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 | 2,063 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro x ⟨hxlb, hxub⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ x ∈ Set.Ico (max n₀ 2) (2 * max n₀ 2), f x = f (max n₀ 2) | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ f x = f (max n₀ 2) | (:forall x (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ico) (:c Real) (:c Real.instPreorder) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2)... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:forall x :explicit (:c Real) (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"intro","sourceEnd":8279,"sourceStart":8274,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":8281,"sourceStart":8280,"tag":"identifier"},{"children":[{"source":"⟨","sourceEnd":8285,"sourceStart":8282,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","sour... | [{"role":"fresh_name","source":"x","source_end":8281,"source_start":8280,"syntax_kind":"ident"},{"role":"fresh_name","source":"hxlb","source_end":8289,"source_start":8285,"syntax_kind":"ident"},{"role":"fresh_name","source":"hxub","source_end":8295,"source_start":8291,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 115 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 388043a0f1b6a1a027709dd974959fd0b5f512f970fc652f762be5a85ba1b837 | 5d5f2448ec24cbddef0152f54423fc0a8747f29eaaf034b1b759ef8959377681 | 04f3ffdf01158247d3853cb5f22af2cd4c4ef5bcf6e5a4104a47353ee985a4d9 | 9142bdf1eb411af6c905709d87861784321d56e9f85d1bb464f917763a430e61 |
cat-searcher/leandojo-benchmark-4-random | test | 2,064 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₁ := calc n₀ ≤ 1 * <a>Max.max</a> n₀ 2 := by simp _ ≤ 2 * <a>Max.max</a> n₀ 2 := by gcongr; norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ f x = f (max n₀ 2) | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
⊢ f x = f (max n₀ 2) | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.48937)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV10)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":8311,"sourceStart":8307,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":8316,"sourceStart":8312,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₁","sourceEnd":8316,"sourceStart":8312,"tag":"node"},{"... | [] | [{"source":"calc n₀ ≤ 1 * max n₀ 2 := by simp\n _ ≤ 2 * max n₀ 2 := by gcongr; norm_num","source_end":8427,"source_start":8320,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 116 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48f99d0b015cec9ef9535f138f97176c0661aa83ac75ad64ec1b4b5914c255a4 | 9142bdf1eb411af6c905709d87861784321d56e9f85d1bb464f917763a430e61 | e69fda7a2dc841ba5686569b1d8a25fe1f4a9d26ce8028f0c5e6924c611a2f17 | 9d012c68ee5e29eda18b27dd08832c62285a4fe59958111687ee9071c8b4f111 |
cat-searcher/leandojo-benchmark-4-random | test | 2,065 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₂ := hn₀ (2 * <a>Max.max</a> n₀ 2) h₁ (<a>Max.max</a> n₀ 2) ⟨by simp [-<a>max_le_iff</a>, hxlb], by linarith⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
⊢ f x = f (max n₀ 2) | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
h₂ : f (max n₀ 2) = c₂ * f (2 * max n₀ 2)
⊢ f x = f (max n₀ 2) | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.48937)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV10)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":8440,"sourceStart":8436,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":8445,"sourceStart":8441,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₂","sourceEnd":8445,"sourceStart":8441,"tag":"node"},{"... | [] | [{"source":"hn₀ (2 * max n₀ 2) h₁ (max n₀ 2) ⟨by simp [-max_le_iff, hxlb], by linarith⟩","source_end":8536,"source_start":8449,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 129 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8d3d68f5105a8528662c3628d53afa79a292193dd2007d9f9b0444fcce425abb | 9d012c68ee5e29eda18b27dd08832c62285a4fe59958111687ee9071c8b4f111 | d8a052f699d48f5bab5bb522360f46fa2468d0bf09860f201b30c0850c12f316 | eb84b9521e845ea4567a125efffff97109e5167a94588255bfa8ad841b104bf4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,066 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h₂] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
h₂ : f (max n₀ 2) = c₂ * f (2 * max n₀ 2)
⊢ f x = f (max n₀ 2) | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
h₂ : f (max n₀ 2) = c₂ * f (2 * max n₀ 2)
⊢ f x = c₂ * f (2 * max n₀ 2) | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.48937)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV10)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":8547,"sourceStart":8545,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":8549,"sourceStart":8548,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":14,"semanticR... | [] | [{"source":"h₂","source_end":8553,"source_start":8549,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 140 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5c7d9c5abbf28e301d6fa92298b846a872aa3fdb5cff3f6ad6524a5ab5364223 | eb84b9521e845ea4567a125efffff97109e5167a94588255bfa8ad841b104bf4 | 1485872777d10e5a4cc52b951f1dc67aa5a124583eb42e62794c7cef5cc71623 | 64e2e9c2330ad614657cdeca63c523fa57cb5166f36fcf0bd2ae41ccc5685237 |
cat-searcher/leandojo-benchmark-4-random | test | 2,067 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hn₀ (2 * <a>Max.max</a> n₀ 2) h₁ x ⟨by simp [-<a>max_le_iff</a>, hxlb], <a>le_of_lt</a> hxub⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
h₂ : f (max n₀ 2) = c₂ * f (2 * max n₀ 2)
⊢ f x = c₂ * f (2 * max n₀ 2) | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.48937)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.35515) ((:fv _uniq.34812) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c inst... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV10)))) (: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) (:arg :explicit 0... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":8568,"sourceStart":8563,"tag":"atom"},{"children":[{"contextIndex":9,"semanticRole":"local","source":"hn₀","sourceEnd":8574,"sourceStart":8569,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":8576,"sourceStart":8575,"tag":"atom"},{"children":[{"children"... | [] | [{"source":"hn₀ (2 * max n₀ 2) h₁ x ⟨by simp [-max_le_iff, hxlb], le_of_lt hxub⟩","source_end":8647,"source_start":8569,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 143 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a52a77db3159156a5119b4df0dfbd5579617a08a610875309293364acd6a8283 | 64e2e9c2330ad614657cdeca63c523fa57cb5166f36fcf0bd2ae41ccc5685237 | 2f8284c47a65d78c4ee2784d8a536e1850749a1fba73827353e20e8233240735 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,068 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ n₀ ≤ 1 * max n₀ 2 | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.47240) ((: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))) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrde... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 FV8)) (:arg :explicit 3 (: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 (:i... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8359,"sourceStart":8355,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 119 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f82f1604974cd61567179392c8f36bd0b19d29f0933a59bb4eb47246a995f737 | 45496eb6581aacb7351e075dc3c1134938048d98a034970efe099937c1fff450 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,069 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ 1 * max n₀ 2 ≤ 2 * max n₀ 2 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ 1 ≤ 2 | ((: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 OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _un... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":8417,"sourceStart":8411,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":8417,"sourceStart":8411,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 126 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8934e715daf7ec24c1017257f46ad747d587068eb7620c4770d7b56be7be3bc4 | 9b6b645df8d38f1a845d1cdcf5e91410e428715f2314316d13c69f0a30859e83 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 35de7693c2d551082f064d61a85b28dda9142c4684d22095ba15dc19ab53dbbb |
cat-searcher/leandojo-benchmark-4-random | test | 2,070 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
⊢ 1 ≤ 2 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:l... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"norm_num","sourceEnd":8427,"sourceStart":8419,"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"}],"kind":"Mathlib... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 128 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf22f098c3ee464ac5ee1c243da1980de15c3893888addbff0b901440658b79a | 35de7693c2d551082f064d61a85b28dda9142c4684d22095ba15dc19ab53dbbb | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,071 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [-<a>max_le_iff</a>, hxlb] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
⊢ 1 / 2 * (2 * max n₀ 2) ≤ max n₀ 2 | ((: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 HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8500,"sourceStart":8496,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"max_le_iff","source_end":8513,"source_start":8503,"syntax_kind":"ident"},{"source":"hxlb","source_end":8519,"source_start":8515,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 132 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bbeadc7024749811521192b8b453c638c08cd29bd172c8a4eb9d987f1bd51790 | ae7c826a85327a6835dcc999d4bf39bf2795f50356f255e459722f5fac46d09a | 84604a089c6e682cf6993135547429f232eb55aa31da4d0ee8bd713cef984361 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,072 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
⊢ max n₀ 2 ≤ 2 * max n₀ 2 | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":8533,"sourceStart":8525,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 137 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93d232bc7a55d254809517d720302857f7a67edf8486f6c04715c82f9c06c682 | da34527b24e5bcaa7aa926f8282c4ba58d3a6f575696d20ac615b7edac3fe529 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,073 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [-<a>max_le_iff</a>, hxlb] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
x : ℝ
hxlb : max n₀ 2 ≤ x
hxub : x < 2 * max n₀ 2
h₁ : n₀ ≤ 2 * max n₀ 2
h₂ : f (max n₀ 2) = c₂ * f (2 * max n₀ 2)
⊢ 1 / 2 * (2 * max n₀ 2) ≤ x | ((: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 HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":8609,"sourceStart":8605,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"max_le_iff","source_end":8622,"source_start":8612,"syntax_kind":"ident"},{"source":"hxlb","source_end":8628,"source_start":8624,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 146 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7d7a6f84633396aa09166c3b9c051c1f2926abf6c38a021619ad963cd6c4a237 | c0abff9751e81bdd8a154f31808c17da3098b7fb48d44403309e95399cfaeda4 | 84604a089c6e682cf6993135547429f232eb55aa31da4d0ee8bd713cef984361 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,074 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro n hn hyp_ind z hz | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
⊢ ∀ n ≥ 1,
(∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)) →
∀ z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2), f z = f (ma... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | (:forall n (:c Nat) (:forall _ ((:c GE.ge) (:c Nat) (:c instLENat) 0 ((:c OfNat.ofNat) (:c Nat) (:lit 1) ((:c instOfNatNat) (:lit 1)))) (:forall _ (:forall z (:c Real) (:forall _ ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) 0 ((:c Set.Ico) (:c Real) (:c Real.instPreorder) ((:c... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:forall n :explicit (:c Nat) (:forall _ :explicit (:app (:c GE.ge) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 0) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"intro","sourceEnd":8680,"sourceStart":8675,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"n","sourceEnd":8682,"sourceStart":8681,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hn","sourceEnd":8685,"sourceStart":8683,"tag":"identifier"},{"semanticRole":"scoped_l... | [{"role":"fresh_name","source":"n","source_end":8682,"source_start":8681,"syntax_kind":"ident"},{"role":"fresh_name","source":"hn","source_end":8685,"source_start":8683,"syntax_kind":"ident"},{"role":"fresh_name","source":"hyp_ind","source_end":8693,"source_start":8686,"syntax_kind":"ident"},{"role":"fresh_name","sourc... | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 153 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d2d47b6b9deb9cda3cc2ec110307712dbc2119b4b43d3ffd2a4d8b2fa09631c4 | 3798f1feac075133931064b369406ca393763d2e2352f317404729ae3d628c7e | 39bf6039fcc8b7b8b5a9e5757d8b3424abf29aef223dbfa2efd428de1e3ca2b9 | dfac52100e2e4a78e594dc09fdac14a87f534a4550a0874e053d9b8cd29821ca |
cat-searcher/leandojo-benchmark-4-random | test | 2,075 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have z_nonneg : 0 ≤ z := by calc (0:ℝ) ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := by exact <a>mul_nonneg</a> (<a>pow_nonneg</a> (by norm_num) _) (by norm_num) _ ≤ z := by exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":8711,"sourceStart":8707,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"z_nonneg","sourceEnd":8720,"sourceStart":8712,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"z_nonneg","sourceEnd":8720,"sourceStart":8712,"tag... | [] | [{"source":"0 ≤ z","source_end":8730,"source_start":8723,"syntax_kind":"«term_≤_»"},{"source":"(0:ℝ) ≤ (2:ℝ)^n * max n₀ 2","source_end":8786,"source_start":8752,"syntax_kind":"«term_≤_»"},{"source":"mul_nonneg (pow_nonneg (by norm_num) _) (by norm_num)","source_end":8876,"source_start":8823,"syntax_kind":"Lean.Parser.T... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 154 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e598fa7b0beacbd742b365fe7915f810ba904a575793ae438f268f8ceccb75fd | dfac52100e2e4a78e594dc09fdac14a87f534a4550a0874e053d9b8cd29821ca | b61af8dce9d134a59f4228b062c12ec2c2c3e8f010b4dd3b83af31ebceb198fd | 7ffbdf9aa45af47af3a2288e197a23fb6f1c83d4a150b0377f799f8ed37adaef |
cat-searcher/leandojo-benchmark-4-random | test | 2,076 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have le_2n : <a>Max.max</a> n₀ 2 ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := by nth_rewrite 1 [← <a>one_mul</a> (<a>Max.max</a> n₀ 2)] gcongr exact <a>one_le_pow_of_one_le</a> (by norm_num : (1:ℝ) ≤ 2) _ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":8941,"sourceStart":8937,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"le_2n","sourceEnd":8947,"sourceStart":8942,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"le_2n","sourceEnd":8947,"sourceStart":8942,"tag":"nod... | [] | [{"source":"max n₀ 2 ≤ (2:ℝ)^n * max n₀ 2","source_end":8987,"source_start":8950,"syntax_kind":"«term_≤_»"},{"source":"one_mul (max n₀ 2)","source_end":9043,"source_start":9023,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_le_pow_of_one_le (by norm_num : (1:ℝ) ≤ 2) _","source_end":9130,"source_start":9078,"synta... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 177 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cad4381dae522421040bae935bf796a678f105c7b81e67d51078835304270022 | 7ffbdf9aa45af47af3a2288e197a23fb6f1c83d4a150b0377f799f8ed37adaef | 6a3893d55ff326524eca0ecdaf8957e065c5ebd2d4a2e4aa7cd34a603651f2bc | d71fa490f7740aa08730259cb8613b9b1c647469e031996d6c21053d5bf41a4f |
cat-searcher/leandojo-benchmark-4-random | test | 2,077 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have n₀_le_z : n₀ ≤ z := by calc n₀ ≤ <a>Max.max</a> n₀ 2 := by simp _ ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := le_2n _ ≤ _ := by exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":9143,"sourceStart":9139,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"n₀_le_z","sourceEnd":9153,"sourceStart":9144,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"n₀_le_z","sourceEnd":9153,"sourceStart":9144,"tag":... | [] | [{"source":"n₀ ≤ z","source_end":9166,"source_start":9156,"syntax_kind":"«term_≤_»"},{"source":"n₀ ≤ max n₀ 2","source_end":9207,"source_start":9188,"syntax_kind":"«term_≤_»"},{"source":"_","source_end":9236,"source_start":9235,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"(2:ℝ)^n * max n₀ 2","source_end":9263,"sou... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 189 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bc7ce5f5348b5b4d7520fca4d31744114302ab39e9ec45ed086461eb0721a1df | d71fa490f7740aa08730259cb8613b9b1c647469e031996d6c21053d5bf41a4f | 48e7d9fdde9506768fd1c6e3754d4514c70afa7e5703d04b8527e65909b77971 | 60f28fa94365dea31bb2621c9deb47f64d8eae4264a531807356607b57823713 |
