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 | 307 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"positivity","sourceEnd":36087,"sourceStart":36077,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":36087,"sourceStart":36077,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 89 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9b69ba9fb9b64ab1d0250363bac7423a518392eb65e263fb6462b6f8012da1d4 | 5a515267bd1765a26401b614296f0ab5ace2c6598befd91fdf8b98fa4cb8b8f9 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 308 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.h.h₁.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ ... | case h.h.h.h₁.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ ... | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.723658) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":36109,"sourceStart":36107,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36111,"sourceStart":36110,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":36125,"source_start":36111,"syntax_kind":"ident"},{"source":"hu","source_end":36132,"source_start":36130,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 94 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d5f158dba463247332be1c0cdc4744d7130a080c4e503ab8275593ae05dff210 | a3c68152db72f3853c8dda8052b88b08183d13ce2523bdc6e2690337b26c00f6 | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | 8e1d2d5fc1cd938b6386c6445a58d8c9367b98641a6c52de3bd0456a779ba912 |
cat-searcher/leandojo-benchmark-4-random | test | 309 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>le_of_lt</a> hu.2 | case h.h.h.h₁.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ ... | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.723658) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":36156,"sourceStart":36151,"tag":"atom"},{"children":[{"name":"le_of_lt","semanticRole":"global","source":"le_of_lt","sourceEnd":36165,"sourceStart":36157,"tag":"identifier"},{"children":[{"children":[{"contextIndex":33,"semanticRole":"local","source":"hu","sourceEnd":36168,"so... | [] | [{"source":"le_of_lt hu.2","source_end":36170,"source_start":36157,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 97 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ee52bc1408282e644cfd0d3b66a3d2d8afefe7de341d217d0ac94746983e5bce | 8e1d2d5fc1cd938b6386c6445a58d8c9367b98641a6c52de3bd0456a779ba912 | d274537ecd72765c6eb966b003c575536663ce9cd727169654b0f9e374edb3d4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 310 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c GE.ge) (: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 Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":36293,"sourceStart":36287,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":36293,"sourceStart":36287,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 102 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d771ecb59c82953cb6ef656fc60ae180a1f2d9d380ad720c810744617cc18954 | ee0a1ac4fcf4d20fb9c17b09a22dc25a54812a7f4e67276d41b947fe88e784cf | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | d20ca948cdf267e483789509c9fe87f7a1dd067d109f967e67a83e1e17306f1f |
cat-searcher/leandojo-benchmark-4-random | test | 311 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Finset.card_nsmul_le_sum</a> _ _ _ (fun x _ => by rfl) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HSMul.hSMul) (:c Nat) (:c Real) (:c Real) ((:c instHSMul) (:c Nat) (:c Real) ((:c AddMonoid.toNatSMul) (:c Real) (:c Real.instAddMonoid))) ((:c Finset.card) (:c Nat) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c Str... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 HSMul.hSMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HSMul) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":36300,"sourceStart":36295,"tag":"atom"},{"children":[{"name":"Finset.card_nsmul_le_sum","semanticRole":"global","source":"Finset.card_nsmul_le_sum","sourceEnd":36325,"sourceStart":36301,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":36327,"sourceStart"... | [] | [{"source":"Finset.card_nsmul_le_sum _ _ _ (fun x _ => by rfl)","source_end":36351,"source_start":36301,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 104 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | edb6c096eb1177629679d6dd5c32816488294d7c950157424e044cc00aa7e57e | d20ca948cdf267e483789509c9fe87f7a1dd067d109f967e67a83e1e17306f1f | 71e5078428783271fe09af98b4d14fac5e0c120a7b1e755def217160e8571502 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 312 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c OrderedAddCommMonoid.toPartialOrder) (:c Real) (:c Real.orderedAddCommMonoid)))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedFiel... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":36350,"sourceStart":36347,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":36350,"sourceStart":36347,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":36350,"sourceStart":36347,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 107 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 01c056af7ddb2461a0b4d333b6541c1a5068b02e72b9ecb18080c833c5971687 | ac9142ac7c78d6ae1f1ef234194de9e4c94bd93fff4e4d2002da6b4456bd438d | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 313 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>nsmul_eq_mul</a>, <a>mul_assoc</a>] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence.p) (:fv _uniq.67230... