source_start":31903,"syntax_kind":"Lean.Parser.Term.a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 95 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa72586725b0ceca73613e6252fa1b58cd6adf0abdd780febf826119735f361c | 7ca9a39d97f47fd5f7cc3569ac55fa4cd84ece88a7359769332e823b74f684c0 | 6c2777803a6c8b48a823aed1d587a02dd016d1307271ef494dee5cb3df8a3a2e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 591 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.norm_of_nonneg</a> (hf_pos u hu.1)] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.437916) (:fv _uniq.453606)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606))))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 (:fv FV2) (:arg :explicit 0 (:fv FV31)))) (:arg :explicit 3 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-ty... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"rw","sourceEnd":31853,"sourceStart":31851,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":31855,"sourceStart":31854,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":31858,"sourceSt... | [] | [{"source":"Real.norm_of_nonneg (hf_pos u hu.1)","source_end":31894,"source_start":31859,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 102 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a365ca768e76bbe3c1098229224a63cef388d035306962ac569852751b62993f | e25952d1928ee5c03b24076442024590e02df7e4bdb4897f31f6ff0e55a59868 | f870d82afa8484f4f28767a4004d16770f79e3036babac0b1ec02eaf300e8c55 | fa4e490bef49d49a2d315c9c55db22e39c2bd31e209ad9d2b7f4287cc8b7f841 |
cat-searcher/leandojo-benchmark-4-random | test | 592 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h_ub u hu.1 | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437916) (:fv _uniq.453606))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606))))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV2) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31902,"sourceStart":31897,"tag":"atom"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"h_ub","sourceEnd":31907,"sourceStart":31903,"tag":"identifier"},{"children":[{"contextIndex":31,"semanticRole":"local","source":"u","sourceEnd":31909,"sourceStart":31908,"t... | [] | [{"source":"h_ub u hu.1","source_end":31914,"source_start":31903,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 106 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a5255b27743bb3c815434755c1eb715e37e4f87e7d811f8bd358445ea9ff44ad | fa4e490bef49d49a2d315c9c55db22e39c2bd31e209ad9d2b7f4287cc8b7f841 | 46c3b3f99809e9a2f0053540baa85aa23e3a9a4fb7ca2d705a02bf7829e23f01 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 593 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606)))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul))... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"gcongr","sourceEnd":31965,"sourceStart":31959,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":31965,"sourceStart":31959,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 111 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ac6f7104f38a5cfbde3374f2f22f2200b29f375b021c5e32c84469e10a5b2f82 | ff156392cbe1bc7b7808954ce97046fd38de93ee15e9a51b68a0cafdeb0da0dc | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 140e348308f830153792359a3b5c3e8bf0fc51351f97551f66890612f5000d98 |
cat-searcher/leandojo-benchmark-4-random | test | 594 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (hg_bound u hu).2 | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453606))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438501) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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 Norm.norm) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Norm) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV3) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":31972,"sourceStart":31967,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":31974,"sourceStart":31973,"tag":"atom"},{"children":[{"contextIndex":34,"semanticRole":"local","source":"hg_bound","sourceEnd":31982,"sourceStart":31974,"tag":"identifier"},{"children":... | [] | [{"source":"(hg_bound