cat-searcher/leandojo-benchmark-4-random | test | 2,078 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have fz_eq_c₂fz : f z = c₂ * f z := hn₀ z n₀_le_z z ⟨by linarith, <a>le_rfl</a>⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":9335,"sourceStart":9331,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"fz_eq_c₂fz","sourceEnd":9348,"sourceStart":9336,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"fz_eq_c₂fz","sourceEnd":9348,"sourceStart":9336,... | [] | [{"source":"f z = c₂ * f z","source_end":9367,"source_start":9351,"syntax_kind":"«term_=_»"},{"source":"hn₀ z n₀_le_z z ⟨by linarith, le_rfl⟩","source_end":9416,"source_start":9371,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 202 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8e0a6c06c02f17612cd4b0d71bb0f8cdd2a38d5629258550c777e6efb6ab3b7a | 60f28fa94365dea31bb2621c9deb47f64d8eae4264a531807356607b57823713 | 83ceb61c29b8e19419b0d452930eba2eff30c4d633db2a2aa3630bedcd5faee1 | 61eb7895eac44c061d1c27379fd4b7f42b3bcf7fb024cb2b425c58b457581346 |
cat-searcher/leandojo-benchmark-4-random | test | 2,079 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have z_to_half_z' : f (1/2 * z) = c₂ * f z := hn₀ z n₀_le_z (1/2 * z) ⟨<a>le_rfl</a>, by linarith⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":9429,"sourceStart":9425,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"z_to_half_z'","sourceEnd":9442,"sourceStart":9430,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"z_to_half_z'","sourceEnd":9442,"sourceStart":9... | [] | [{"source":"f (1/2 * z) = c₂ * f z","source_end":9469,"source_start":9445,"syntax_kind":"«term_=_»"},{"source":"hn₀ z n₀_le_z (1/2 * z) ⟨le_rfl, by linarith⟩","source_end":9526,"source_start":9473,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 208 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 05bacef88b8536236df97bc66f13d67f7c954821b1dad044dc6753a413f5d90f | 61eb7895eac44c061d1c27379fd4b7f42b3bcf7fb024cb2b425c58b457581346 | 2cca52a7bac8e2fcb5c2de1d269fd568059ed6ee9c12cbb56c8edfd63f5691be | dedbb5bbba9f5c57ff9abed55cdc8787fe23678750ddaab076494b01bda98993 |
cat-searcher/leandojo-benchmark-4-random | test | 2,080 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have z_to_half_z : f (1/2 * z) = f z := by rwa [← fz_eq_c₂fz] at z_to_half_z' | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":9539,"sourceStart":9535,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"z_to_half_z","sourceEnd":9551,"sourceStart":9540,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"z_to_half_z","sourceEnd":9551,"sourceStart":954... | [] | [{"source":"f (1/2 * z) = f z","source_end":9571,"source_start":9554,"syntax_kind":"«term_=_»"},{"source":"fz_eq_c₂fz","source_end":9599,"source_start":9587,"syntax_kind":"ident"},{"source":"z_to_half_z'","source_end":9616,"source_start":9604,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 214 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77efbca940e7a4ec71cf1293e929bfec9a100fbce55000e89ffb7ad1a6bd4ffa | dedbb5bbba9f5c57ff9abed55cdc8787fe23678750ddaab076494b01bda98993 | cb49b67f6cf5d8cf903b5c4df10ca39cfa6184fba52b76e7331082bba22dda4c | dbe741b4e12c4c6faadb74e73cd234d00a031b5e7407ef5b605c96d353daf02d |
cat-searcher/leandojo-benchmark-4-random | test | 2,081 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have half_z_to_base : f (1/2 * z) = f (<a>Max.max</a> n₀ 2) := by refine hyp_ind (1/2 * z) ⟨?lb, ?ub⟩ case lb => calc <a>Max.max</a> n₀ 2 ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ 1 * <a>Max.max</a> n₀ 2 := by simp _ ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ n * <a>Max.max</a> n₀ 2 := by gcongr; norm_num _ ≤ _ := by rw [<a>mul_assoc</a>]; gcongr; exa... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":9629,"sourceStart":9625,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"half_z_to_base","sourceEnd":9644,"sourceStart":9630,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"half_z_to_base","sourceEnd":9644,"sourceStar... | [] | [{"source":"f (1/2 * z) = f (max n₀ 2)","source_end":9675,"source_start":9647,"syntax_kind":"«term_=_»"},{"source":"hyp_ind (1/2 * z) ⟨?lb, ?ub⟩","source_end":9731,"source_start":9699,"syntax_kind":"Lean.Parser.Term.app"},{"source":"max n₀ 2 ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ 1 * max n₀ 2","source_end":9830,"source_start":9770... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 219 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 32758c8041c1e005d7b83deba51bfc15ab824b85b9dec7041dc55903e5a4d55a | dbe741b4e12c4c6faadb74e73cd234d00a031b5e7407ef5b605c96d353daf02d | 7743861157da61dc1f05e94d95d4ac5e6ef243219ffa0ae24b3fff56e39de960 | 21abcfffaac9c1264369904d04a4bcee89feba7b6baef2a0314b1e4b5b8ee536 |
cat-searcher/leandojo-benchmark-4-random | test | 2,082 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← z_to_half_z, half_z_to_base] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) (:fv _uniq.64611)) ((:fv _uniq.34812) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (:fv FV13)))) (:arg :explicit 2 (:app (:fv FV0) (:arg :explicit 0 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":10277,"sourceStart":10275,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10279,"sourceStart":10278,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":10282,"sourceSt... | [] | [{"source":"z_to_half_z","source_end":10294,"source_start":10283,"syntax_kind":"ident"},{"source":"half_z_to_base","source_end":10310,"source_start":10296,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 268 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae20d50ee6be1bbad51766e49e6e5d630fff2c843ced448c0b1b91747b62fb25 | 21abcfffaac9c1264369904d04a4bcee89feba7b6baef2a0314b1e4b5b8ee536 | 8c972a4aa1a9a2166cb740f6e2abeabe2765aa76efebe068e5de473df462d6fa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,083 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc (0:ℝ) ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := by exact <a>mul_nonneg</a> (<a>pow_nonneg</a> (by norm_num) _) (by norm_num) _ ≤ z := by exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) (:fv _uniq.64611)) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"calc","sourceEnd":8751,"sourceStart":8747,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"(","sourceEnd":8753,"sourceStart":8752,"tag":"atom"},{"children":[{"source":"0","sourceEnd":8754,"sourceStart":8753,"tag":"atom"}],"kind":"num","source":"0","sourceEnd":8754,"so... | [] | [{"source":"(0:ℝ) ≤ (2:ℝ)^n * max n₀ 2","source_end":8786,"source_start":8752,"syntax_kind":"«term_≤_»"},{"source":"mul_nonneg (pow_nonneg (by norm_num) _) (by norm_num)","source_end":8876,"source_start":8823,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":8896,"source_start":8895,"syntax_kind":"Lean.P... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 156 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7df12a34c57299485d549b1ae726350b043045a6804330b2bf6ed85cf704ba80 | 06ed14a8f38e4bc86debbc993e7607c89baebffe04624d63e946100359637bec | 0e60f24a75365dfe03204bb329f78f1e83f6c18ee6d57c9cc968f097a2f95e3c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,084 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>mul_nonneg</a> (<a>pow_nonneg</a> (by norm_num) _) (by norm_num) | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | ((:c LE.le) (:c Real) (:c Real.instLE) ((: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 HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":8822,"sourceStart":8817,"tag":"atom"},{"children":[{"name":"mul_nonneg","semanticRole":"global","source":"mul_nonneg","sourceEnd":8833,"sourceStart":8823,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":8835,"source... | [] | [{"source":"mul_nonneg (pow_nonneg (by norm_num) _) (by norm_num)","source_end":8876,"source_start":8823,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 159 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 59733e18b9038d3a5da6e01cdbd5cc731dbf3a4824b28613747686efe67685a3 | 30fc12f2d84f63f0957d10edeff75bb164bfea84323c0d4346bbbee964365cd1 | 8f9b977717da7d5cc971a0e5d7260bdb1964c36e381138a03dac07109742b24e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,085 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c OrderedSemiring.toPartialOrder) (:c Real) (:c Real.orderedSemiring)))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MonoidWithZero.toZero) (:c Real) ((:c Semiring.toMonoidWithZero) (:c Real) ((:c ... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":8858,"sourceStart":8850,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 164 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bed996e14086ee460ea2f6628ed92f47678ae6e6c9a71309d18522b8dd431e15 | 82873527103c0da24d9ca5e0020320395d2f5641f978a7472f275dffced7a792 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,086 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) ((:c MulZeroClass.toZero) (:c Real) ((:c NonUnitalNonAssocSemiring.toMulZeroClass) (:c Real) ((:c NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring) (:c Real) ((:c NonUn... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":8875,"sourceStart":8867,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 169 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9eb9d9e94fdfa8281306338dd02095f51552148d3ffff95505ab56988fbf8da7 | df9636988511652ea6225fb5baba0a6ed1aa02955461a0eb9fc5d8bc7a169ebb | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,087 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
⊢... | ((: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 HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeas... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"exact_mod_cast","sourceEnd":8923,"sourceStart":8909,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hz","sourceEnd":8926,"sourceStart":8924,"tag":"identifier"},{"source":".","sourceEnd":8927,"sourceStart":8926,"tag":"atom"},{"... | [] | [{"source":"hz.1","source_end":8928,"source_start":8924,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 174 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4db6287ebe0f42e6c301561ad96f2fe0be33c955ab64548eb1b8513dc65566d7 | 142d1eee10bb4e0aa47f6d5b91d57fa6b2dd6b2e240e8ed6581f2dc09aa81fdd | 31812a125fd3d2935595b2bac7b5c8dfd589b759b5976ec215fb218f44c2ed0b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,088 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | nth_rewrite 1 [← <a>one_mul</a> (<a>Max.max</a> n₀ 2)] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"nth_rewrite","sourceEnd":9015,"sourceStart":9004,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"1","sourceEnd":9017,"sourceStart":9016,"tag":"atom"}],"kind":"num","source":"1","sourceEnd":9017,"sourceStart":9016,"tag":"node"},{"children":[{"source":"... | [] | [{"source":"one_mul (max n₀ 2)","source_end":9043,"source_start":9023,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 179 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ea24908579579fe86ed0401548d2aefeb9c37c057769d329c9ef86421f97f6ef | 64eff2c6fad8e6c6a77c58a489cfef9def14612d98d6d28fcfefbd8fb001eb61 | 09e3294165815347a36f3842ecc3297887c152e9a0cf2914ce1e36d82ed08d73 | c4e31480aa204b2d5a7002a6d5005d587ad79a43005676b7dfc78321f34bf5e1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,089 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c MulOneClass.toMul) (:c Real) ((:c MulZeroOneClass.toMulOneClass) (:c Real) ((:c NonAssocSemiring.toMulZeroOneClass) (:c Real) ((:c Semiring.toNonAssocSemiring) (:c Real) (:c Real.semiring)))))) ((:c OfNat.... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":9061,"sourceStart":9055,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":9061,"sourceStart":9055,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 182 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d25ee0494d87bdc169c89918e6138a323080ff96c23c248883e51efca3414b87 | c4e31480aa204b2d5a7002a6d5005d587ad79a43005676b7dfc78321f34bf5e1 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d5a2fcf1cc1667ea693a4c2947b7c1d49ad5cc42a6097f44fd02ee53cbd446f7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,090 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>one_le_pow_of_one_le</a> (by norm_num : (1:ℝ) ≤ 2) _ | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) ((:c MulOneClass.toOne) (:c Real) ((:c MulZeroOneClass.toMulOneClass) (:c Real) ((:c NonAssocSemiring.toMulZeroOneClass) (:c Real) ((:c Semiring.toNonAssocSemiring) (:c Real) (:c... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":9077,"sourceStart":9072,"tag":"atom"},{"children":[{"name":"one_le_pow_of_one_le","semanticRole":"global","source":"one_le_pow_of_one_le","sourceEnd":9098,"sourceStart":9078,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":9100,"sourceStart":9099,"tag":"... | [] | [{"source":"one_le_pow_of_one_le (by norm_num : (1:ℝ) ≤ 2) _","source_end":9130,"source_start":9078,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 183 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44a31540341c1fd3776fc62c572bc8a83f3b5ff4737203260b9fe6ad221e8560 | d5a2fcf1cc1667ea693a4c2947b7c1d49ad5cc42a6097f44fd02ee53cbd446f7 | b8e204a7b0842d48ce43e3e9748ecbe03edbf0646e5697e6dd091fb315272641 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,091 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) (:c Real.instOne))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0)))))... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"norm_num","sourceEnd":9111,"sourceStart":9103,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","so... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 186 | exact | true | 1 | 15 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3cbbab43c3df926606e5a03f619280dbf8915a06ba5fdc334c06fb7b8888621a | fe990c2361904b5588ffa9f90ee94f324b044d9bcd28028b44500f39e1eafc11 | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,092 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc n₀ ≤ <a>Max.max</a> n₀ 2 := by simp _ ≤ (2:ℝ)^n * <a>Max.max</a> n₀ 2 := le_2n _ ≤ _ := by exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.47240) (:fv _uniq.64611)) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 FV8)) (:arg :explicit 3 (:fv FV13))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"calc","sourceEnd":9187,"sourceStart":9183,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":8,"semanticRole":"local","source":"n₀","sourceEnd":9192,"sourceStart":9188,"tag":"identifier"},{"source":"≤","sourceEnd":9196,"sourceStart":9193,"tag":"atom"},{"children":[{"name":"Max.... | [] | [{"source":"n₀ ≤ max n₀ 2","source_end":9207,"source_start":9188,"syntax_kind":"«term_≤_»"},{"source":"_","source_end":9236,"source_start":9235,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"(2:ℝ)^n * max n₀ 2","source_end":9263,"source_start":9241,"syntax_kind":"«term_*_»"},{"source":"le_2n","source_end":9272,"sour... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 191 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5fc26e03e1b73852399df26bc0e7bfbf29dae082542f12cbcacbc1a5e1fa51be | b634b189ecd46c7ce364f52c517369bacae2a5e364d2331dcbe317e58e130903 | 637f2d4fc9fed907554b0b7441e11658bdabab524ef0daecc0b19d12ba0ebd7e | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,093 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) (:c Real.instLE) (:fv _uniq.47240) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 FV8)) (:arg :explicit 3 (:app (:c Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9218,"sourceStart":9214,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 194 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48b3045b81f15817f37e75ef8e64999c62901e34f59bd09ef367e928715cc8eb | 33b0d5a0bee26567dd6f2dc2f1f6007035965122c219557df5f810bdfa56609a | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,094 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((: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 HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeas... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"exact_mod_cast","sourceEnd":9317,"sourceStart":9303,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hz","sourceEnd":9320,"sourceStart":9318,"tag":"identifier"},{"source":".","sourceEnd":9321,"sourceStart":9320,"tag":"atom"},{"... | [] | [{"source":"hz.1","source_end":9322,"source_start":9318,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 199 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 55c0875f4a2a73e6a3dceabaa12bc2aeb9cd6de224dbeef1e0ebd55948853cc3 | 237ea5428a4c85648ca4f76f183fb30bb632845110beccbec4d4d1f8ff8114bc | 31812a125fd3d2935595b2bac7b5c8dfd589b759b5976ec215fb218f44c2ed0b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,095 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((: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 HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":9405,"sourceStart":9397,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 205 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d76f50e5c854483775b2e8140c6093408735ed5ebecd00eb57c6267d284f50e3 | 4c234967d44cb6702d648454c7a2376e9ce321826fb02386a29a0eb0adab3603 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,096 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | linarith | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((: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 HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"linarith","sourceEnd":9523,"sourceStart":9515,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kin... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 211 | exact | true | 1 | 18 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c8400d2883819b30d41627794e419bb86eb381b87cb9eda236b89a0c38b172d | f9edd5aad043b42c4ad62ebccf01cfbfdcf8ef8fdd12a8c4888bc78ed3870510 | 2c587e2f140ae41533b8e0551e8c940d4f70fbd4b1f4245ea1c9efcde110c9af | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,097 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← fz_eq_c₂fz] at z_to_half_z' | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:fv _uniq.34812) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (: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 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rwa","sourceEnd":9581,"sourceStart":9578,"tag":"atom"},{"children":[{"source":"[","sourceEnd":9583,"sourceStart":9582,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9586,"sourceStart":9583,"tag":"atom"}],"kind":"token.«← »","source":"←","... | [] | [{"source":"fz_eq_c₂fz","source_end":9599,"source_start":9587,"syntax_kind":"ident"},{"source":"z_to_half_z'","source_end":9616,"source_start":9604,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 216 | exact | true | 1 | 19 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 07160dce5b08ee355c0a06d43b9de4aabb57c381c85f3a2e924337ed0f66d577 | 4e9b284c67f78609eeed6faa75a384bcb1ea89f61d60bb61619b0aaeae2fe0f5 | 62d22030063574e92b688a068499ea5cd7bb41863d41e95169c21ff76ffff0fe | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,098 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hyp_ind (1/2 * z) ⟨?lb, ?ub⟩ | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | case lb
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max... | ((:c Eq) (:c Real) ((:fv _uniq.34812) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:fv FV0) (:arg :explicit 0 (: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 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"refine","sourceEnd":9698,"sourceStart":9692,"tag":"atom"},{"children":[{"contextIndex":12,"semanticRole":"local","source":"hyp_ind","sourceEnd":9706,"sourceStart":9699,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":9708,"sourceStart":9707,"tag":"atom"},{"children":[{"chi... | [] | [{"source":"hyp_ind (1/2 * z) ⟨?lb, ?ub⟩","source_end":9731,"source_start":9699,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 221 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f70aec385bd029f916e0753352a4a169e561c4a2b4cda03b4612b553425351c9 | efbb10e54c3fd29f41ff6a5da5dedc506bfb2e85a2900bf88249692b25cfaaa2 | 4a0a8211323567d834f5c6e4c9532ae1e88d72fae29ede2aedfdc9ac8ef2f23f | 6af1f3c9cca3a485990fdda048653204b4127aa0396a957fede72859accd3ec6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,100 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | case ub => have h₁ : (2:ℝ)^n = ((1:ℝ)/(2:ℝ)) * (2:ℝ)^(n+1) := by rw [<a>one_div</a>, <a>pow_add</a>, <a>pow_one</a>] ring rw [h₁, <a>mul_assoc</a>] gcongr exact_mod_cast hz.2 | case ub
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"case","sourceEnd":10036,"sourceStart":10032,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"ub","sourceEnd":10039,"sourceStart":10037,"tag":"identifier"}],"kind":"Lean.binderIdent","source":"ub","sourceEnd":10039,"sourceStart":10037,"tag":"node"},{"children":[],"kind":"null","sou... | [] | [{"source":"(2:ℝ)^n = ((1:ℝ)/(2:ℝ)) * (2:ℝ)^(n+1)","source_end":10112,"source_start":10067,"syntax_kind":"«term_=_»"},{"source":"one_div","source_end":10144,"source_start":10137,"syntax_kind":"ident"},{"source":"pow_add","source_end":10153,"source_start":10146,"syntax_kind":"ident"},{"source":"pow_one","source_end":101... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 250 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bae75867cec8db204dabb7abc4c42af6ee8a5e6ee0f692515418592bae6b26b5 | bd996cce34fe89af952136be059d8edf86bc0a9397718c9a05c4c74b5c08bbde | d49dddbfbdb0d8c5bd74195d0c9573cdfe99eff408c78530ba1f1fbaf6dacf1f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,101 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc <a>Max.max</a> n₀ 2 ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ 1 * <a>Max.max</a> n₀ 2 := by simp _ ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ n * <a>Max.max</a> n₀ 2 := by gcongr; norm_num _ ≤ _ := by rw [<a>mul_assoc</a>]; gcongr; exact_mod_cast hz.1 | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) (... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"calc","sourceEnd":9769,"sourceStart":9765,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"name":"Max.max","semanticRole":"global","source":"max","sourceEnd":9773,"sourceStart":9770,"tag":"identifier"},{"children":[{"contextIndex":8,"sema... | [] | [{"source":"max n₀ 2 ≤ ((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ 1 * max n₀ 2","source_end":9830,"source_start":9770,"syntax_kind":"«term_≤_»"},{"source":"_","source_end":9867,"source_start":9866,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"((1:ℝ)/(2:ℝ)) * (2:ℝ) ^ n * max n₀ 2","source_end":9916,"source_start":9872,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 224 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b50f4b9d47dc4822f2d3ae7056aedc779c512f0e731540bbaf273e53caf7cf3f | 39575b4d19e227fe1ac6a32eadb04469d82052016cc0aa40106faf9d86882d29 | d55ad75824c7ad348b4a44c7ac322a103d31a3997a8a64b422831df1110474aa | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,102 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Max.max) (:c Real) ((:c LinearOrderedRing.toMax) (:c Real) (:c Real.instLinearOrderedRing)) (:fv _uniq.47240) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 Max.max) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Max) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV8)) (:arg :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":9841,"sourceStart":9837,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 229 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f19c41efa9033be547e1062b77679fb4883027875abbfdb5be91902d52653009 | f511e8c8fa885c40ffb7ce31aac89bac700ba44a60ed6b1c26878d08f75f1d7d | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,103 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | case h.h.ha
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) *... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv)... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":9929,"sourceStart":9923,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":9929,"sourceStart":9923,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 236 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e7616eb166d79ba4365f73ebaa7a1342c107f6bd922918ec7f9435452d868d9 | e6461eecc5fbbb09ea5e13b604fd897ca9d6d26ef6647ef6bcad817096e1ba63 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | e83c97e73169d53aec704447ac5d9d56289861d25e652de1f31e8bab4602098e |
cat-searcher/leandojo-benchmark-4-random | test | 2,104 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_num | case h.h.ha
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) *... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c OrderedSemiring.toPartialOrder) (:c Real) (:c Real.orderedSemiring)))) ((:c OfNat.ofNat) (:c Real) (:lit 1) ((:c One.toOfNat1) (:c Real) ((:c Semiring.toOne) (:c Real) ((:c OrderedSemiring.toSemiring) (:c Real) (:c Real.ord... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"norm_num","sourceEnd":9939,"sourceStart":9931,"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"}],"kind":"Mathlib... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 238 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d26a1397c6df39d31f8867a1bf153e22fb57bb8f076dbf0c5210fc01323579df | e83c97e73169d53aec704447ac5d9d56289861d25e652de1f31e8bab4602098e | 7c64df8336d5a348b5f037e1d91facb19224fdef00e798d5c48c07a184602a59 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,105 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>mul_assoc</a>] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((: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 HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv)... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":9980,"sourceStart":9978,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":9982,"sourceStart":9981,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"mul_assoc","semantic... | [] | [{"source":"mul_assoc","source_end":9991,"source_start":9982,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 243 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f164e58b768ac0bff088f5b18d661f36afe88bf74faca4e8879883022c97451a | 100f0e0e7aa789030c53001ddfa72eb58eec1d6abc36cddf539016286b1422ff | 8ebbf76e58d41daf96b6a2b588d6f47da32eb2c9832c6aed00aeb49f558bf96c | d782362448f00c0e72128e84e2029063d2212238d0bb74b85f6056510dae84be |
cat-searcher/leandojo-benchmark-4-random | test | 2,106 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c Semigroup.toMul) (:c Real) (:c Real.instSemigroup))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c ... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":10000,"sourceStart":9994,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":10000,"sourceStart":9994,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 247 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fbbe41954a197d386635ea57078d33a38c12d8070326c9752a78602d7d3e5a38 | d782362448f00c0e72128e84e2029063d2212238d0bb74b85f6056510dae84be | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | aeda7b3eb4ad6b0f5fa78a549fef23bd4255154d8d37dad4d8dad03adcd9cd19 |
cat-searcher/leandojo-benchmark-4-random | test | 2,107 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hz.1 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max ... | ((: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 Semigroup.toMul) (:c Real) (:c Real.instSemigroup))) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c ... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact_mod_cast","sourceEnd":10016,"sourceStart":10002,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hz","sourceEnd":10019,"sourceStart":10017,"tag":"identifier"},{"source":".","sourceEnd":10020,"sourceStart":10019,"tag":"atom"},{"children":[{"source":"1","sourceE... | [] | [{"source":"hz.1","source_end":10021,"source_start":10017,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 249 | exact | true | 1 | 20 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ae310b85b345aecd15429145a4b8d19a0f255fc7c5d9c65c75347505a39ee6e0 | aeda7b3eb4ad6b0f5fa78a549fef23bd4255154d8d37dad4d8dad03adcd9cd19 | 31812a125fd3d2935595b2bac7b5c8dfd589b759b5976ec215fb218f44c2ed0b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,108 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₁ : (2:ℝ)^n = ((1:ℝ)/(2:ℝ)) * (2:ℝ)^(n+1) := by rw [<a>one_div</a>, <a>pow_add</a>, <a>pow_one</a>] ring | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"have","sourceEnd":10059,"sourceStart":10055,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₁","sourceEnd":10064,"sourceStart":10060,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₁","sourceEnd":10064,"sourceStart":10060,"tag":"nod... | [] | [{"source":"(2:ℝ)^n = ((1:ℝ)/(2:ℝ)) * (2:ℝ)^(n+1)","source_end":10112,"source_start":10067,"syntax_kind":"«term_=_»"},{"source":"one_div","source_end":10144,"source_start":10137,"syntax_kind":"ident"},{"source":"pow_add","source_end":10153,"source_start":10146,"syntax_kind":"ident"},{"source":"pow_one","source_end":101... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 254 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 743a544051142707b842e8b3acf0bb0a6dae95bbc5902b6774ae3d2bed646de7 | 478eda521951c6107cc1a01406138d333af47d1c01412287319ee40241f62db7 | 471c474ef0c0a174de4f3a6b24a4137a5b5b39d4c9e0338ff2c1f990ace5d3a6 | b4a9dc972520d3ff0a36c00760a7b47ef03cb6658e91cfc619697e764809c79e |
cat-searcher/leandojo-benchmark-4-random | test | 2,109 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [h₁, <a>mul_assoc</a>] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":10197,"sourceStart":10195,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10199,"sourceStart":10198,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":21,"seman... | [] | [{"source":"h₁","source_end":10203,"source_start":10199,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":10214,"source_start":10205,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 262 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50920de2c03da434027bcab2354ab119b3ef2615f092e9190faef7b3327ed8e9 | b4a9dc972520d3ff0a36c00760a7b47ef03cb6658e91cfc619697e764809c79e | 4f913a6bccbbc718059ac3406e90b3eb4687c7a42ea2290d6c14229e067d1bfa | 655aa03ef0a8a079332601b7ec1264c2b0c4071d84e7da61476b68ee5617a04a |
cat-searcher/leandojo-benchmark-4-random | test | 2,110 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | case bc
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c Of... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 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.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"gcongr","sourceEnd":10234,"sourceStart":10228,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":10234,"sourceStart":10228,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 266 | exact | true | 1 | 21 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 10a13b93094880b4e1f0825e1a87f4cd45a062dd10e01cfeb90ec819ef512daa | 655aa03ef0a8a079332601b7ec1264c2b0c4071d84e7da61476b68ee5617a04a | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | caa6dfed72a4d41631484810764ecd68d9cee4286c45e6d8724b88cfdef18840 |
cat-searcher/leandojo-benchmark-4-random | test | 2,111 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hz.2 | case bc
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) (:fv _uniq.64611) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) ((:c Semigroup.toMul) (:c Real) (:c Real.instSemigroup))) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatP... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV13)) (:arg :explicit 3 (: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 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact_mod_cast","sourceEnd":10261,"sourceStart":10247,"tag":"atom"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"hz","sourceEnd":10264,"sourceStart":10262,"tag":"identifier"},{"source":".","sourceEnd":10265,"sourceStart":10264,"tag":"atom"},{"children":[{"source":"2","sourceE... | [] | [{"source":"hz.2","source_end":10266,"source_start":10262,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 267 | exact | true | 1 | 21 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de7e736308e6994aeae779677023fd805673da81bf145b875ebfd5b775e5986b | caa6dfed72a4d41631484810764ecd68d9cee4286c45e6d8724b88cfdef18840 | 2f38a66e6018cd3d6fe5bf2a4fb75d6683c34deedeb559da0c9d2513750cd670 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,112 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>one_div</a>, <a>pow_add</a>, <a>pow_one</a>] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"rw","sourceEnd":10135,"sourceStart":10133,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10137,"sourceStart":10136,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"one_div","semant... | [] | [{"source":"one_div","source_end":10144,"source_start":10137,"syntax_kind":"ident"},{"source":"pow_add","source_end":10153,"source_start":10146,"syntax_kind":"ident"},{"source":"pow_one","source_end":10162,"source_start":10155,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 256 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 23ebf63011abc88c9afdad1cbeb619401786b26c9273f9cc40c2b864b07b741c | 96d089dc53762e6b725ebeec433cfb9b79a2533b5b368d0148e9ddf39c3a762f | 48db81e6b3b00728a26af0b47cbadd5831088a217303af5d2030d76a231670cb | 12a98b7120756a212875a91ea879c6a7ec923a7a325d8455628500381b174307 |