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":36466,"sourceStart":36464,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36468,"sourceStart":36467,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"nsmul_eq_mul","source_end":36480,"source_start":36468,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":36491,"source_start":36482,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 112 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8b819c894841f8797f7abb963f03e29bf4929435ed739f0d68beb25a1348eadf | 776b8f0b7debc6c397e65bae30084239f7ad4632f08a721d48be59524e1d9452 | 662a107411ae853a509cd24106594811cbaf0c555f89cde2110b9b8df430a191 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 314 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case e_a.e_a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"congr","sourceEnd":36594,"sourceStart":36589,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":36594,"sourceStart":36589,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 122 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3999c7b994535465e8fbe52b8f7879bc438d90f8f1fa1de72a9b9976c651032 | ada142c56fcccd7c48013026221ef8721d9b829068b98f31fd69f7a2a31630c4 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | dfaccdd6b332fda9ede2d254505a59a00c7d1e8fc3e1efc38c34ec85352cd918 |
cat-searcher/leandojo-benchmark-4-random | test | 315 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.card_Ico</a>, <a>Nat.cast_sub</a> (<a>le_of_lt</a> <| hr_lt_n i)] | case e_a.e_a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Eq) (:c Real) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:c Finset.card) (:c Nat) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:fv _uniq.672328) (:fv _uniq.685884) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Finset.card) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.Ico) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":36598,"sourceStart":36596,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36600,"sourceStart":36599,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.card_Ico","s... | [] | [{"source":"Nat.card_Ico","source_end":36612,"source_start":36600,"syntax_kind":"ident"},{"source":"Nat.cast_sub (le_of_lt <| hr_lt_n i)","source_end":36650,"source_start":36614,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 124 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 08ad03bd001ea5e99cb9413ba7d4cb1527c3cb39ac7a1ec43ed54a0d664fd8aa | dfaccdd6b332fda9ede2d254505a59a00c7d1e8fc3e1efc38c34ec85352cd918 | 3983a3d60ef8ca39e098470625e9e31be7044d58d4aaf40224a5c9d7e1003998 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 316 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c GE.ge) (: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 HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":36759,"sourceStart":36753,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":36759,"sourceStart":36753,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 132 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c2c838aff6fd335bc7685262301df8597f7079569fab8b9b3d486289c919938 | 030bf75d1ea641a05470e25cb07d4eaec1fe9fab32c857249ebab33a0f53a937 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 6a9ad46f6a67d9e2422c4fc9ac1e590ffb7b8645de3f3e1c1f55b844636c2031 |
cat-searcher/leandojo-benchmark-4-random | test | 317 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hn₃ i | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673438) ((:c Nat.cast) (:c Real) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV7) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":36766,"sourceStart":36761,"tag":"atom"},{"children":[{"contextIndex":24,"semanticRole":"local","source":"hn₃","sourceEnd":36772,"sourceStart":36767,"tag":"identifier"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"i","sourceEnd":36774,"sourceStart":36773,"ta... | [] | [{"source":"hn₃ i","source_end":36774,"source_start":36767,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 134 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c95e92d63ebbc300aedf5cfa1f40bb2e14d4c7d53205e1b175b35f393b4cca6a | 6a9ad46f6a67d9e2422c4fc9ac1e590ffb7b8645de3f3e1c1f55b844636c2031 | 48b3eb454f6c66a0aeeed6efeb0f7a0f269c5adab2e24a55ff787c1fa73e3f53 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 318 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":36862,"sourceStart":36858,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":36862,"sourceStart":36858,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":36862,"sourceStart":36858,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 137 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c955505c931dd74e01c52e682090269cdcef90f92d1f309b9205f2cc4c4a4abe | 3e45b0c8457d805d9661c4b8f99c45eadab15a559702f3a1ff4f28c12582b48b | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 319 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.rpow_add_one</a> (by positivity) (<a>AkraBazziRecurrence.p</a> a b)] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c R... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":36966,"sourceStart":36964,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":36968,"sourceStart":36967,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":36971,"sourceSt... | [] | [{"source":"Real.rpow_add_one (by positivity) (p a b)","source_end":37013,"source_start":36972,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 144 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1717d5876ff57b0f1c7286a656dc933d1048359150a6f835619f351b019a39c2 | f08bcbdee405cda4f35c3b9c1d4786e6254fdd3dafe47d8ffb4aa0245f0155ff | c5e92108013a14e69201b1079e3dc4922b9d84649a49d9b136a80cb30bd363ac | e84035fcd6cdd65e29a5b22a95d2d9d8ca5b3e8bab2df03727322ed2a76e6e8f |