u hu).2","source_end":31990,"source_start":31973,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 113 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7bf1e8cd47ff90a24ee06f64698283cc961c5fa30104381748ad44af34bdce70 | 140e348308f830153792359a3b5c3e8bf0fc51351f97551f66890612f5000d98 | 2191af8ec733dfe97b87523e9a9ac7af060d64f98b9da2d60ee3a5063163db79 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 595 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [c₁_cancel] | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438501) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453578)))))... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"simp","sourceEnd":32056,"sourceStart":32052,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32058,"sourceStart":32057,"tag":"a... | [] | [{"source":"c₁_cancel","source_end":32069,"source_start":32058,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 118 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c0ac65d100237d715e9138a95a14cb17780e3e5b68d74069970bb0b4ddd5a6a7 | de5ad53304ba5b8a7a9ecfba3fa480a12e9fa800c1363256f8c61768b7a5c503 | 46fd68878c96f3b2d7cac7337354c85bb04d84ba2ee03894a94278be91b78935 | 1de794909942c886dffc50a54d6fb1d6c9ac843c06e99dc0677263343991d761 |
cat-searcher/leandojo-benchmark-4-random | test | 596 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438501) ((:c abs) (:c Real) (:c Real.lattice) (:c Real.instAddGroup) ((:fv _uniq.437917) (:... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"ring","sourceEnd":32076,"sourceStart":32072,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":32076,"sourceStart":32072,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 120 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 766264b8b2440c222d7916dcaf24e00302b609328f420554aef0a3fa2f287d9e | 1de794909942c886dffc50a54d6fb1d6c9ac843c06e99dc0677263343991d761 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 597 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | ((:c Eq) (:c Real) ((: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) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438336) (:fv _uniq.4... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (:c Real) (:c Real) (... | (: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.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":32142,"sourceStart":32138,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":32142,"sourceStart":32138,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":32142,"sourceStart":32138,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 123 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66bfb443a884162e3c6662d1a455ec30649d27416334e505769327b5abf35018 | c5efc725c288206fb4c320938009941efdf8848f51cf322e1d1fcee565c7c825 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 598 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
hc₄_pos ... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((: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 HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"gcongr","sourceEnd":32213,"sourceStart":32207,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":32213,"sourceStart":32207,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 130 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 644cfb924040528ec968f574d3e422771a3dc72aac8437d64542511d2637f36c | b6360a8bfac99e794bf24b1089d8dd7127d02d5e78f8f9c0e25aadba0435496c | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 978b528fb968ab419eed7424658b57641f229e0df57db23882376239739b8e0f |
cat-searcher/leandojo-benchmark-4-random | test | 599 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.norm_of_nonneg</a> (hf_pos x hbx)] | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453578)))) ((:fv _uniq.437916) (:fv _uniq.453578))) | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"rw","sourceEnd":32232,"sourceStart":32230,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":32234,"sourceStart":32233,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":32237,"sourceSt... | [] | [{"source":"Real.norm_of_nonneg (hf_pos x hbx)","source_end":32272,"source_start":32238,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 131 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f8be8136dae6b88853e8606155fc610ac6f05ca7262e444db2fe9624b14282f | 978b528fb968ab419eed7424658b57641f229e0df57db23882376239739b8e0f | 3238a17fcb0211871666238e8dec83ac6808365be8dc275bf2ed69590f6991d1 | 1c861a84db3b53bafabc38f426eb43311d5adefdf1b0a25c743868cd85955841 |