cat-searcher/leandojo-benchmark-4-random | test | 2,113 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
heq : c₁ = c₂
n₀ : ℝ
hn₀ : ∀ b ≥ n₀, ∀ u ∈ Set.Icc (1 / 2 * b) b, f u = c₂ * f b
n : ℕ
hn : n ≥ 1
hyp_ind : ∀ z ∈ Set.Ico (max n₀ 2) (2 ^ n * max n₀ 2), f z = f (max n₀ 2)
z : ℝ
hz : z ∈ Set.Ico (2 ^ n * max n₀ 2) (2 ^ (n + 1) * max n₀ 2)
z... | ((:c Eq) (:c Real) ((:c HPow.hPow) (:c Real) (:c Nat) (:c Real) ((:c instHPow) (:c Real) (:c Nat) ((:c Monoid.toNatPow) (:c Real) (:c Real.instMonoid))) ((:c OfNat.ofNat) (:c Real) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Real) (:lit 2) (:c Real.instNatCast) ((:c instNatAtLeastTwo) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Nat)) (:arg :explicit 2 (:c Real)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"ring","sourceEnd":10182,"sourceStart":10178,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":10182,"sourceStart":10178,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 261 | exact | true | 1 | 20 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4ebff935bf48a4a70ed08ce6c44706c34eeb2ead5374444780ea1dd74462664 | 12a98b7120756a212875a91ea879c6a7ec923a7a325d8455628500381b174307 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,114 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Or.inl</a> <| by filter_upwards [hc] with _ hc; simpa only [hc] | case intro.inl
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
hpos : 0 ≤ c
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":10401,"sourceStart":10396,"tag":"atom"},{"children":[{"name":"Or.inl","semanticRole":"constructor","source":"Or.inl","sourceEnd":10408,"sourceStart":10402,"tag":"identifier"},{"source":"<|","sourceEnd":10411,"sourceStart":10409,"tag":"ato... | [] | [{"source":"Or.inl <| by filter_upwards [hc] with _ hc; simpa only [hc]","source_end":10461,"source_start":10402,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 276 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d57d489edd5554c90f784ee1af2519855d26dd917fa8ad7efaf73010be80d524 | 468f8ff60d20d3a56d998e0287cfa18608dba787026e4ffabec14ff93802beb1 | 417bfc0b1bbed33fed4d0d156a91a36fae86b627ee2abbc665cac46601eed22d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,115 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hc] with _ hc | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
hpos : 0 ≤ c
⊢ ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc✝ : ∀ᶠ (x : ℝ) in atTop, f x = c
hpos : 0 ≤ c
a✝ : ℝ
hc : f a✝ = c
⊢ 0 ≤ f a✝ | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"filter_upwards","sourceEnd":10429,"sourceStart":10415,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10431,"sourceStart":10430,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hc","sourceEnd":10433,"sourceStart":10431,"tag":"identifier"}],"kind":"null","source... | [] | [{"source":"hc","source_end":10433,"source_start":10431,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 283 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0c06f91926a5dffa0a25ad34f9ab7cac59458ac3f06f5070d4ca7c2090a8cb85 | 697e298f08575efce6fb18963807d6d53719aaa9a78740e1bd7e80a65fa954db | f2e0c1bd77a88e70409d4d3d9dbed5057ec031f3a1100501d66f5e8cc0663496 | f9def9452a2d4ea863acfdf730c85700931dc2e601a4b042a10bca97b1c4777b |
cat-searcher/leandojo-benchmark-4-random | test | 2,116 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [hc] | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc✝ : ∀ᶠ (x : ℝ) in atTop, f x = c
hpos : 0 ≤ c
a✝ : ℝ
hc : f a✝ = c
⊢ 0 ≤ f a✝ | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) (:fv _uniq.100613))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"simpa","sourceEnd":10451,"sourceStart":10446,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"ch... | [] | [{"source":"hc","source_end":10460,"source_start":10458,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 285 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 33e38eeccd864bab7adc0ed436f998295a688577ddc5a699eaedacd4d02ccb79 | f9def9452a2d4ea863acfdf730c85700931dc2e601a4b042a10bca97b1c4777b | 185bb5ca3faf760abdaa744848ed7f019989d87730c79fd89d139b1a61f7dac0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,117 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | right | case intro.inr
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
⊢ (∀ᶠ (x : ℝ) in atTop, 0 ≤ f x) ∨ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case intro.inr.h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
⊢ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | ((:c Or) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:fv _uniq.34812) 0))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) ((:c Filter.Eventually) (:c Real) (:lambda x (:c Re... | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Or) (:arg :explicit 0 (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (:c Real) (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"right","sourceEnd":10491,"sourceStart":10486,"tag":"atom"}],"kind":"Lean.Parser.Tactic.right","source":"right","sourceEnd":10491,"sourceStart":10486,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 289 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74235a10f532ec64668d76b4c73eb4a0f1b189db2bbaa2471f2f0630aa595e18 | ccc93d1cdef0dbe75e7a355b018c08462006d9028d4b69b2392ade7652062277 | 27042f4e6eca7d0b2a7ee4026df2ecfa51d3339e6d122aa099118ecd8563bad9 | fb85b96d399b31183a7ced368e8dd5995b4d2d969b7b3ed32779ac9687bd2cb6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,118 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | filter_upwards [hc] with x hc | case intro.inr.h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
⊢ ∀ᶠ (x : ℝ) in atTop, f x ≤ 0 | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc✝ : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
x : ℝ
hc : f x = c
⊢ f x ≤ 0 | ((:c Filter.Eventually) (:c Real) (:lambda x (:c Real) ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) 0) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))) ((:c Filter.atTop) (:c Real) (:c Real.instPreorder))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (:app (:c Filter.Eventually) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lambda x :explicit (: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 FV0) (:arg :explicit 0 0))) (:arg :explicit 3 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"filter_upwards","sourceEnd":10512,"sourceStart":10498,"tag":"atom"},{"children":[{"source":"[","sourceEnd":10514,"sourceStart":10513,"tag":"atom"},{"children":[{"contextIndex":10,"semanticRole":"local","source":"hc","sourceEnd":10516,"sourceStart":10514,"tag":"identifier"}],"kind":"null","source... | [] | [{"source":"hc","source_end":10516,"source_start":10514,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 290 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 404d574eaf8f0f2e2ab68da104484322bf4b49e42f77ae694ce9f188613d5aee | fb85b96d399b31183a7ced368e8dd5995b4d2d969b7b3ed32779ac9687bd2cb6 | 2edcb206f2415a4ec541166e0d1166dda7570d6e0b7624fdad061ffb9983476f | 0fb7fb76886710fb98d6632167a8558580aa90a78f9172582431501bddfae3b6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,119 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_of_lt</a> <| by simpa only [hc] | case h
f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc✝ : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
x : ℝ
hc : f x = c
⊢ f x ≤ 0 | ((:c LE.le) (:c Real) (:c Real.instLE) ((:fv _uniq.34812) (:fv _uniq.100782)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 FV0) (:arg :explicit 0 (:fv FV12)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"source":"exact","sourceEnd":10539,"sourceStart":10534,"tag":"atom"},{"children":[{"name":"le_of_lt","semanticRole":"global","source":"le_of_lt","sourceEnd":10548,"sourceStart":10540,"tag":"identifier"},{"source":"<|","sourceEnd":10551,"sourceStart":10549,"tag":"atom"},{"children":[{"source":"by","sourceE... | [] | [{"source":"le_of_lt <| by simpa only [hc]","source_end":10570,"source_start":10540,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 291 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 039c782cd1e0859bcb6122f6d2374051560fb63f2bd947fef2fba7ec342d61e0 | 0fb7fb76886710fb98d6632167a8558580aa90a78f9172582431501bddfae3b6 | 735ff0496644b2e4486fd99e2658b63fa0a4ef52f2a9adb73f85aba40f3fdab9 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,120 | AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos | Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [hc] | f : ℝ → ℝ
hf : GrowsPolynomially f
c₁ : ℝ
left✝¹ : c₁ > 0
c₂ : ℝ
left✝ : c₂ > 0
h : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)
heq : c₁ = c₂
c : ℝ
hc✝ : ∀ᶠ (x : ℝ) in atTop, f x = c
hneg : c < 0
x : ℝ
hc : f x = c
⊢ f x < 0 | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) (:c Real.instPreorder)) ((:fv _uniq.34812) (:fv _uniq.100782)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"f","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"hf","sexp":"((:c AkraBazziRecurrence.GrowsPolynomially) (:fv _uniq.34812))"},{"name":"c₁","sexp":"(:c Real)"},{"name":"left✝¹","sexp":"((:c GT.gt) (:c Real) (:c Real.instLT) (:fv _uniq.35475) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Rea... | (: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 (:fv FV0) (:arg :explicit 0 (:fv FV12)))) (:arg :explicit 3 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:in... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"name":"f","sexp":"(:forall _ :explicit (:c Real) (:c Real))"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"name":"hf","sexp":"(:app (:c AkraBa... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":10560,"sourceStart":10555,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind... | [] | [{"source":"hc","source_end":10569,"source_start":10567,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.34812","is_instance":false,"is_let":false,"user_name":"f"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.34994","is_instance":false,"is_let":false,"user_name":"hf"},{"binder_role":":explicit","context_index":3,"internal_name":"_u... | 14 | 294 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd0aa48b54b7528318b9de8cbcc357400bb72adae76584fe9dd48357f0fc93df | a3caf8f5202720034c1db80cc96b4246e0a3bd2dcbd0d54a993c6a490fc8ffb5 | 185bb5ca3faf760abdaa744848ed7f019989d87730c79fd89d139b1a61f7dac0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,121 | IsBoundedBilinearMap.fderivWithin | Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>DifferentiableAt.fderivWithin</a> (h.differentiableAt p) hxs] | 𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ : NormedSpac... | 𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ : NormedSpac... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.62424) (:fv _uniq.62424) ((:c DivisionSemiring.toSemiring) (:fv _uniq.62424) ((:c Semifield.toDivisionSemiring) (:fv _uniq.62424) ((:c Field.toSemifield) (:fv _uniq.62424) ((:c NormedField.toField) (:fv _uniq.62424) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.624... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.62424))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.62430))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.62424) (:fv _uniq.62430) ((:c Nontriv... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62424","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.62427","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFiel... | {"children":[{"source":"rw","sourceEnd":4571,"sourceStart":4569,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4573,"sourceStart":4572,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"Differe... | [] | [{"source":"DifferentiableAt.fderivWithin (h.differentiableAt p) hxs","source_end":4629,"source_start":4573,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62424","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.62427","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"inter... | 34 | 4 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | de9dc4a72340f8434dd4c5a2d737b839f3307028d17c1ccb603843942983cbd5 | 9626eecaa430beb27f1f3e695492921228b6faf29c78123c80b51d5f7cd5fef6 | 6e8b7f2ba0215a4b39b1638574ea4a8f6b452f8a6380bd196c9a577dfb7d8c51 | 1166928a2b29d12fa5c9eabb3445e8b811aec1c89ce28674ba9fd5284f2ce68d |
cat-searcher/leandojo-benchmark-4-random | test | 2,122 | IsBoundedBilinearMap.fderivWithin | Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact h.fderiv p | 𝕜 : Type u_1
inst✝⁸ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
F : Type u_3
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
G : Type u_4
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
G' : Type u_5
inst✝¹ : NormedAddCommGroup G'
inst✝ : NormedSpac... | ((:c Eq) ((:c ContinuousLinearMap) (:fv _uniq.62424) (:fv _uniq.62424) ((:c DivisionSemiring.toSemiring) (:fv _uniq.62424) ((:c Semifield.toDivisionSemiring) (:fv _uniq.62424) ((:c Field.toSemifield) (:fv _uniq.62424) ((:c NormedField.toField) (:fv _uniq.62424) ((:c NontriviallyNormedField.toNormedField) (:fv _uniq.624... | [{"name":"𝕜","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁸","sexp":"((:c NontriviallyNormedField) (:fv _uniq.62424))"},{"name":"E","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝⁷","sexp":"((:c NormedAddCommGroup) (:fv _uniq.62430))"},{"name":"inst✝⁶","sexp":"((:c NormedSpace) (:fv _uniq.62424) (:fv _uniq.62430) ((:c Nontriv... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c ContinuousLinearMap) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62424","is_instance":false,"is_let":false,"name":"𝕜","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.62427","is_instance":true,"is_let":false,"name":"inst✝⁸","sexp":"(:app (:c NontriviallyNormedFiel... | {"children":[{"source":"exact","sourceEnd":4638,"sourceStart":4633,"tag":"atom"},{"children":[{"source":"h.fderiv","sourceEnd":4647,"sourceStart":4639,"tag":"identifier"},{"children":[{"contextIndex":33,"semanticRole":"local","source":"p","sourceEnd":4649,"sourceStart":4648,"tag":"identifier"}],"kind":"null","source":"... | [] | [{"source":"h.fderiv p","source_end":4649,"source_start":4639,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.62424","is_instance":false,"is_let":false,"user_name":"𝕜"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.62427","is_instance":true,"is_let":false,"user_name":"inst✝⁸"},{"binder_role":":implicit","context_index":2,"inter... | 34 | 7 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c7b81a621d3cafba2c79826284a09728085407c67d283736bb451342fca1f796 | 1166928a2b29d12fa5c9eabb3445e8b811aec1c89ce28674ba9fd5284f2ce68d | cb01143ab30e131d972f7c5c8c49a565f08018f776264765bc62d92f5e724b98 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,123 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>lt_trichotomy</a> θ.toReal 0 with (h | h | h) | θ : Angle
⊢ 0 ≤ θ.toReal ↔ 0 ≤ θ.sign | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.ins... | [{"name":"θ","sexp":"(:c Real.Angle)"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"rcases","sourceEnd":40935,"sourceStart":40929,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"lt_trichotomy","semanticRole":"global","source":"lt_trichotomy","sourceEnd":40949,"sourceStart... | [] | [{"source":"lt_trichotomy θ.toReal 0","source_end":40961,"source_start":40936,"syntax_kind":"Lean.Parser.Term.app"},{"source":"(h | h | h)","source_end":40978,"source_start":40967,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.paren"},{"source":"⟨fun hn => False.elim (h.not_le hn), fun hn => ?_⟩","source_end":41045,"sourc... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"}] | 311 | 2 | branch_opener | false | 1 | 1 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 42ec5c2698614f8d559cf0857bd99510a82637e7fcd0c416341deb9c8b009dbf | deda6fed977552ad05fefbe62eab1051b4d5c928a833744ae080f8db4a42e943 | 437a4fbaf6fa5946c302ec9180bd5cf80587511af434c5744353aa8b6dae3e5b | 35dbd05fec700ab4ee6bee4fa629a859403bbbdb824fa20951676ce6388873ac | |
cat-searcher/leandojo-benchmark-4-random | test | 2,124 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun hn => <a>False.elim</a> (h.not_le hn), fun hn => ?_⟩ | case inl
θ : Angle
h : θ.toReal < 0
⊢ 0 ≤ θ.toReal ↔ 0 ≤ θ.sign | case inl
θ : Angle
h : θ.toReal < 0
hn : 0 ≤ θ.sign