cat-searcher/leandojo-benchmark-4-random | test | 320 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"ring","sourceEnd":37020,"sourceStart":37016,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":37020,"sourceStart":37016,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 153 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4c8798ee992d2512467a1892c6392645a5a3b07554d68d3cac77994ed2e4de24 | e84035fcd6cdd65e29a5b22a95d2d9d8ca5b3e8bab2df03727322ed2a76e6e8f | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 321 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Ne) (:c Real) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV21)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":37004,"sourceStart":36994,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":37004,"sourceStart":36994,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":37004,"sourceStart":369... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 148 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fc9a5464f352850c0921f51f829b78982014e553151b47e79ff56a391f613446 | 7e56382244903eb8b0b17ba2cdcbd5df34441bce4a082a7b0a78921ef00dd3e2 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 322 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>div_self</a> (by positivity), <a>mul_one</a>] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673364) ((:c HSub.hS... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":37066,"sourceStart":37064,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37068,"sourceStart":37067,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"div_self (by positivity)","source_end":37092,"source_start":37068,"syntax_kind":"Lean.Parser.Term.app"},{"source":"mul_one","source_end":37101,"source_start":37094,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 156 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3d9f20b4dfeed087a917023f6410c205b2e4bec7dbbd89447857dbe5ea95c05c | 5ed88ab05f8dc56f338e462c7e6a46dc01a3400d4166583a5cc09f3ff0d4e81e | 8ded361ab91bc39a8887e646b32a3330ad14a45f03872aab531365842ceedfea | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 323 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Ne) (:c Real) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c AkraBazziRecurrence.p) (:fv _uniq.67230... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (: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 HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":37091,"sourceStart":37081,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":37091,"sourceStart":37081,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":37091,"sourceStart":370... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 162 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 50f5c4403bbcc411f3d39c91c8be714a84b12cbbf9e2130cbf960813d3178775 | cb4aa992e1759394c778e16f9937e22a21b9612a6f373f730ef3696d68625885 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 324 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c GE.ge) (: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)) (:fv _uniq.673364) ((:c HSub.hSub) (:c Real) (:c Real) (:c Real) ((:c instHSub) (:c Real) (:c Real.in... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":37219,"sourceStart":37213,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":37219,"sourceStart":37213,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 171 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a9513546ca104e0a50269f8ff4ee451516011f45c59d04fc63861b9a6ca95336 | dc3fd252354b22844e066d6e85efc51e192007bfed231508fd47a7a21599b493 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 5f871a4a9d5aea7c6e1a7eab842bae4018575f8dc7513554e00a5c506bb29c11 |
cat-searcher/leandojo-benchmark-4-random | test | 325 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>min_le_left</a> _ _ | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673364) ((:c HSub.hSub) (:c Real) (:c Real) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 Min.min) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Min) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":37226,"sourceStart":37221,"tag":"atom"},{"children":[{"name":"min_le_left","semanticRole":"global","source":"min_le_left","sourceEnd":37238,"sourceStart":37227,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":37240,"sourceStart":37239,"tag":"atom"}],"kin... | [] | [{"source":"min_le_left _ _","source_end":37242,"source_start":37227,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 173 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | bde16111dfd976400662e23b127b1d60811039cbbc532498172071c3b430ac3b | 5f871a4a9d5aea7c6e1a7eab842bae4018575f8dc7513554e00a5c506bb29c11 | f334fe0c032b0a83b8f2f5ed96e878303a4c4b46bc708c0bbc35465962da3066 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 326 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c AkraBazziRecurrence.sumTransform) ((:c AkraBazziRecurrence.p) (:fv _uniq.672300) (:fv _uniq.672303) (:fv _uniq.672318) (:fv _uniq.672322)) (:fv _uniq.672314) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857)) (:fv _uniq.685857)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c AkraBazziRecurrence.sumTransform) (:arg :explicit 0 (:app (:c AkraBazziRecurrence.p) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Fintype) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV5)) (:arg :explic... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":37411,"sourceStart":37408,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":37411,"sourceStart":37408,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":37411,"sourceStart":37408,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 180 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fad59b4cdeaef468cf2c1b411036ba24778095cc137bd52e985e0b4bf915a4d8 | 5bbe9c4447abbddf58db1cb7bfd75c5813c057aff2088777b73b75329aedd50e | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 327 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr with u hu | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c GE.ge) (: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 Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":37528,"sourceStart":37522,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"with","sourceEnd":37533,"sourceStart":37529,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"u","sourceEnd":37535,"sourceStar... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 187 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 070db9826a9191ad50175aae5e398422c832e38903fc30426224969ab4a643c6 | 27149cad7ab295ca6a8f0d55523c0aa6e11d8711d54404962e4e05dddf27c5ba | e1ea6cbd757ecb01d4c26fae2d34b3e0eb9712d2944f09cef170e96a3fc37fb8 | 07a4f944cb23132c10f234c466e5b1a8bde107fea7a58b8e38f8021acbea19cb |
cat-searcher/leandojo-benchmark-4-random | test | 328 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":37554,"sourceStart":37552,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37556,"sourceStart":37555,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":37570,"source_start":37556,"syntax_kind":"ident"},{"source":"hu","source_end":37577,"source_start":37575,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 188 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8c5abcecf67f312ed3fbacd689fa705dfd30b7c0cf420739458bcc9bd7e6444b | 07a4f944cb23132c10f234c466e5b1a8bde107fea7a58b8e38f8021acbea19cb | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | afc0fef1433278d46aedd008c4cebad9df3357fb91416e8ba2bfa6eca7cf7111 |
cat-searcher/leandojo-benchmark-4-random | test | 329 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hu' : u ∈ <a>Set.Icc</a> (r i n) n := ⟨hu.1, by omega⟩ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":37595,"sourceStart":37591,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hu'","sourceEnd":37599,"sourceStart":37596,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hu'","sourceEnd":37599,"sourceStart":37596,"tag":"n... | [] | [{"source":"u ∈ Set.Icc (r i n) n","source_end":37625,"source_start":37602,"syntax_kind":"«term_∈_»"},{"source":"⟨hu.1, by omega⟩","source_end":37649,"source_start":37629,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 191 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f41a291cf56890ae204b0f7ffd3b1e9285c3365067c2ba356226364967706fb6 | afc0fef1433278d46aedd008c4cebad9df3357fb91416e8ba2bfa6eca7cf7111 | 34ee9d553bf40589f62d039cfa083e7551133cc008253c89b99e8052030099e4 | da6ee4e93fde6f072bb85ead5d1f35dc2fc456e2ef4041fb6e7f9ef35c8ad59c |
cat-searcher/leandojo-benchmark-4-random | test | 330 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine hn₂ u ?_ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":37669,"sourceStart":37663,"tag":"atom"},{"children":[{"contextIndex":23,"semanticRole":"local","source":"hn₂","sourceEnd":37675,"sourceStart":37670,"tag":"identifier"},{"children":[{"contextIndex":32,"semanticRole":"local","source":"u","sourceEnd":37677,"sourceStart":37676,"t... | [] | [{"source":"hn₂ u ?_","source_end":37680,"source_start":37670,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 197 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73485c3965e399fa5a3b8525123b3703005a1c313a2fe49580c53f7a9394f964 | da6ee4e93fde6f072bb85ead5d1f35dc2fc456e2ef4041fb6e7f9ef35c8ad59c | 49a91b5362fdc92f75a9c65a12820be4cd55d1861edbadf2fc036501814b3fa7 | 75ae1b4a5c3ad29cd333e2ede9e2e2b3efa46968e55ad173a77b9286f4850194 |
cat-searcher/leandojo-benchmark-4-random | test | 331 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Set.mem_Icc</a>] | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Membership.mem) (:c Real) ((:c Set) (:c Real)) ((:c Set.instMembership) (:c Real)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.832267)) ((:c Set.Icc) (:c Real) (:c Real.instPreorder) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:c Real)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:c Real))))))) (:arg :explicit 3 (:app (:c Nat.cast) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":37696,"sourceStart":37694,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":37698,"sourceStart":37697,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.mem_Icc","se... | [] | [{"source":"Set.mem_Icc","source_end":37709,"source_start":37698,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 198 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 470980dfb3f7e5e3b1fa59cc4a0c943a7098060bc94920d404240c8a3a4e67a5 | 75ae1b4a5c3ad29cd333e2ede9e2e2b3efa46968e55ad173a77b9286f4850194 | 7860e98a80f38e7bc18c1fe77ce3f4ad43754d2b1aac472b17191699e19eba20 | 4f011ba227375c30090521e45dc12aee159bad599350c62d873a44d8f035fb64 |