cat-searcher/leandojo-benchmark-4-random | test | 600 | AkraBazziRecurrence.GrowsPolynomially.of_isTheta | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h_lb x hbx | case h
f✝ f g : ℝ → ℝ
hg✝ : GrowsPolynomially g
hf : f =Θ[atTop] g
hf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x
b : ℝ
hb : b ∈ Set.Ioo 0 1
hb_pos : 0 < b
c₁ : ℝ
hc₁_pos : 0 < c₁
hf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖
c₂ : ℝ
hc₂_pos : 0 < c₂
hf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖
c₃ : ℝ
hc₃_pos : 0 < c₃
c₄ : ℝ
h... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.438254) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq.437917) (:fv _uniq.453578)))) ((:c Norm.norm) (:c Real) (:c Real.norm) ((:fv _uniq... | [{"name":"f✝","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hg✝","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.437917))"},{"name":"hf","sexp":"((:c Asymptotics.IsTheta) (: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":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"name":"f✝","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :ex... | {"children":[{"source":"exact","sourceEnd":32295,"sourceStart":32290,"tag":"atom"},{"children":[{"contextIndex":27,"semanticRole":"local","source":"h_lb","sourceEnd":32300,"sourceStart":32296,"tag":"identifier"},{"children":[{"contextIndex":25,"semanticRole":"local","source":"x","sourceEnd":32302,"sourceStart":32301,"t... | [] | [{"source":"h_lb x hbx","source_end":32306,"source_start":32296,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.437599","is_instance":false,"is_let":false,"user_name":"f✝"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.437916","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":implicit","context_index":3,"internal_name":"... | 37 | 134 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2b026093b2a1a7f49f7b54adeb62c7c93e131901e063810db0ec4cf1f9102e34 | 1c861a84db3b53bafabc38f426eb43311d5adefdf1b0a25c743868cd85955841 | 82e40b78c84bb95bc2e702a7f89a3f02bcacfb2187a71b38f3399be2ed44fb5a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 601 | IsOrderRightAdjoint.orderIso_comp | Mathlib/Order/SemiconjSup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa [e.le_symm_apply] using h (e.symm y) | α : Type u_1
β : Type u_2
γ : Type u_3
inst✝² : Preorder α
inst✝¹ : Preorder β
inst✝ : Preorder γ
f : α → β
g : β → α
h : IsOrderRightAdjoint f g
e : β ≃o γ
y : γ
⊢ IsLUB {x | (⇑e ∘ f) x ≤ y} ((g ∘ ⇑e.symm) y) | ((:c IsLUB) (:fv _uniq.1080) (:fv _uniq.1448) ((:c setOf) (:fv _uniq.1080) (:lambda x (:fv _uniq.1080) ((:c LE.le) (:fv _uniq.1086) ((:c Preorder.toLE) (:fv _uniq.1086) (:fv _uniq.1450)) ((:c Function.comp) (:fv _uniq.1080) (:fv _uniq.1083) (:fv _uniq.1086) ((:c DFunLike.coe) ((:c OrderIso) (:fv _uniq.1083) (:fv _uniq.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝²","sexp":"((:c Preorder) (:fv _uniq.1080))"},{"name":"inst✝¹","sexp":"((:c Preorder) (:fv _uniq.1083))"},{"name":"inst✝","sexp":"((:c Preorder) (:fv _uniq.1086))"},{"name":"f","sexp":"... | (:app (:c IsLUB) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c setOf) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c LE.le) (:arg :implicit-type 0 (:fv FV2)) (:arg :instance ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1080","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1083","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":3512,"sourceStart":3507,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"e.le_symm_apply","source_end":3529,"source_start":3514,"syntax_kind":"ident"},{"source":"h (e.symm