⊢ 0 ≤ θ.toReal | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.ins... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c Real.Angle.toReal) (:fv _uniq.208811)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) ... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"refine","sourceEnd":40990,"sourceStart":40984,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":40994,"sourceStart":40991,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":40997,"sourceStart":40994,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun hn => False.elim (h.not_le hn), fun hn => ?_⟩","source_end":41045,"source_start":40991,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"user_name":"h"}] | 311 | 9 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 208c692882f808414dca4347a5e6ba1e956e7b5b133fbff760bec45965894c43 | 2dc92f36237211ce7bbc971381a4a6dc235ff519d8914e565af63554cabadaef | a746fbde27fba904ee6155420d2ca6e2811bd8538f9915b4ef636353b819ea56 | c96d8bbcb2dd7bdafe3fceeb83767a31241e35626044a2ee6468870652cc0171 |
cat-searcher/leandojo-benchmark-4-random | test | 2,125 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.Angle.toReal_neg_iff_sign_neg</a>.1 h] at hn | case inl
θ : Angle
h : θ.toReal < 0
hn : 0 ≤ θ.sign
⊢ 0 ≤ θ.toReal | case inl
θ : Angle
h : θ.toReal < 0
hn : 0 ≤ -1
⊢ 0 ≤ θ.toReal | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c Real.Angle.toReal) (:fv _uniq.208811)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"rw","sourceEnd":41052,"sourceStart":41050,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41054,"sourceStart":41053,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":... | [] | [{"source":"hn","source_end":41088,"source_start":41086,"syntax_kind":"ident"},{"source":"toReal_neg_iff_sign_neg.1 h","source_end":41081,"source_start":41054,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 311 | 10 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 155217fae6d9558b069c9055172ca3c56f3f224cb157e9a93987fc13812732ba | c96d8bbcb2dd7bdafe3fceeb83767a31241e35626044a2ee6468870652cc0171 | c32fb7fe615f38a294e92618f2ea05362b10a9bc5891d879405df8a98b890f92 | c16d6abc59a007ee61af78929bf424018937e6839de83f736892d24b1cd99df5 |
cat-searcher/leandojo-benchmark-4-random | test | 2,126 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>False.elim</a> (hn.not_lt (by decide)) | case inl
θ : Angle
h : θ.toReal < 0
hn : 0 ≤ -1
⊢ 0 ≤ θ.toReal | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c Real.Angle.toReal) (:fv _uniq.208811)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"exact","sourceEnd":41098,"sourceStart":41093,"tag":"atom"},{"children":[{"name":"False.elim","semanticRole":"global","source":"False.elim","sourceEnd":41109,"sourceStart":41099,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":41111,"sourceStart":41110,"tag":"atom"},{"child... | [] | [{"source":"False.elim (hn.not_lt (by decide))","source_end":41133,"source_start":41099,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 311 | 13 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a609372b2172fe2ba96abac35bfdc9ab28fa09533cb5bd54cd3d52e1f721a64e | c16d6abc59a007ee61af78929bf424018937e6839de83f736892d24b1cd99df5 | 25c4ea6906ca7b7cd514370ab5c70da08eb6fba52201af321d50ece311c633e4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,127 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | decide | θ : Angle
h : θ.toReal < 0
hn : 0 ≤ -1
⊢ -1 < 0 | ((:c LT.lt) (:c SignType) ((:c Preorder.toLT) (:c SignType) ((:c PartialOrder.toPreorder) (:c SignType) ((:c SemilatticeInf.toPartialOrder) (:c SignType) ((:c Lattice.toSemilatticeInf) (:c SignType) ((:c DistribLattice.toLattice) (:c SignType) ((:c instDistribLatticeOfLinearOrder) (:c SignType) (:c SignType.instLinearO... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c Real.Angle.toReal) (:fv _uniq.208811)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c SignType)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c SignType))))) (:arg :explicit 2 (:app (:c Neg.neg) (:arg :implicit-type 0 (:c SignType)) (:arg :instance 1 (:instance-of (:app (:c Neg) (:arg :explicit 0 (:c SignType))))) (:arg :explicit 2 (:app (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"children":[{"children":[{"children":[{"source":"decide","sourceEnd":41131,"sourceStart":41125,"tag":"atom"}],"kind":"Lean.Parser.Tactic.decide","source":"decide","sourceEnd":41131,"sourceStart":41125,"tag":"node"}],"kind":"null","source":"decide","sourceEnd":41131,"sourceStart":41125,"tag":"node"}],"kind... | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208855","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 311 | 16 | exact | true | 1 | 3 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3b7cdcb39edd8e5ea92b08c395ade73bfd3a0b462046c754115588525738dba6 | 7caccb171d94fc49d8f527a6a8258b3337de8c2e0ea77d3dec2c29ad350ba0fd | 5589aa5863c2d85622d06d651add002416e5513afdbb455666cdde01bb3e257d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,128 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h, <a>Real.Angle.sign</a>, ← <a>Real.Angle.sin_toReal</a>] | case inr.inl
θ : Angle
h : θ.toReal = 0
⊢ 0 ≤ θ.toReal ↔ 0 ≤ θ.sign | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.ins... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c Eq) (:c Real) ((:c Real.Angle.toReal) (:fv _uniq.208811)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))))"}] | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208878","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c Eq) (:arg :implicit-type 0 (:c ... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":41143,"sourceStart":41139,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"h","source_end":41146,"source_start":41145,"syntax_kind":"ident"},{"source":"sign","source_end":41152,"source_start":41148,"syntax_kind":"ident"},{"source":"sin_toReal","source_end":41168,"source_start":41158,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208878","is_instance":false,"is_let":false,"user_name":"h"}] | 311 | 21 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e373b035cd778c7cb59e5be2695950839d58a1b7d88eb96959ccc99b24e922d3 | 014ff063d4a4856d1256afa4d948e97bfa8b15a03d29f57584effa6ada9fb57c | 59091b63661cc3bfcb168e66c2b8256951a97d29425388460dd018559c7d3146 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,129 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun _ => ?_, fun _ => h.le⟩ | case inr.inr
θ : Angle
h : 0 < θ.toReal
⊢ 0 ≤ θ.toReal ↔ 0 ≤ θ.sign | case inr.inr
θ : Angle
h : 0 < θ.toReal
x✝ : 0 ≤ θ.toReal
⊢ 0 ≤ θ.sign | ((:c Iff) ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Angle.toReal) (:fv _uniq.208811))) ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.ins... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Ang... | (:app (:c Iff) (:arg :explicit 0 (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"refine","sourceEnd":41181,"sourceStart":41175,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":41185,"sourceStart":41182,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":41188,"sourceStart":41185,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"_","sourceEnd... | [] | [{"source":"⟨fun _ => ?_, fun _ => h.le⟩","source_end":41214,"source_start":41182,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"user_name":"h"}] | 311 | 28 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e66610d7d10aed12305b9363861913e5d5f8fd48a70a23ba46e96d568100070e | e659da68dda1b7706d099f50861972817bc54f93847cfe20521f132ab5ffe558 | f5ea8c3beb9292b1072fc7ee152dc7c1bed21f98ac4ffffc8e792bae5ad8f2ec | d93c4488415b69d6c955c5ee14a4ad4eda157b59c3effb2b68eb80b13a7795d6 |
cat-searcher/leandojo-benchmark-4-random | test | 2,130 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.Angle.sign</a>, ← <a>Real.Angle.sin_toReal</a>, <a>sign_nonneg_iff</a>] | case inr.inr
θ : Angle
h : 0 < θ.toReal
x✝ : 0 ≤ θ.toReal
⊢ 0 ≤ θ.sign | case inr.inr
θ : Angle
h : 0 < θ.toReal
x✝ : 0 ≤ θ.toReal
⊢ 0 ≤ Real.sin θ.toReal | ((:c LE.le) (:c SignType) (:c SignType.instLE) ((:c OfNat.ofNat) (:c SignType) (:lit 0) ((:c Zero.toOfNat0) (:c SignType) (:c SignType.instZero))) ((:c Real.Angle.sign) (:fv _uniq.208811))) | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Ang... | (:app (:c LE.le) (:arg :implicit-type 0 (:c SignType)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c SignType))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c SignType)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c SignT... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"rw","sourceEnd":41221,"sourceStart":41219,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":41223,"sourceStart":41222,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Real.Angle.sign"... | [] | [{"source":"sign","source_end":41227,"source_start":41223,"syntax_kind":"ident"},{"source":"sin_toReal","source_end":41243,"source_start":41233,"syntax_kind":"ident"},{"source":"sign_nonneg_iff","source_end":41260,"source_start":41245,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 311 | 29 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0d56b72c04f941742af2d4ca1bd6cb0417d6599cf649bb461310a33f845476e1 | d93c4488415b69d6c955c5ee14a4ad4eda157b59c3effb2b68eb80b13a7795d6 | a282d3585241cb137cf07d6d0311a9feb1664d39ab36e6135f44c1c0e8a8b638 | 41ac0a04e9e8346a4e6f4257ba659306d7ef4873a6f33bccf8c45155f3f719d4 |
cat-searcher/leandojo-benchmark-4-random | test | 2,131 | Real.Angle.toReal_nonneg_iff_sign_nonneg | Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Real.sin_nonneg_of_nonneg_of_le_pi</a> h.le (<a>Real.Angle.toReal_le_pi</a> θ) | case inr.inr
θ : Angle
h : 0 < θ.toReal
x✝ : 0 ≤ θ.toReal
⊢ 0 ≤ Real.sin θ.toReal | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c SemilatticeInf.toPartialOrder) (:c Real) ((:c Lattice.toSemilatticeInf) (:c Real) ((:c DistribLattice.toLattice) (:c Real) ((:c instDistribLatticeOfLinearOrder) (:c Real) (:c Real.linearOrder))))))) ((:c OfNat.ofNat) (:c Re... | [{"name":"θ","sexp":"(:c Real.Angle)"},{"name":"h","sexp":"((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c LinearOrder.toPartialOrder) (:c Real) (:c Real.linearOrder)))) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Real.Ang... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"name":"θ","sexp":"(:c Real.Angle)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"name":"h","sexp":"(:app (:c LT.lt) (:arg :implicit-type 0 (... | {"children":[{"source":"exact","sourceEnd":41271,"sourceStart":41266,"tag":"atom"},{"children":[{"name":"Real.sin_nonneg_of_nonneg_of_le_pi","semanticRole":"global","source":"sin_nonneg_of_nonneg_of_le_pi","sourceEnd":41301,"sourceStart":41272,"tag":"identifier"},{"children":[{"name":"LT.lt.le","semanticRole":"global",... | [] | [{"source":"sin_nonneg_of_nonneg_of_le_pi h.le (toReal_le_pi θ)","source_end":41324,"source_start":41272,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.208811","is_instance":false,"is_let":false,"user_name":"θ"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.208883","is_instance":false,"is_let":false,"user_name":"h"},{"binder_role":":explicit","context_index":3,"internal_name":"_... | 311 | 34 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 74e719370193728dc82006e9e2531cd7a5db2828f067a63cbed442af1a5292be | 41ac0a04e9e8346a4e6f4257ba659306d7ef4873a6f33bccf8c45155f3f719d4 | c701be2303d2a50215222190d57cfee32184919992197883444d5a6354179470 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,132 | DirectSum.IsInternal.addSubmonoid_iSup_eq_top | Mathlib/Algebra/DirectSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>AddSubmonoid.iSup_eq_mrange_dfinsupp_sumAddHom</a>, <a>AddMonoidHom.mrange_top_iff_surjective</a>] | ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ iSup A = ⊤ | ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ Surjective ⇑(DFinsupp.sumAddHom fun i => (A i).subtype) | ((:c Eq) ((:c AddSubmonoid) (:fv _uniq.172681) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.172681) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.172681) (:fv _uniq.172683)))) ((:c iSup) ((:c AddSubmonoid) (:fv _uniq.172681) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.172681) ((:c AddCommMonoid.toAddMonoid) (:fv _uniq.172681) ... | [{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"dec_ι","sexp":"((:c DecidableEq) (:fv _uniq.171932))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.171932) (:sort (+ w 1)))"},{"name":"inst✝³","sexp":"(:forall i (:fv _uniq.171932) ((:c AddCommMonoid) ((:fv _uniq.171945) 0)))"},{"name":"γ","sexp":"(:sort (+ u₁ 1))"},{"name"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV7)) (:arg :instance 1 (:instance-of (:app (:c AddZeroClass) (:arg :explicit 0 (:fv FV7))))))) (:arg :explicit 1 (:app (:c iSup) (:arg :implicit-type 0 (:app (:c AddSubmonoid) (:arg :explicit 0 (:fv FV7)) (:arg :instance 1 (:instance-o... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171932","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.171939","is_instance":true,"is_let":false,"name":"dec_ι","sexp":"(:app (:c DecidableEq) (:arg :ex... | {"children":[{"source":"rw","sourceEnd":15671,"sourceStart":15669,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":15673,"sourceStart":15672,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"AddSubmonoid.iSu... | [] | [{"source":"AddSubmonoid.iSup_eq_mrange_dfinsupp_sumAddHom","source_end":15719,"source_start":15673,"syntax_kind":"ident"},{"source":"AddMonoidHom.mrange_top_iff_surjective","source_end":15759,"source_start":15721,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171932","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.171939","is_instance":true,"is_let":false,"user_name":"dec_ι"},{"binder_role":":implicit","context_index":2,"inter... | 121 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7e2f7a7a12fa4ffc72c234ced87f70a9f6e5c1154b74f6274dd6aaaf1d1a26a7 | e7cd9335a3dca876d29407429d9bdd063bf891696f3a8ed4a58605dc7d0cb97c | 905e672c3b28fd63149a5be76c4a47516185c4d4c859541ba2fedee490c93072 | 854aa96869ddd46b9290dd6ea1682835ff72197ba2f39562c08c38c586e03d8c |
cat-searcher/leandojo-benchmark-4-random | test | 2,133 | DirectSum.IsInternal.addSubmonoid_iSup_eq_top | Mathlib/Algebra/DirectSum/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Function.Bijective.surjective</a> h | ι : Type v
dec_ι : DecidableEq ι
β : ι → Type w
inst✝³ : (i : ι) → AddCommMonoid (β i)
γ : Type u₁
inst✝² : AddCommMonoid γ
M : Type u_1
inst✝¹ : DecidableEq ι
inst✝ : AddCommMonoid M
A : ι → AddSubmonoid M
h : IsInternal A
⊢ Surjective ⇑(DFinsupp.sumAddHom fun i => (A i).subtype) | ((:c Function.Surjective) ((:c DFinsupp) (:fv _uniq.171932) (:lambda i (:fv _uniq.171932) ((:c Subtype) (:fv _uniq.172681) (:lambda x (:fv _uniq.172681) ((:c Membership.mem) (:fv _uniq.172681) ((:c AddSubmonoid) (:fv _uniq.172681) ((:c AddMonoid.toAddZeroClass) (:fv _uniq.172681) ((:c AddCommMonoid.toAddMonoid) (:fv _u... | [{"name":"ι","sexp":"(:sort (+ v 1))"},{"name":"dec_ι","sexp":"((:c DecidableEq) (:fv _uniq.171932))"},{"name":"β","sexp":"(:forall _ (:fv _uniq.171932) (:sort (+ w 1)))"},{"name":"inst✝³","sexp":"(:forall i (:fv _uniq.171932) ((:c AddCommMonoid) ((:fv _uniq.171945) 0)))"},{"name":"γ","sexp":"(:sort (+ u₁ 1))"},{"name"... | (:app (:c Function.Surjective) (:arg :implicit-type 0 (:app (:c DFinsupp) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda i :explicit (:fv FV0) (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV7)) (:arg :explicit 1 (:lambda x :explicit (:fv FV7) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV7)) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171932","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.171939","is_instance":true,"is_let":false,"name":"dec_ι","sexp":"(:app (:c DecidableEq) (:arg :ex... | {"children":[{"source":"exact","sourceEnd":15768,"sourceStart":15763,"tag":"atom"},{"children":[{"name":"Function.Bijective.surjective","semanticRole":"global","source":"Function.Bijective.surjective","sourceEnd":15798,"sourceStart":15769,"tag":"identifier"},{"children":[{"contextIndex":11,"semanticRole":"local","sourc... | [] | [{"source":"Function.Bijective.surjective h","source_end":15800,"source_start":15769,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.171932","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.171939","is_instance":true,"is_let":false,"user_name":"dec_ι"},{"binder_role":":implicit","context_index":2,"inter... | 121 | 8 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fbf36156449b924d195d829d4092eb78bad63027f59fbdb42e635de95b8213a1 | 854aa96869ddd46b9290dd6ea1682835ff72197ba2f39562c08c38c586e03d8c | b2bbe5f510e0bcc2d836a6fa28ac0b122047a94b959de0c679fddf887bcd4739 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,134 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases' <a>Nat.eq_zero_or_pos</a> n with n_zero n_pos | x : ℝ≥0∞
n : ℕ
⊢ (x ^ n).log = ↑↑n * x.log | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"}] | {"children":[{"children":[{"children":[{"children":[{"source":"cases'","sourceEnd":7024,"sourceStart":7018,"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":7043,"sour... | [] | [{"source":"Nat.eq_zero_or_pos n","source_end":7045,"source_start":7025,"syntax_kind":"Lean.Parser.Term.app"},{"source":"n_zero","source_end":7081,"source_start":7075,"syntax_kind":"ident"},{"source":"pow_zero x","source_end":7093,"source_start":7083,"syntax_kind":"Lean.Parser.Term.app"},{"source":"ENNReal.trichotomy x... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"}] | 38 | 2 | branch_opener | false | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f27ca17d740f24564f30a6e3194b514dace68ff2574ee205aee0b34d9f812b01 | 972a820f814a547f4955fd56ce6b28bfdd7d5509035a403a68b8936e937b2cda | 3671df8822a6c23e590e3ba88cfd962ce400f39e3d022017fb2f1353fd3211c8 | 59e9c16ab1b76d85429eb7745c304b825072b5913bcefdc0353f316e83354a47 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,136 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [n_zero, <a>pow_zero</a> x] | case inl
x : ℝ≥0∞
n : ℕ
n_zero : n = 0
⊢ (x ^ n).log = ↑↑n * x.log | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_zero","sexp":"((:c Eq) (:c Nat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":7073,"sourceStart":7069,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"n_zero","source_end":7081,"source_start":7075,"syntax_kind":"ident"},{"source":"pow_zero x","source_end":7093,"source_start":7083,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 7 | exact | true | 1 | 3 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab863d101a7c822e568c9587b4688bd4a5b18012cef962b5b4cf2412ac304be0 | aa0f287e95709ae555e1b4e6775408127c3aae7b5f043931d8bc4e34e4287a67 | 0ffbdc3fea9238ba9e2c8df7ddcd231d10f3a752c3f35010d8da801a3d8b526c | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,137 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>zero_pow</a> (<a>Ne.symm</a> (<a>ne_of_lt</a> n_pos)), <a>ENNReal.log_zero</a>, <a>EReal.mul_bot_of_pos</a>] | case inr.inl
n : ℕ
n_pos : n > 0
⊢ (0 ^ n).log = ↑↑n * log 0 | case inr.inl
n : ℕ
n_pos : n > 0
⊢ 0 < ↑↑n | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"name":"n_pos","sexp":"(:app (:c GT.gt) (:arg :implicit-type 0 (:c Na... | {"children":[{"source":"rw","sourceEnd":7158,"sourceStart":7156,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7160,"sourceStart":7159,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"zero_po... | [] | [{"source":"zero_pow (Ne.symm (ne_of_lt n_pos))","source_end":7195,"source_start":7160,"syntax_kind":"Lean.Parser.Term.app"},{"source":"log_zero","source_end":7205,"source_start":7197,"syntax_kind":"ident"},{"source":"EReal.mul_bot_of_pos","source_end":7227,"source_start":7207,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"user_name":"n_pos"}] | 38 | 15 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 180dbb3d19742c1fabe12bdbf97129d1bd2fd9c260751915a7505b5dc75601c3 | ae154578c282322fc12551ebc6da4a97b8b0109a47be9a3872a5516f84ff67b3 | b2f87dc3c42a86168ad0d0b4f36fc23452061712514c5c166254b012e2ef4533 | a4c2a12a89294477b46a8a531240fa43e1c932c6faff95ff6c01f22a3fd057fe |
cat-searcher/leandojo-benchmark-4-random | test | 2,138 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | case inr.inl
n : ℕ
n_pos : n > 0
⊢ 0 < ↑↑n | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c ENNReal.toEReal) ((:c Nat.cast) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENNRe... | [{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"name":"n_pos","sexp":"(:app (:c GT.gt) (:arg :implicit-type 0 (:c Na... | {"children":[{"source":"norm_cast","sourceEnd":7239,"sourceStart":7230,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":7239,"sourceStart":7230,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"user_name":"n_pos"}] | 38 | 21 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 52f484ce6082a374f6d4f6bc86788327604a8e35655d63c131812166d82f19be | a4c2a12a89294477b46a8a531240fa43e1c932c6faff95ff6c01f22a3fd057fe | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,139 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>ENNReal.top_pow</a> n_pos, <a>ENNReal.log_top</a>, <a>EReal.mul_top_of_pos</a>] | case inr.inr.inl
n : ℕ
n_pos : n > 0
⊢ (⊤ ^ n).log = ↑↑n * ⊤.log | case inr.inr.inl
n : ℕ
n_pos : n > 0
⊢ 0 < ↑↑n | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"name":"n_pos","sexp":"(:app (:c GT.gt) (:arg :implicit-type 0 (:c Na... | {"children":[{"source":"rw","sourceEnd":7247,"sourceStart":7245,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":7249,"sourceStart":7248,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"ENNReal... | [] | [{"source":"ENNReal.top_pow n_pos","source_end":7270,"source_start":7249,"syntax_kind":"Lean.Parser.Term.app"},{"source":"log_top","source_end":7279,"source_start":7272,"syntax_kind":"ident"},{"source":"EReal.mul_top_of_pos","source_end":7301,"source_start":7281,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"user_name":"n_pos"}] | 38 | 26 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8216c6d3a9609058d2275ae8c099784ac322e58d7e4adb302f470bbc36fd892d | 686e1374d3ea10505b813890f593ef5aef648e6c7f0869f6b5e46f11c44896ef | 8178a4252cbe7a0eea5004d2549bd35abbb4a83d72335eda7ef1e7369ed76d06 | da956a374ac4742f649df9f8b05ca2164c158d93b25fb82a192b7f7ee8bb2072 |
cat-searcher/leandojo-benchmark-4-random | test | 2,140 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | case inr.inr.inl
n : ℕ
n_pos : n > 0
⊢ 0 < ↑↑n | ((:c LT.lt) (:c EReal) ((:c Preorder.toLT) (:c EReal) ((:c PartialOrder.toPreorder) (:c EReal) (:c instERealPartialOrder))) ((:c OfNat.ofNat) (:c EReal) (:lit 0) ((:c Zero.toOfNat0) (:c EReal) (:c instERealZero))) ((:c ENNReal.toEReal) ((:c Nat.cast) (:c ENNReal) ((:c CanonicallyOrderedCommSemiring.toNatCast) (:c ENNRe... | [{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"}] | (:app (:c LT.lt) (:arg :implicit-type 0 (:c EReal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c EReal))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c EReal)) (:arg ... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"name":"n_pos","sexp":"(:app (:c GT.gt) (:arg :implicit-type 0 (:c Na... | {"children":[{"source":"norm_cast","sourceEnd":7313,"sourceStart":7304,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":7313,"sourceStart":7304,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.18269","is_instance":false,"is_let":false,"user_name":"n_pos"}] | 38 | 32 | exact | true | 1 | 2 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2fb955a677194ea9018e6200427fd8f6c3aa7dacc80da9936efa08a778081aea | da956a374ac4742f649df9f8b05ca2164c158d93b25fb82a192b7f7ee8bb2072 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,141 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | replace x_real := <a>ENNReal.toReal_pos_iff</a>.1 x_real | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x.toReal
⊢ (x ^ n).log = ↑↑n * x.log | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
⊢ (x ^ n).log = ↑↑n * x.log | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x_real","sexp":"((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c ... | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"replace","sourceEnd":7326,"sourceStart":7319,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x_real","sourceEnd":7333,"sourceStart":7327,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"x_real","sourceEnd":7333,"sourceStart":7327,"tag"... | [] | [{"source":"ENNReal.toReal_pos_iff.1 x_real","source_end":7368,"source_start":7337,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 37 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 228ff21f1297a3e672d318b514af32ddd4c5e556692776a964d92dae7f2b7a98 | d3304f83c3abd62d46857166f969084fdcfd63037328d79d4eaf4f1a16a36cf9 | b13d122098ef0c85c719cd485c395bfd9cf11b9cc5095164920d3007df77e688 | a7812d9caef4f45d0c9420c538230956017fe82d03e321b56b67678aabb8d743 |
cat-searcher/leandojo-benchmark-4-random | test | 2,142 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have x_ne_zero := <a>Ne.symm</a> (<a>LT.lt.ne</a> x_real.1) | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
⊢ (x ^ n).log = ↑↑n * x.log | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
⊢ (x ^ n).log = ↑↑n * x.log | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x_real","sexp":"((:c And) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialO... | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"have","sourceEnd":7377,"sourceStart":7373,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x_ne_zero","sourceEnd":7387,"sourceStart":7378,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"x_ne_zero","sourceEnd":7387,"sourceStart":7378,"t... | [] | [{"source":"Ne.symm (LT.lt.ne x_real.1)","source_end":7418,"source_start":7391,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 38 | exact | true | 1 | 4 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ad8b95b1f9ad5d0e447f5d69f16cd0c42480f65ea6e6a11002472d9236e79e8 | a7812d9caef4f45d0c9420c538230956017fe82d03e321b56b67678aabb8d743 | 1ca623d06f73a53d49418c6e7b427654de526f0df7ab61957312ac453a727b0b | d5933c3664e372bd26b416e0a851c81b19a3c43bbaad23d3f1bce510dc9e565e |
cat-searcher/leandojo-benchmark-4-random | test | 2,143 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have x_ne_top := <a>LT.lt.ne</a> x_real.2 | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
⊢ (x ^ n).log = ↑↑n * x.log | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
x_ne_top : x ≠ ⊤
⊢ (x ^ n).log = ↑↑n * x.log | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x_real","sexp":"((:c And) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialO... | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"have","sourceEnd":7427,"sourceStart":7423,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x_ne_top","sourceEnd":7436,"sourceStart":7428,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"x_ne_top","sourceEnd":7436,"sourceStart":7428,"tag... | [] | [{"source":"LT.lt.ne x_real.2","source_end":7457,"source_start":7440,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 39 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2f99be401bb4bd5478222d41384b72092c9b3da52c7631ba26eea87e78a71e3f | d5933c3664e372bd26b416e0a851c81b19a3c43bbaad23d3f1bce510dc9e565e | a884bcb6b217e6b441704569cef1bf5fdfa17db60e3571925bc69239f25657f0 | bf3f56493c3ca0a315c49a647bbc5d20d60defc6dd59af400ea27daefd505924 |
cat-searcher/leandojo-benchmark-4-random | test | 2,144 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>ENNReal.log</a>, <a>pow_eq_zero_iff'</a>, x_ne_zero, <a>ne_eq</a>, <a>false_and</a>, ↓<a>reduceIte</a>, <a>ENNReal.pow_eq_top_iff</a>, x_ne_top, <a>ENNReal.toReal_pow</a>, <a>Real.log_pow</a>, <a>EReal.coe_mul</a>] | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
x_ne_top : x ≠ ⊤
⊢ (x ^ n).log = ↑↑n * x.log | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
x_ne_top : x ≠ ⊤
⊢ ↑↑n * ↑(Real.log x.toReal) = ↑↑n * ↑(Real.log x.toReal) | ((:c Eq) (:c EReal) ((:c ENNReal.log) ((:c HPow.hPow) (:c ENNReal) (:c Nat) (:c ENNReal) ((:c instHPow) (:c ENNReal) (:c Nat) ((:c Monoid.toNatPow) (:c ENNReal) ((:c MonoidWithZero.toMonoid) (:c ENNReal) ((:c Semiring.toMonoidWithZero) (:c ENNReal) ((:c OrderedSemiring.toSemiring) (:c ENNReal) ((:c OrderedCommSemiring.... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x_real","sexp":"((:c And) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialO... | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c ENNReal.log) (:arg :explicit 0 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c ENNReal)) (:arg :implicit-type 1 (:c Nat)) (:arg :implicit-type 2 (:c ENNReal)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:arg :explicit 0 (:c ENNReal)) (:ar... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"simp","sourceEnd":7466,"sourceStart":7462,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":7471,"sourceStart":7467,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":7471,"s... | [] | [{"source":"log","source_end":7476,"source_start":7473,"syntax_kind":"ident"},{"source":"pow_eq_zero_iff'","source_end":7494,"source_start":7478,"syntax_kind":"ident"},{"source":"x_ne_zero","source_end":7505,"source_start":7496,"syntax_kind":"ident"},{"source":"ne_eq","source_end":7512,"source_start":7507,"syntax_kind"... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 40 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7353b486459e4b7d167f324ac02a889ce4af3e33a8f45d0343592299312766ed | bf3f56493c3ca0a315c49a647bbc5d20d60defc6dd59af400ea27daefd505924 | 651d6f3809e7a5d96b21539992b7ad92961682cd3ac99703d1277bbd61af0e4f | 087e2ab73f027281ad374c7514fa110f845785ece8c28b4402f05567ef7d78a3 |
cat-searcher/leandojo-benchmark-4-random | test | 2,145 | ENNReal.log_pow | Mathlib/Analysis/SpecialFunctions/Log/ENNReal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | case inr.inr.inr
x : ℝ≥0∞
n : ℕ
n_pos : n > 0
x_real : 0 < x ∧ x < ⊤
x_ne_zero : x ≠ 0
x_ne_top : x ≠ ⊤
⊢ ↑↑n * ↑(Real.log x.toReal) = ↑↑n * ↑(Real.log x.toReal) | ((:c Eq) (:c EReal) ((:c HMul.hMul) (:c EReal) (:c EReal) (:c EReal) ((:c instHMul) (:c EReal) (:c EReal.instMul)) ((:c Real.toEReal) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.18221))) ((:c Real.toEReal) ((:c Real.log) ((:c ENNReal.toReal) (:fv _uniq.18220))))) ((:c HMul.hMul) (:c EReal) (:c EReal) (:c ... | [{"name":"x","sexp":"(:c ENNReal)"},{"name":"n","sexp":"(:c Nat)"},{"name":"n_pos","sexp":"((:c GT.gt) (:c Nat) (:c instLTNat) (:fv _uniq.18221) ((:c OfNat.ofNat) (:c Nat) (:lit 0) ((:c instOfNatNat) (:lit 0))))"},{"name":"x_real","sexp":"((:c And) ((:c LT.lt) (:c ENNReal) ((:c Preorder.toLT) (:c ENNReal) ((:c PartialO... | (:app (:c Eq) (:arg :implicit-type 0 (:c EReal)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c EReal)) (:arg :implicit-type 1 (:c EReal)) (:arg :implicit-type 2 (:c EReal)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c EReal)) (:arg :explicit 1 (:c EReal)) (:arg :explicit 2 (... | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"name":"x","sexp":"(:c ENNReal)"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"name":"n","sexp":"(:c Nat)"},{"binder_role":":explicit","context... | {"children":[{"source":"rfl","sourceEnd":7619,"sourceStart":7616,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":7619,"sourceStart":7616,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.18220","is_instance":false,"is_let":false,"user_name":"x"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.18221","is_instance":false,"is_let":false,"user_name":"n"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 38 | 41 | exact | true | 1 | 6 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f78d0791cad9b3461d8b6915fb134ce03951753930faddf0bdc2a6c77ad83b4a | 087e2ab73f027281ad374c7514fa110f845785ece8c28b4402f05567ef7d78a3 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,146 | List.count_attach | Mathlib/Data/List/Count.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>Subtype.ext_iff</a>] | α : Type u_1
l : List α
inst✝ : DecidableEq α
a x✝¹ : { x // x ∈ l }
x✝ : x✝¹ ∈ l.attach
⊢ (x✝¹ == a) = true ↔ (↑x✝¹ == ↑a) = true | ((:c Iff) ((:c Eq) (:c Bool) ((:c BEq.beq) ((:c Subtype) (:fv _uniq.4029) (:lambda x (:fv _uniq.4029) ((:c Membership.mem) (:fv _uniq.4029) ((:c List) (:fv _uniq.4029)) ((:c List.instMembership) (:fv _uniq.4029)) 0 (:fv _uniq.4032)))) ((:c instBEqOfDecidableEq) ((:c Subtype) (:fv _uniq.4029) (:lambda x (:fv _uniq.4029)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"l","sexp":"((:c List) (:fv _uniq.4029))"},{"name":"inst✝","sexp":"((:c DecidableEq) (:fv _uniq.4029))"},{"name":"a","sexp":"((:c Subtype) (:fv _uniq.4029) (:lambda x (:fv _uniq.4029) ((:c Membership.mem) (:fv _uniq.4029) ((:c List) (:fv _uniq.4029)) ((:c List.instMember... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:c Bool)) (:arg :explicit 1 (:app (:c BEq.beq) (:arg :implicit-type 0 (:app (:c Subtype) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:lambda x :explicit (:fv FV0) (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-t... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4029","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4032","is_instance":false,"is_let":false,"name":"l","sexp":"(:app (:c List) (:arg :explicit 0 (:fv FV0)))"},... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":4146,"sourceStart":4142,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEn... | [] | [{"source":"Subtype.ext_iff","source_end":4163,"source_start":4148,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.4029","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.4032","is_instance":false,"is_let":false,"user_name":"l"},{"binder_role":":instance-implicit","context_index":2,"internal_nam... | 63 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 011f690002ee92bde7eeaf5caefd2541017ace2f2d21c44a64111b9523dabe65 | 138c5eda22e11f8a0e0ab3ed1b483663dff914e3f9fe2a1fb04a45672bd3bab5 | 5c8f702cc04c6bed68269e4cd4d063bda577e4328160e9cb67818eba6099862a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,147 | LinearMap.range_zero | Mathlib/Algebra/Module/Submodule/Range.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simpa only [<a>LinearMap.range_eq_map</a>] using <a>Submodule.map_zero</a> _ | R : Type u_1