y)","source_end":3549,"source_start":3537,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1080","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.1083","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 15 | 2 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b55310a7dd5598db3308e3fccd6c16309648b086140caaee44d30d855c2c213 | 69aa176b6712f5ce9dfd5d51e68691b1b336d88ae8880760189518a4c99ab9a4 | ba70f307104716bef3b40a48314de4a546614a4184025a45c839f06bf43c5bdd | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 602 | List.mem_dedup | Mathlib/Data/List/Dedup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>List.dedup</a>, <a>List.forall_mem_ne</a>, <a>Classical.not_not</a>] using this | case refine_2
α : Type u
inst✝ : DecidableEq α
a : α
l : List α
this : (¬∀ b ∈ pwFilter (fun x x_1 => x ≠ x_1) l, a ≠ b) ↔ ¬∀ b ∈ l, a ≠ b
⊢ a ∈ l.dedup ↔ a ∈ l | ((:c Iff) ((:c Membership.mem) (:fv _uniq.1464) ((:c List) (:fv _uniq.1464)) ((:c List.instMembership) (:fv _uniq.1464)) (:fv _uniq.1573) ((:c List.dedup) (:fv _uniq.1464) (:fv _uniq.1471) (:fv _uniq.1574))) ((:c Membership.mem) (:fv _uniq.1464) ((:c List) (:fv _uniq.1464)) ((:c List.instMembership) (:fv _uniq.1464)) (... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.1464))"},{"name":"a","sexp":"(:fv _uniq.1464)"},{"name":"l","sexp":"((:c List) (:fv _uniq.1464))"},{"name":"this","sexp":"((:c Iff) ((:c Not) (:forall b (:fv _uniq.1464) (:forall _ ((:c Membership.mem) (:fv _uniq.1464) ((:c List... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c List) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:app (:c List) (:arg :explicit 0 (:fv FV0))))))) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":1381,"sourceStart":1376,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"dedup","source_end":1393,"source_start":1388,"syntax_kind":"ident"},{"source":"forall_mem_ne","source_end":1408,"source_start":1395,"syntax_kind":"ident"},{"source":"not_not","source_end":1417,"source_start":1410,"syntax_kind":"ident"},{"source":"this","source_end":1429,"source_start":1425,"syntax_kind":"id... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 11 | 7 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54d46007de3f790152a4fafa3312d406d10d58b286fafafd7f11845057ab1394 | 489457f3b946c49e6c8483270d1cceac24510fffe38b588bbabc816fc3a0c887 | 6fae1c3fbfd7b10830f2d71a97adb3f3267f2a39fb2137b1c577075bb89e75a9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 603 | List.mem_dedup | Mathlib/Data/List/Dedup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intros x y z xz | case refine_1
α : Type u
inst✝ : DecidableEq α
a : α
l : List α
⊢ ∀ {x y z : α}, (fun x x_1 => x ≠ x_1) x z → (fun x x_1 => x ≠ x_1) x y ∨ (fun x x_1 => x ≠ x_1) y z | case refine_1
α : Type u
inst✝ : DecidableEq α
a : α
l : List α
x y z : α
xz : x ≠ z
⊢ (fun x x_1 => x ≠ x_1) x y ∨ (fun x x_1 => x ≠ x_1) y z | (:forall x (:fv _uniq.1464) (:forall y (:fv _uniq.1464) (:forall z (:fv _uniq.1464) (:forall _ ((:c Ne) (:fv _uniq.1464) 2 0) ((:c Or) ((:lambda _ (:fv _uniq.1464) (:lambda _ (:fv _uniq.1464) ((:c Ne) (:fv _uniq.1464) 1 0))) 3 2) ((:lambda _ (:fv _uniq.1464) (:lambda _ (:fv _uniq.1464) ((:c Ne) (:fv _uniq.1464) 1 0))) ... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.1464))"},{"name":"a","sexp":"(:fv _uniq.1464)"},{"name":"l","sexp":"((:c List) (:fv _uniq.1464))"}] | (:forall x :implicit (:fv FV0) (:forall y :implicit (:fv FV0) (:forall z :implicit (:fv FV0) (:forall _ :explicit (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 2) (:arg :explicit 2 0)) (:app (:c Or) (:arg :explicit 0 (:app (:lambda _ :explicit (:fv FV0) (:lambda _ :explicit (:fv FV0) (:app (:c Ne) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :explic... | {"children":[{"source":"intros","sourceEnd":1441,"sourceStart":1435,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":1443,"sourceStart":1442,"tag":"identifier"},{"semanticRole":"scoped_local","source":"y","sourceEnd":1445,"sourceStart":1444,"tag":"identifier"},{"semanticRole":"scoped_l... | [{"role":"fresh_name","source":"x","source_end":1443,"source_start":1442,"syntax_kind":"ident"},{"role":"fresh_name","source":"y","source_end":1445,"source_start":1444,"syntax_kind":"ident"},{"role":"fresh_name","source":"z","source_end":1447,"source_start":1446,"syntax_kind":"ident"},{"role":"fresh_name","source":"xz"... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 11 | 14 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b6fd0ad718c1c7fbfb7592ab287e3659110381105c23e5a787bc8b0890313c18 | 57af2897df8066159a72575716c531d9d6792ad4824ec2445214c5e5aa1efd41 | 8a99347bdca9a6918dd7d0482a59a33697b3679cc72cbc177eb873215ff1ad5e | 49752e26e1b5fd01cbd952729f46306a7a4ed2368dff7085cf0f6edbd6a9dbbd |