R₂ : Type u_2
R₃ : Type u_3
K : Type u_4
K₂ : Type u_5
M : Type u_6
M₂ : Type u_7
M₃ : Type u_8
V : Type u_9
V₂ : Type u_10
inst✝¹³ : Semiring R
inst✝¹² : Semiring R₂
inst✝¹¹ : Semiring R₃
inst✝¹⁰ : AddCommMonoid M
inst✝⁹ : AddCommMonoid M₂
inst✝⁸ : AddCommMonoid M₃
σ₁₂ : R →+* R₂
σ₂₃ : R₂ →+* R₃
σ₁₃ : R →... | ((:c Eq) ((:c Submodule) (:fv _uniq.58812) (:fv _uniq.58827) (:fv _uniq.58842) (:fv _uniq.58851) (:fv _uniq.59073)) ((:c LinearMap.range) (:fv _uniq.58809) (:fv _uniq.58812) (:fv _uniq.58824) (:fv _uniq.58827) (:fv _uniq.58839) (:fv _uniq.58842) (:fv _uniq.58848) (:fv _uniq.58851) (:fv _uniq.59051) (:fv _uniq.59073) (:... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"R₂","sexp":"(:sort (+ u_2 1))"},{"name":"R₃","sexp":"(:sort (+ u_3 1))"},{"name":"K","sexp":"(:sort (+ u_4 1))"},{"name":"K₂","sexp":"(:sort (+ u_5 1))"},{"name":"M","sexp":"(:sort (+ u_6 1))"},{"name":"M₂","sexp":"(:sort (+ u_7 1))"},{"name":"M₃","sexp":"(:sort (+ u_8 ... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Submodule) (:arg :explicit 0 (:fv FV1)) (:arg :explicit 1 (:fv FV6)) (:arg :instance 2 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :instance 3 (:instance-of (:app (:c AddCommMonoid) (:arg :explicit 0 (:fv FV6))))) (:arg :instance 4 (:instance-of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.58809","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.58812","is_instance":false,"is_let":false,"name":"R₂","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"children":[{"children":[{"children":[{"source":"simpa","sourceEnd":8116,"sourceStart":8111,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":... | [] | [{"source":"range_eq_map","source_end":8135,"source_start":8123,"syntax_kind":"ident"},{"source":"Submodule.map_zero _","source_end":8163,"source_start":8143,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.58809","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.58812","is_instance":false,"is_let":false,"user_name":"R₂"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 62 | 2 | exact | true | 1 | 32 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9588098e4db5bd6b5a509451cfc28d28735c135c9c6665e675b0974ffab5f698 | 0827fa77403b06e5e517fd0fffcda611e04860a65f0655189a1d060d7d8f7093 | f219f8e162667ba2ae361a16cbb8980802c94fe924bd96d9b8ea700b5fef3ef7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,148 | MetricSpace.ext | Mathlib/Topology/MetricSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases m | α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
m m' : MetricSpace α
h : PseudoMetricSpace.toDist = PseudoMetricSpace.toDist
⊢ m = m' | case mk
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
m' : MetricSpace α
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x = y
h : PseudoMetricSpace.toDist = PseudoMetricSpace.toDist
⊢ mk eq_of_dist_eq_zero✝ = m' | ((:c Eq) ((:c MetricSpace) (:fv _uniq.180)) (:fv _uniq.181) (:fv _uniq.182)) | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.140))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"m","sexp":"((:c MetricSpace) (:fv _uniq.180))"... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV8))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","contex... | {"children":[{"source":"cases","sourceEnd":1557,"sourceStart":1552,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"m","sourceEnd":1559,"sourceStart":1558,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","source... | [] | [{"source":"m","source_end":1559,"source_start":1558,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 9 | 4 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a710b4fc24df4dc8e5548119ca166a10f7916c1129b43e18b8eb88e4cbc0d1ec | a533642543a9b1388f096abdd6fa0fd4720e2d9d313c624291de25da22399658 | c1a7d81ba119070bb3353deb955870f55038321f8c3a72a62430c7c98208b258 | 0d2eddf690d548cedfcea181439be9f576c8c71bc904e6dd8f251f6c30c3cf59 |
cat-searcher/leandojo-benchmark-4-random | test | 2,149 | MetricSpace.ext | Mathlib/Topology/MetricSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | cases m' | case mk
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
m' : MetricSpace α
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x = y
h : PseudoMetricSpace.toDist = PseudoMetricSpace.toDist
⊢ mk eq_of_dist_eq_zero✝ = m' | case mk.mk
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x = y
h : PseudoMetricSp... | ((:c Eq) ((:c MetricSpace) (:fv _uniq.180)) ((:c MetricSpace.mk) (:fv _uniq.180) (:fv _uniq.208) (:fv _uniq.209)) (:fv _uniq.182)) | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.140))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"m'","sexp":"((:c MetricSpace) (:fv _uniq.180))... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c MetricSpace.mk) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:metavar))))) (:arg :proof 2 (:proof-of (:forall x :implicit (:metavar)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","contex... | {"children":[{"source":"cases","sourceEnd":1566,"sourceStart":1561,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":7,"semanticRole":"local","source":"m'","sourceEnd":1569,"sourceStart":1567,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","sourc... | [] | [{"source":"m'","source_end":1569,"source_start":1567,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 9 | 6 | exact | true | 1 | 10 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 71fa7db07b6d2efb159c1a1fcc5a49bb411bac8d4bee24b9c5bc57900fe72a86 | 0d2eddf690d548cedfcea181439be9f576c8c71bc904e6dd8f251f6c30c3cf59 | 4cdd90bdf6055217a0e7ceee7b491576c748b4e706b7bf8ad09520ba5b4506b3 | ca1330133d16679ab71ee92662f0a3cd47183838df44d3980f5b41c0b945283f |
cat-searcher/leandojo-benchmark-4-random | test | 2,150 | MetricSpace.ext | Mathlib/Topology/MetricSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | case mk.mk
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x = y
h : PseudoMetricSp... | case mk.mk.e_toPseudoMetricSpace
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x ... | ((:c Eq) ((:c MetricSpace) (:fv _uniq.180)) ((:c MetricSpace.mk) (:fv _uniq.180) (:fv _uniq.208) (:fv _uniq.209)) ((:c MetricSpace.mk) (:fv _uniq.180) (:fv _uniq.251) (:fv _uniq.252))) | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.140))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"toPseudoMetricSpace✝¹","sexp":"((:c PseudoMetr... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c MetricSpace) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c MetricSpace.mk) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:metavar))))) (:arg :proof 2 (:proof-of (:forall x :implicit (:metavar)... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","contex... | {"children":[{"source":"congr","sourceEnd":1576,"sourceStart":1571,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":1576,"sourceStart":1571,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 9 | 8 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | aa6f71794163846d1f4e8f517c0ce92c04d5a83add8ec215677f9f4e63d90664 | ca1330133d16679ab71ee92662f0a3cd47183838df44d3980f5b41c0b945283f | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | 1fe6123d2a7779c98807ea7549bbc2cb2314468ae5d2baa2441840ae870d955d |
cat-searcher/leandojo-benchmark-4-random | test | 2,151 | MetricSpace.ext | Mathlib/Topology/MetricSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext1 | case mk.mk.e_toPseudoMetricSpace
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x ... | case mk.mk.e_toPseudoMetricSpace.h
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → ... | ((:c Eq) ((:c PseudoMetricSpace) (:fv _uniq.180)) (:fv _uniq.208) (:fv _uniq.251)) | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.140))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"toPseudoMetricSpace✝¹","sexp":"((:c PseudoMetr... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:fv FV7)) (:arg :explicit 2 (:fv FV9))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","contex... | {"children":[{"source":"ext1","sourceEnd":1582,"sourceStart":1578,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.tacticExt1___","source":"ext1","sourceEnd":1582,"sourceStart":1578,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 9 | 10 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a5dc8cb6d396211d13b18f63eaeee274ff2daf627c24181c04faf6fd8ae824b4 | 1fe6123d2a7779c98807ea7549bbc2cb2314468ae5d2baa2441840ae870d955d | e7fe907b3287888acfd1b4783f3ce5b528593e6c60d4d7f2923662da6d41fe8b | 9ef7403dfd14985773c9cd30c02fe14a298471ae54824afbc96b900518c3dcc1 |
cat-searcher/leandojo-benchmark-4-random | test | 2,152 | MetricSpace.ext | Mathlib/Topology/MetricSpace/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | assumption | case mk.mk.e_toPseudoMetricSpace.h
α✝ : Type u
β : Type v
X : Type u_1
ι : Type u_2
inst✝ : PseudoMetricSpace α✝
α : Type u_3
toPseudoMetricSpace✝¹ : PseudoMetricSpace α
eq_of_dist_eq_zero✝¹ : ∀ {x y : α}, dist x y = 0 → x = y
toPseudoMetricSpace✝ : PseudoMetricSpace α
eq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → ... | ((:c Eq) ((:c Dist) (:fv _uniq.180)) ((:c PseudoMetricSpace.toDist) (:fv _uniq.180) (:fv _uniq.208)) ((:c PseudoMetricSpace.toDist) (:fv _uniq.180) (:fv _uniq.251))) | [{"name":"α✝","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"X","sexp":"(:sort (+ u_1 1))"},{"name":"ι","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝","sexp":"((:c PseudoMetricSpace) (:fv _uniq.140))"},{"name":"α","sexp":"(:sort (+ u_3 1))"},{"name":"toPseudoMetricSpace✝¹","sexp":"((:c PseudoMetr... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Dist) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c PseudoMetricSpace.toDist) (:arg :implicit-type 0 (:fv FV6)) (:arg :instance 1 (:instance-of (:app (:c PseudoMetricSpace) (:arg :explicit 0 (:metavar))))))) (:arg :explicit 2 (:app (:c PseudoMetricSpace.toDist... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"name":"α✝","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","contex... | {"children":[{"source":"assumption","sourceEnd":1594,"sourceStart":1584,"tag":"atom"}],"kind":"Lean.Parser.Tactic.assumption","source":"assumption","sourceEnd":1594,"sourceStart":1584,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.140","is_instance":false,"is_let":false,"user_name":"α✝"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.142","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq.... | 9 | 12 | exact | true | 1 | 11 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 66e4c76b883b4d853e683ae17fd5fc7d4e939932011c7b454cf566f7c43587d1 | 9ef7403dfd14985773c9cd30c02fe14a298471ae54824afbc96b900518c3dcc1 | c081dd376ba93a530dd044cffc81e70953e86d86f7d0796dc26bc1597302573d | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,153 | Set.image2_image_right | Mathlib/Data/Set/NAry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext | α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
γ' : Type u_6
δ : Type u_7
δ' : Type u_8
ε : Type u_9
ε' : Type u_10
ζ : Type u_11
ζ' : Type u_12
ν : Type u_13
f✝ f' : α → β → γ
g✝ g' : α → β → γ → δ
s s' : Set α
t t' : Set β
u u' : Set γ
v : Set δ
a a' : α
b b' : β
c c' : γ
d d' : δ
f : α → γ → δ
g ... | case h
α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
γ' : Type u_6
δ : Type u_7
δ' : Type u_8
ε : Type u_9
ε' : Type u_10
ζ : Type u_11
ζ' : Type u_12
ν : Type u_13
f✝ f' : α → β → γ
g✝ g' : α → β → γ → δ
s s' : Set α
t t' : Set β
u u' : Set γ
v : Set δ
a a' : α
b b' : β
c c' : γ
d d' : δ
f : α → γ... | ((:c Eq) ((:c Set) (:fv _uniq.29558)) ((:c Set.image2) (:fv _uniq.29540) (:fv _uniq.29552) (:fv _uniq.29558) (:fv _uniq.29703) (:fv _uniq.29607) ((:c Set.image) (:fv _uniq.29546) (:fv _uniq.29552) (:fv _uniq.29704) (:fv _uniq.29613))) ((:c Set.image2) (:fv _uniq.29540) (:fv _uniq.29546) (:fv _uniq.29558) (:lambda a (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"γ'","sexp":"(:sort (+ u_6 1))"},{"name":"δ","sexp":"(:sort (+ u_7 1))"},{"name":"δ'","sexp":"(:sort (+ u_8 1... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :explicit 1 (:app (:c Set.image2) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV4)) (:arg :implicit-type 2 (:fv FV6)) (:arg :explicit 3 (:fv FV33)) (:arg :explicit 4 (:fv FV17)) (:arg :explicit 5 (:app (:c Set.ima... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29540","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29543","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"ext","sourceEnd":9082,"sourceStart":9079,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Elab.Tactic.Ext.ext","source":"ext","sourceEnd":9082,"sourceStart":9079,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29540","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29543","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 90 | 4 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | dd07b4e77e3fcafa1e4b6d3b1dda3adca464566c7762d9bf129dc00bd804272a | be8b052d64f657cd2bd7ae197446ee1535415db17c3957d3792d3d85a4f37868 | a7e7e2f59b128bdb0aa60f56f5211efefdf83b92994b8f4a5d2e18126a0a14de | 81debe23d79aef4656cb861ea1199ac02d75188ff6f093c47c0ee00bf2d085bd |
cat-searcher/leandojo-benchmark-4-random | test | 2,154 | Set.image2_image_right | Mathlib/Data/Set/NAry.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | case h
α : Type u_1
α' : Type u_2
β : Type u_3
β' : Type u_4
γ : Type u_5
γ' : Type u_6
δ : Type u_7
δ' : Type u_8
ε : Type u_9
ε' : Type u_10
ζ : Type u_11
ζ' : Type u_12
ν : Type u_13
f✝ f' : α → β → γ
g✝ g' : α → β → γ → δ
s s' : Set α
t t' : Set β
u u' : Set γ
v : Set δ
a a' : α
b b' : β
c c' : γ
d d' : δ
f : α → γ... | ((:c Iff) ((:c Membership.mem) (:fv _uniq.29558) ((:c Set) (:fv _uniq.29558)) ((:c Set.instMembership) (:fv _uniq.29558)) (:fv _uniq.29728) ((:c Set.image2) (:fv _uniq.29540) (:fv _uniq.29552) (:fv _uniq.29558) (:fv _uniq.29703) (:fv _uniq.29607) ((:c Set.image) (:fv _uniq.29546) (:fv _uniq.29552) (:fv _uniq.29704) (:f... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"α'","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"β'","sexp":"(:sort (+ u_4 1))"},{"name":"γ","sexp":"(:sort (+ u_5 1))"},{"name":"γ'","sexp":"(:sort (+ u_6 1))"},{"name":"δ","sexp":"(:sort (+ u_7 1))"},{"name":"δ'","sexp":"(:sort (+ u_8 1... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV6)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV6)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV6))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29540","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29543","is_instance":false,"is_let":false,"name":"α'","sexp":"(:sort Type)"},{"binder_role":":implicit","co... | {"children":[{"source":"simp","sourceEnd":9088,"sourceStart":9084,"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":0,"internal_name":"_uniq.29540","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29543","is_instance":false,"is_let":false,"user_name":"α'"},{"binder_role":":implicit","context_index":2,"internal_name":"_u... | 90 | 6 | exact | true | 1 | 35 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3e0dd57e63e310c0cfd8b510beff0c804572d02c5b34000c0b52a0c681cd1d2 | 81debe23d79aef4656cb861ea1199ac02d75188ff6f093c47c0ee00bf2d085bd | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,155 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := hs.elim_countable_subcover (fun x : s ↦ <a>interior</a> (U x x.2)) (fun _ ↦ <a>isOpen_interior</a>) fun x hx ↦ <a>Set.mem_iUnion</a>.2 ⟨⟨x, hx⟩, <a>mem_interior_iff_mem_nhds</a>.2 <| hU _ _⟩ | X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, U ↑x ⋯ | X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
this : ∃ r, r.Countable ∧ s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, U ↑x ⋯ | ((:c Exists) ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) (:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) ((:c And) ((:c Set.Countable) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uni... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5))))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":7936,"sourceStart":7932,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":7937,"sourceStart":7937,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":7937,"sourceStart":7937,"tag":"node"}],"kind":"Lean.Parser.Term.haveId","... | [] | [{"source":"hs.elim_countable_subcover (fun x : s ↦ interior (U x x.2)) (fun _ ↦ isOpen_interior)\n fun x hx ↦\n mem_iUnion.2 ⟨⟨x, hx⟩, mem_interior_iff_mem_nhds.2 <| hU _ _⟩","source_end":8122,"source_start":7940,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 4 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 578d5a63496bf56450d24be1b14f249cb5d9050de74f7de39c2a15ac272589b2 | ccd406141d119be13588c159ab3b6bcd750213354203a36e72cd47eb962e8e65 | 78cca2a2709a3e1ada958864792cc74f82434fbfd66f98d54cd444f490d408ab | 5ed114f86ff4285fc8e3f1755848ca820b7a9d108d770db36587b558d173fb38 |
cat-searcher/leandojo-benchmark-4-random | test | 2,156 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases this with ⟨r, ⟨hr, hs⟩⟩ | X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
this : ∃ r, r.Countable ∧ s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, U ↑x ⋯ | case intro.intro
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, ... | ((:c Exists) ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) (:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) ((:c And) ((:c Set.Countable) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uni... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5))))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":8131,"sourceStart":8125,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"contextIndex":11,"semanticRole":"local","source":"this","sourceEnd":8136,"sourceStart":8132,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.casesTarget","s... | [] | [{"source":"this","source_end":8136,"source_start":8132,"syntax_kind":"ident"},{"source":"⟨r, ⟨hr, hs⟩⟩","source_end":8163,"source_start":8142,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 5 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c88343dbf3fbed1473031f039eaf2f275498eed7435c4c0b4fe7f4492752f412 | 5ed114f86ff4285fc8e3f1755848ca820b7a9d108d770db36587b558d173fb38 | bade51e9e85fc6f18e33f01c5b25f93275f8e7e1b4f9eb9737b6d1b34c6cd5d9 | 559dc7fa0a998b7132b43626804acf1a573ae4cd57e7d4c4f9c7972fba6ae1cf |
cat-searcher/leandojo-benchmark-4-random | test | 2,157 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | use r, hr | case intro.intro
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, ... | case right
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ s ⊆ ⋃ x ∈ r, U ↑x ⋯ | ((:c Exists) ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) (:lambda t ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) ((:c And) ((:c Set.Countable) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) 0) ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uni... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))))) (:arg :explicit 1 (:lambda t :explicit (:app (:c Set) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5))))) (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"use","sourceEnd":8169,"sourceStart":8166,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"group","source":"","tag":"node"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"r","sourceEnd":8171,"sourceStart":8170,"tag":"identifier"},{"sour... | [] | [{"source":"r","source_end":8171,"source_start":8170,"syntax_kind":"ident"},{"source":"hr","source_end":8175,"source_start":8173,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 6 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 78f7c2672d7c132d951f8fef0d4b30c314b38987c47a9889ead3213f59b4f693 | 559dc7fa0a998b7132b43626804acf1a573ae4cd57e7d4c4f9c7972fba6ae1cf | 597f6a319daef81a1e6ac524608ad2dc09374842f262efb410064dc98c604eb0 | e25facbd7df0917fb3798d36a5c60cc14f7917e2bab446a57dfd8d456993119b |
cat-searcher/leandojo-benchmark-4-random | test | 2,158 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Set.Subset.trans</a> hs | case right
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ s ⊆ ⋃ x ∈ r, U ↑x ⋯ | case right
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uniq.14143)) (:fv _uniq.14157) ((:c Set.iUnion) (:fv _uniq.14143) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) (:lambda x ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) ((:c Set.iUnion) (:fv _uniq.14143) ((:c Membership.mem) (... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:fv FV5)) (:arg :explicit 3 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":8183,"sourceStart":8178,"tag":"atom"},{"children":[{"name":"Set.Subset.trans","semanticRole":"global","source":"Subset.trans","sourceEnd":8196,"sourceStart":8184,"tag":"identifier"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"hs","sourceEnd":8199,"sourceSt... | [] | [{"source":"Subset.trans hs","source_end":8199,"source_start":8184,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 7 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 77279734c33d4134d5de0c637ea62c717e4d0bec08a5d50ec4e3020d659049f0 | e25facbd7df0917fb3798d36a5c60cc14f7917e2bab446a57dfd8d456993119b | abe860398f554ba01bc05656ade7cb89944065f43924714ef85c9f1057f2ab7c | c22a9480827b391ad054f8ad3fb2099d3e97309dc2ffc752a033dc2c868fe6bf |
cat-searcher/leandojo-benchmark-4-random | test | 2,159 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Set.iUnion₂_subset</a> | case right
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) ... | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∀ i ∈ r, (fun x => interior (U ↑x ⋯)... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uniq.14143)) ((:c Set.iUnion) (:fv _uniq.14143) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) (:lambda i ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) ((:c Set.iUnion) (:fv _uniq.14143) ((:c Membership.mem) ((:c Set.Elem) (:fv... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":8207,"sourceStart":8202,"tag":"atom"},{"name":"Set.iUnion₂_subset","semanticRole":"global","source":"iUnion₂_subset","sourceEnd":8224,"sourceStart":8208,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.apply","source":"apply iUnion₂_subset","sourceEnd":8224,"sourceStart":8202,"... | [] | [{"source":"iUnion₂_subset","source_end":8224,"source_start":8208,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 8 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee072ac0ffe977200debc8f6394e42693cad49243ce5049b213fe4f01afa8fe1 | c22a9480827b391ad054f8ad3fb2099d3e97309dc2ffc752a033dc2c868fe6bf | dc02341b14eb6557de6baf0b66a005c21fab78629942642821798f78b667abd0 | 36f1c2369c8bc4eac882ec5ba79dc4a882ea0966f3dc32ee42b7eb0aa90bdad7 |
cat-searcher/leandojo-benchmark-4-random | test | 2,160 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | intro i hi | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
⊢ ∀ i ∈ r, (fun x => interior (U ↑x ⋯)... | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
i : ↑s
hi : i ∈ r
⊢ (fun x => interior... | (:forall i ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) (:forall j ((:c Membership.mem) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) ((:c Set) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) ((:c Set.instMembership) ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157))) 0 (:fv _uniq.15023)) ((:c HasSub... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:forall i :explicit (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5))) (:forall j :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:fv FV5)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:ap... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"intro","sourceEnd":8232,"sourceStart":8227,"tag":"atom"},{"children":[{"semanticRole":"scoped_local","source":"i","sourceEnd":8234,"sourceStart":8233,"tag":"identifier"},{"semanticRole":"scoped_local","source":"hi","sourceEnd":8237,"sourceStart":8235,"tag":"identifier"}],"kind":"null","source":"... | [{"role":"fresh_name","source":"i","source_end":8234,"source_start":8233,"syntax_kind":"ident"},{"role":"fresh_name","source":"hi","source_end":8237,"source_start":8235,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 9 | exact | true | 1 | 13 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2bcfb098367313b8840d6ad1f9bfc1b497ab49e6adf1d5d579afc29a697e7d80 | 36f1c2369c8bc4eac882ec5ba79dc4a882ea0966f3dc32ee42b7eb0aa90bdad7 | f8dc8efe385c2627ebbcb0000fbf509f2b0935edbac43a186e1157fab879513b | f19d432d2b05b74a2a94842c5fa5b7aa911883a9c41672578e9d570ea8edaf71 |
cat-searcher/leandojo-benchmark-4-random | test | 2,161 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | apply <a>Set.Subset.trans</a> <a>interior_subset</a> | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
i : ↑s
hi : i ∈ r
⊢ (fun x => interior... | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
i : ↑s
hi : i ∈ r
⊢ U ↑i ⋯ ⊆ ⋃ x ∈ r, ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uniq.14143)) ((:lambda x ((:c Set.Elem) (:fv _uniq.14143) (:fv _uniq.14157)) ((:c interior) (:fv _uniq.14143) (:fv _uniq.14151) ((:fv _uniq.14699) ((:c Subtype.val) (:fv _uniq.14143) (:lambda x (:fv _uniq.14143) ((:c Membership.mem) (:fv ... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:lambda x :explicit (:app (:c Set.Elem) (:arg :implicit-type 0 (:fv FV0)) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"apply","sourceEnd":8245,"sourceStart":8240,"tag":"atom"},{"children":[{"name":"Set.Subset.trans","semanticRole":"global","source":"Subset.trans","sourceEnd":8258,"sourceStart":8246,"tag":"identifier"},{"children":[{"name":"interior_subset","semanticRole":"global","source":"interior_subset","sour... | [] | [{"source":"Subset.trans interior_subset","source_end":8274,"source_start":8246,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 10 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e9f544d3d57bb22135c0d25e2df7f9de41a556cc34edb247c3c9c38def5675fe | f19d432d2b05b74a2a94842c5fa5b7aa911883a9c41672578e9d570ea8edaf71 | 209af0b652a19b9508662a4ccafe549680ce2a815bc39370612c7b3085f80c7c | ba8272718369923d4a83fff65e6059799053a71226bdd73196fb3badea4ee7bf |
cat-searcher/leandojo-benchmark-4-random | test | 2,162 | IsLindelof.elim_nhds_subcover' | Mathlib/Topology/Compactness/Lindelof.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Set.subset_iUnion_of_subset</a> i (<a>Set.subset_iUnion_of_subset</a> hi (<a>Set.Subset.refl</a> _)) | case right.h
X : Type u
Y : Type v
ι : Type u_1
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hs✝ : IsLindelof s
U : (x : X) → x ∈ s → Set X
hU : ∀ (x : X) (hx : x ∈ s), U x hx ∈ 𝓝 x
r : Set ↑s
hr : r.Countable
hs : s ⊆ ⋃ i ∈ r, (fun x => interior (U ↑x ⋯)) i
i : ↑s
hi : i ∈ r
⊢ U ↑i ⋯ ⊆ ⋃ x ∈ r, ... | ((:c HasSubset.Subset) ((:c Set) (:fv _uniq.14143)) ((:c Set.instHasSubset) (:fv _uniq.14143)) ((:fv _uniq.14699) ((:c Subtype.val) (:fv _uniq.14143) (:lambda x (:fv _uniq.14143) ((:c Membership.mem) (:fv _uniq.14143) ((:c Set) (:fv _uniq.14143)) ((:c Set.instMembership) (:fv _uniq.14143)) 0 (:fv _uniq.14157))) (:fv _u... | [{"name":"X","sexp":"(:sort (+ u 1))"},{"name":"Y","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.14143))"},{"name":"inst✝","sexp":"((:c TopologicalSpace) (:fv _uniq.14145))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.14143))"},{"name":"t","se... | (:app (:c HasSubset.Subset) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :instance 1 (:instance-of (:app (:c HasSubset) (:arg :explicit 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0))))))) (:arg :explicit 2 (:app (:fv FV9) (:arg :explicit 0 (:app (:c Subtype.val) (:arg :implicit-type 0 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"name":"X","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"name":"Y","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"exact","sourceEnd":8282,"sourceStart":8277,"tag":"atom"},{"children":[{"name":"Set.subset_iUnion_of_subset","semanticRole":"global","source":"subset_iUnion_of_subset","sourceEnd":8306,"sourceStart":8283,"tag":"identifier"},{"children":[{"contextIndex":14,"semanticRole":"local","source":"i","sour... | [] | [{"source":"subset_iUnion_of_subset i (subset_iUnion_of_subset hi (Subset.refl _))","source_end":8353,"source_start":8283,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.14143","is_instance":false,"is_let":false,"user_name":"X"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.14145","is_instance":false,"is_let":false,"user_name":"Y"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 18 | 11 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3f0acf58bb2dffc622f03b71a4fdbdc84c04e821a5ceb89145bce97c13044a7 | ba8272718369923d4a83fff65e6059799053a71226bdd73196fb3badea4ee7bf | cb26f642eb06f43e42828f89911f48a55c83fe5fa473e651cd407e4277e5e45a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 2,163 | TopCat.GlueData.isOpen_iff | Mathlib/Topology/Gluing.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | delta <a>CategoryTheory.GlueData.ι</a> | D : GlueData
U : Set ↑D.glued
⊢ IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(D.ι i) ⁻¹' U) | D : GlueData
U : Set ↑D.glued
⊢ IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(Multicoequalizer.π D.diagram i) ⁻¹' U) | ((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryThe... | [{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.GlueData.glued) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c To... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (... | {"children":[{"source":"delta","sourceEnd":4373,"sourceStart":4368,"tag":"atom"},{"children":[{"name":"CategoryTheory.GlueData.ι","semanticRole":"global","source":"CategoryTheory.GlueData.ι","sourceEnd":4400,"sourceStart":4374,"tag":"identifier"}],"kind":"null","source":"CategoryTheory.GlueData.ι","sourceEnd":4400,"sou... | [] | [{"source":"CategoryTheory.GlueData.ι","source_end":4400,"source_start":4374,"syntax_kind":"ident"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}] | 14 | 4 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 915045f39fa5c040b7085a5df773fa54d80dc85ba1dbdda50f07cd18ca1265f1 | 59616075b506d9405efcb23eb4685f4145482681b472031373f54c19d6797e38 | 55cbee0222368b6460c7c53a9cb1cdb622cf2ae6ab04c894df40dcb30ac95e56 | 2c4df7370ed00998d2dd2f91325cd131c120f5a5e8bad15c3dd75d00b5e32348 |
cat-searcher/leandojo-benchmark-4-random | test | 2,164 | TopCat.GlueData.isOpen_iff | Mathlib/Topology/Gluing.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [← <a>CategoryTheory.Limits.Multicoequalizer.ι_sigmaπ</a> 𝖣.<a>CategoryTheory.GlueData.diagram</a>] | D : GlueData
U : Set ↑D.glued
⊢ IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(Multicoequalizer.π D.diagram i) ⁻¹' U) | D : GlueData
U : Set ↑D.glued
⊢ IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(Sigma.ι D.diagram.right i ≫ Multicoequalizer.sigmaπ D.diagram) ⁻¹' U) | ((:c Iff) ((:c IsOpen) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c TopCat) (:c instTopCatLargeCategory) ((:c CategoryThe... | [{"name":"D","sexp":"(:c TopCat.GlueData)"},{"name":"U","sexp":"((:c Set) ((:c CategoryTheory.Bundled.α) (:c TopologicalSpace) ((:c CategoryTheory.GlueData.glued) (:c TopCat) (:c instTopCatLargeCategory) ((:c TopCat.GlueData.toGlueData) (:fv _uniq.1514)) ((:c CategoryTheory.Limits.hasColimitOfHasColimitsOfShape) (:c To... | (:app (:c Iff) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:app (:c CategoryTheory.Bundled.α) (:arg :implicit 0) (:arg :explicit 1 (:app (:c CategoryTheory.GlueData.glued) (:arg :implicit-type 0 (:c TopCat)) (:arg :instance 1 (:instance-of (:app (:c CategoryTheory.LargeCategory) (:arg :explicit 0 (:c To... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"name":"D","sexp":"(:c TopCat.GlueData)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"name":"U","sexp":"(:app (:c Set) (:arg :explicit 0 (:app (... | {"children":[{"source":"simp_rw","sourceEnd":4410,"sourceStart":4403,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4412,"sourceStart":4411,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":4415,"sourceSt... | [] | [{"source":"Multicoequalizer.ι_sigmaπ 𝖣.diagram","source_end":4456,"source_start":4416,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.1514","is_instance":false,"is_let":false,"user_name":"D"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.2012","is_instance":false,"is_let":false,"user_name":"U"}] | 14 | 5 | exact | true | 1 | 2 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cc4b6a00526d910ba2508bdf1ede9aedeff484803edea800975ee4f6569af76c | 2c4df7370ed00998d2dd2f91325cd131c120f5a5e8bad15c3dd75d00b5e32348 | 6d9dc1c10ff04251d8b09429fb210083bda6c877e601ed8b330becfb958078c2 | 518e977c2bc96a42bf3bbc8712f8383cdb758836aa09852533549c9829961808 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.