cat-searcher/leandojo-benchmark-4-random | test | 604 | List.mem_dedup | Mathlib/Data/List/Dedup.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>not_and_or</a>.1 <| <a>mt</a> (fun h ↦ h.1.<a>Eq.trans</a> h.2) xz | case refine_1
α : Type u
inst✝ : DecidableEq α
a : α
l : List α
x y z : α
xz : x ≠ z
⊢ (fun x x_1 => x ≠ x_1) x y ∨ (fun x x_1 => x ≠ x_1) y z | ((:c Or) ((:lambda _ (:fv _uniq.1464) (:lambda _ (:fv _uniq.1464) ((:c Ne) (:fv _uniq.1464) 1 0))) (:fv _uniq.1996) (:fv _uniq.1997)) ((:lambda _ (:fv _uniq.1464) (:lambda _ (:fv _uniq.1464) ((:c Ne) (:fv _uniq.1464) 1 0))) (:fv _uniq.1997) (:fv _uniq.1998))) | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.1464))"},{"name":"a","sexp":"(:fv _uniq.1464)"},{"name":"l","sexp":"((:c List) (:fv _uniq.1464))"},{"name":"x","sexp":"(:fv _uniq.1464)"},{"name":"y","sexp":"(:fv _uniq.1464)"},{"name":"z","sexp":"(:fv _uniq.1464)"},{"name":"xz"... | (:app (:c Or) (:arg :explicit 0 (:app (:lambda _ :explicit (:fv FV0) (:lambda _ :explicit (:fv FV0) (:app (:c Ne) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 1) (:arg :explicit 2 0)))) (:arg :explicit 0 (:fv FV5)) (:arg :explicit 1 (:fv FV6)))) (:arg :explicit 1 (:app (:lambda _ :explicit (:fv FV0) (:lambda _ :... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"name":"inst✝","sexp":"(:app (:c DecidableEq) (:arg :explic... | {"children":[{"source":"exact","sourceEnd":1460,"sourceStart":1455,"tag":"atom"},{"children":[{"children":[{"name":"not_and_or","semanticRole":"global","source":"not_and_or","sourceEnd":1471,"sourceStart":1461,"tag":"identifier"},{"source":".","sourceEnd":1472,"sourceStart":1471,"tag":"atom"},{"children":[{"source":"1"... | [] | [{"source":"not_and_or.1 <| mt (fun h ↦ h.1.trans h.2) xz","source_end":1508,"source_start":1461,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.1464","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.1471","is_instance":true,"is_let":false,"user_name":"inst✝"},{"binder_role":":implicit","context_index":3,"internal_... | 11 | 15 | exact | true | 1 | 8 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ff5715912ea53b877c084a8a27fefd1facb2f3dd454aba2c95a8a03fee6b5a22 | 49752e26e1b5fd01cbd952729f46306a7a4ed2368dff7085cf0f6edbd6a9dbbd | d4233e173c2e55cb1d73fd0411f529be6b9bf825b452da51564bdfa8060751c1 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 605 | HasDerivAt.mul_const | Mathlib/Analysis/Calculus/Deriv/Mul.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>hasDerivWithinAt_univ</a>] at * | 𝕜 : Type u
inst✝¹⁰ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
E : Type w
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
G : Type u_1
inst✝⁵ : NormedAddCommGroup G
inst✝⁴ : NormedSpace 𝕜 G
f f₀ f₁ g : 𝕜 → F
f' f₀' f₁' g' : F
x : 𝕜
s t : Set 𝕜
L L₁ L₂ : F... | 𝕜 : Type u
inst✝¹⁰ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
E : Type w
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
G : Type u_1
inst✝⁵ : NormedAddCommGroup G
inst✝⁴ : NormedSpace 𝕜 G
f f₀ f₁ g : 𝕜 → F
f' f₀' f₁' g' : F
x : 𝕜
s t : Set 𝕜
L L₁ L₂ : F... | ((:c HasDerivAt) (:fv _uniq.369971) (:fv _uniq.369974) (:fv _uniq.370351) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.370351) ((:c NormedRing.toNonUnitalNormedRing) (:fv _uniq.370351) (:fv _uniq.370357))) ((:c NormedAlgebra.toNormedSpace') (:fv _uniq.369971) ((:c NontriviallyNormedField.toNormedField) (:f... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.369971))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.369976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.369971) (:fv _uniq.369976) ((:c Nontri... | (:app (:c HasDerivAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV26)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV26))))) (:arg :instance 4 (:instance-of (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.369971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.369974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"rw","sourceEnd":10987,"sourceStart":10985,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10989,"sourceStart":10988,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10992,"sourceSt... | [] | [{"source":"hasDerivWithinAt_univ","source_end":11014,"source_start":10993,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.369971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.369974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in... | 80 | 4 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ce85f35aa66a732848b8767789d911c0e79f8d3704749f703ed5546b577124b0 | 3116af85da7d21483ed779809dcdef8dc4cc74802d3a272e94a130e307768387 | 5b583150be43ebff426646de32e0772667b9218a713e63f4be9578030ae74232 | ae78cb337a31a5199c5d36e04a1ca2860c7d21f040b80b17126c901bcb8babc0 |
cat-searcher/leandojo-benchmark-4-random | test | 606 | HasDerivAt.mul_const | Mathlib/Analysis/Calculus/Deriv/Mul.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hc.mul_const d | 𝕜 : Type u
inst✝¹⁰ : NontriviallyNormedField 𝕜
F : Type v
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace 𝕜 F
E : Type w
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
G : Type u_1
inst✝⁵ : NormedAddCommGroup G
inst✝⁴ : NormedSpace 𝕜 G
f f₀ f₁ g : 𝕜 → F
f' f₀' f₁' g' : F
x : 𝕜
s t : Set 𝕜
L L₁ L₂ : F... | ((:c HasDerivWithinAt) (:fv _uniq.369971) (:fv _uniq.369974) (:fv _uniq.370351) ((:c NonUnitalNormedRing.toNormedAddCommGroup) (:fv _uniq.370351) ((:c NormedRing.toNonUnitalNormedRing) (:fv _uniq.370351) (:fv _uniq.370357))) ((:c NormedAlgebra.toNormedSpace') (:fv _uniq.369971) ((:c NontriviallyNormedField.toNormedFiel... | [{"name":"𝕜","sexp":"(:sort (+ u 1))"},{"name":"inst✝¹⁰","sexp":"((:c NontriviallyNormedField) (:fv _uniq.369971))"},{"name":"F","sexp":"(:sort (+ v 1))"},{"name":"inst✝⁹","sexp":"((:c NormedAddCommGroup) (:fv _uniq.369976))"},{"name":"inst✝⁸","sexp":"((:c NormedSpace) (:fv _uniq.369971) (:fv _uniq.369976) ((:c Nontri... | (:app (:c HasDerivWithinAt) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c NontriviallyNormedField) (:arg :explicit 0 (:fv FV0))))) (:arg :implicit-type 2 (:fv FV26)) (:arg :instance 3 (:instance-of (:app (:c NormedAddCommGroup) (:arg :explicit 0 (:fv FV26))))) (:arg :instance 4 (:instance-... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.369971","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.369974","is_instance":true,"is_let":false,"name":"inst✝¹⁰","sexp":"(:app (:c NontriviallyNormedF... | {"children":[{"source":"exact","sourceEnd":11028,"sourceStart":11023,"tag":"atom"},{"children":[{"source":"hc.mul_const","sourceEnd":11041,"sourceStart":11029,"tag":"identifier"},{"children":[{"contextIndex":39,"semanticRole":"local","source":"d","sourceEnd":11043,"sourceStart":11042,"tag":"identifier"}],"kind":"null",... | [] | [{"source":"hc.mul_const d","source_end":11043,"source_start":11029,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.369971","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.369974","is_instance":true,"is_let":false,"user_name":"inst✝¹⁰"},{"binder_role":":implicit","context_index":2,"in... | 80 | 7 | exact | true | 1 | 39 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fff188c09d24063d1d37495579b14c37037ffdc2270bff58d53bb4b26dcf6b43 | ae78cb337a31a5199c5d36e04a1ca2860c7d21f040b80b17126c901bcb8babc0 | 63434d28bfe923131e65dec97c79472961d2d850387c13251f6404f3d948a487 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 607 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>MeasureTheory.lmarginal_congr</a> | δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
⊢ (∫⋯∫⁻... | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | ((:c Eq) (:c ENNReal) ((:c MeasureTheory.lmarginal) (:fv _uniq.13502) (:fv _uniq.13510) (:fv _uniq.13518) (:fv _uniq.13554) (:fv _uniq.13533) (:fv _uniq.13559) (:fv _uniq.13856) ((:c Function.update) (:fv _uniq.13502) (:fv _uniq.13510) (:fv _uniq.13554) (:fv _uniq.13857) (:fv _uniq.13854) (:fv _uniq.13858))) ((:c Measu... | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:app (:c Eq) (:arg :implicit-type 0 (:c ENNReal)) (:arg :explicit 1 (:app (:c MeasureTheory.lmarginal) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit 1) (:arg :instance 2 (:instance-of (:forall x :explicit (:fv FV0) (:app (:c MeasurableSpace) (:arg :explicit 0 (:app (:fv FV2) (:arg :explicit 0 0))))))) (:arg :insta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"apply","sourceEnd":4963,"sourceStart":4958,"tag":"atom"},{"name":"MeasureTheory.lmarginal_congr","semanticRole":"global","source":"lmarginal_congr","sourceEnd":4979,"sourceStart":4964,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply lmarginal_congr","sourceEnd":4979,"source... | [] | [{"source":"lmarginal_congr","source_end":4979,"source_start":4964,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 4 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | eaa9ff9fac7e47b9b0b0f893cb9631eed6ecf7894ba17edad6abca49e862a2e0 | abbe684947c94194cf7e2ccd1c1c302d2ccc8a49b14f7534f9c6427c80ca9bf0 | eadad28c9bf3906b49a9ce95ceea3a735eb15fd7e1b5181c0a8d99a3d0022d44 | 3463273c167cc224780378fb663126b96f5b042000792a9f73dd0b6aa11782ef |
cat-searcher/leandojo-benchmark-4-random | test | 608 | MeasureTheory.lmarginal_update_of_mem | Mathlib/MeasureTheory/Integral/Marginal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro j hj | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | case h
δ : Type u_1
δ' : Type u_2
π : δ → Type u_3
inst✝² : (x : δ) → MeasurableSpace (π x)
μ : (i : δ) → Measure (π i)
inst✝¹ : ∀ (i : δ), SigmaFinite (μ i)
inst✝ : DecidableEq δ
s t : Finset δ
f✝ g : ((i : δ) → π i) → ℝ≥0∞
x✝ y✝ : (i : δ) → π i
i✝ i : δ
hi : i ∈ s
f : ((i : δ) → π i) → ℝ≥0∞
x : (i : δ) → π i
y : π i
... | (:forall i (:fv _uniq.13502) (:forall _ ((:c Not) ((:c Membership.mem) (:fv _uniq.13502) ((:c Finset) (:fv _uniq.13502)) ((:c Finset.instMembership) (:fv _uniq.13502)) 0 (:fv _uniq.13559))) ((:c Eq) ((:fv _uniq.13510) 1) ((:c Function.update) (:fv _uniq.13502) (:fv _uniq.13510) (:fv _uniq.13554) (:fv _uniq.13857) (:fv ... | [{"name":"δ","sexp":"(:sort (+ u_1 1))"},{"name":"δ'","sexp":"(:sort (+ u_2 1))"},{"name":"π","sexp":"(:forall _ (:fv _uniq.13502) (:sort (+ u_3 1)))"},{"name":"inst✝²","sexp":"(:forall x (:fv _uniq.13502) ((:c MeasurableSpace) ((:fv _uniq.13510) 0)))"},{"name":"μ","sexp":"(:forall i (:fv _uniq.13502) ((:c MeasureTheor... | (:forall i :explicit (:fv FV0) (:forall _ :explicit (:app (:c Not) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Finset) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"name":"δ","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"name":"δ'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"intro","sourceEnd":4987,"sourceStart":4982,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"j","sourceEnd":4989,"sourceStart":4988,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hj","sourceEnd":4992,"sourceStart":4990,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"j","source_end":4989,"source_start":4988,"syntax_kind":"ident"},{"role":"fresh_name","source":"hj","source_end":4992,"source_start":4990,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.13502","is_instance":false,"is_let":false,"user_name":"δ"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.13505","is_instance":false,"is_let":false,"user_name":"δ'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 16 | 5 | exact | true | 1 | 19 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e2926150d4484d37cc17f96f834053d40497e00c9c5877843275cbe9f23b25f1 | 3463273c167cc224780378fb663126b96f5b042000792a9f73dd0b6aa11782ef | 2c6f7de6deb1d764e2d728878273bea667a814af38045ef846061e455553a039 | eee3408b2e0e69a58fd19769846b45f4e33a4e1b8528abd01317d9267171fa7d |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.