cat-searcher/leandojo-benchmark-4-random | test | 332 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, by norm_cast; omega⟩ | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c And) ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c And) (: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 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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"refine","sourceEnd":37730,"sourceStart":37724,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":37734,"sourceStart":37731,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":37735,"sourceStart":37734,"tag":"atom"},{"children":[{"source":"_","sourceEnd":37736,"sourceStart":37735,... | [] | [{"source":"⟨?_, by norm_cast; omega⟩","source_end":37760,"source_start":37731,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 201 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 573b6a13e40f8bb5fe90ba1c753799f885793e996570f0dc5c21c9ab5ae2edaf | 4f011ba227375c30090521e45dc12aee159bad599350c62d873a44d8f035fb64 | f9f28c7ff323c57081f0986fcf931274387da7f2dc085f339fc9b7b60ccf07b1 | 0340483a0926475917fd541a2481bd6c8ace4f1263a6cc10e78f35ba989bc74d |
cat-searcher/leandojo-benchmark-4-random | test | 333 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | calc c₁ * n ≤ r i n := by exact hn₁ i _ ≤ u := by exact_mod_cast hu'.1 | case h.h.hab
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.832267))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"calc","sourceEnd":37778,"sourceStart":37774,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":10,"semanticRole":"local","source":"c₁","sourceEnd":37783,"sourceStart":37779,"tag":"identifier"},{"source":"*","sourceEnd":37785,"sourceStart":37784,"tag":"atom"},{"cont... | [] | [{"source":"c₁ * n ≤ r i n","source_end":37797,"source_start":37779,"syntax_kind":"«term_≤_»"},{"source":"hn₁ i","source_end":37817,"source_start":37810,"syntax_kind":"Lean.Parser.Term.app"},{"source":"_","source_end":37842,"source_start":37841,"syntax_kind":"Lean.Parser.Term.hole"},{"source":"u","source_end":37848,"so... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 209 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 48d8026ad031ba681543a76b96ad86c095da81cb3168aa5a128515a3693a5a2b | 0340483a0926475917fd541a2481bd6c8ace4f1263a6cc10e78f35ba989bc74d | 78a9b87523d43682844003a3cbd796ef057f3f88725881b1a5f5cd2ec5fad5e6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 334 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Nat) ((:c Preorder.toLE) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring)))) (:fv _uniq.832267) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"omega","sourceEnd":37646,"sourceStart":37641,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":37646,"sourceStart":37641,"tag":"node"}],"kind":"null","source":"omega","source... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 194 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0a62cc2b9ee6c679992b1551093120af1c43ffef5caf31e7820d73983ef5c45b | 2e32d836d7337865d27b85eba13bd19b3d7400c1d53dd2646b7a5f7a991ec36d | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 335 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | norm_cast | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.832267)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV32)))) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"norm_cast","sourceEnd":37750,"sourceStart":37741,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.tacticNorm_cast_","source":"norm_cast","sourceEnd":37750,"sourceStart":37741,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 206 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 0bf04eef491a8418f8d650ed134497906a32395527c5b982ab303f05952dac95 | d33d33c179504d70daaa51249070f65fadc828589106be671f0cdf2c3d533b81 | 4526560ee387a60af0a3f42ddce7258b27dc8bd6782a63271dc2d5aa462e81b2 | ff6c192f994a145219c749d2c0664a19410379f338d2ae94f891334510f7ed14 |
cat-searcher/leandojo-benchmark-4-random | test | 336 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | omega | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Nat) (:c instLENat) (:fv _uniq.832267) (:fv _uniq.685857)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Nat)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Nat))))) (:arg :explicit 2 (:fv FV32)) (:arg :explicit 3 (:fv FV21))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"omega","sourceEnd":37757,"sourceStart":37752,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.omega","source":"omega","sourceEnd":37757,"sourceStart":37752,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 208 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 2dbd77e5764a0c422e7c9358ba4bfac70216295ac05e5b65c4973860304efc72 | ff6c192f994a145219c749d2c0664a19410379f338d2ae94f891334510f7ed14 | 304b4a90a76a1cbe4c112e074b30e75181f54df43d60f883597457844293b341 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 337 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hn₁ i | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857)... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact","sourceEnd":37809,"sourceStart":37804,"tag":"atom"},{"children":[{"contextIndex":22,"semanticRole":"local","source":"hn₁","sourceEnd":37815,"sourceStart":37810,"tag":"identifier"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"i","s... | [] | [{"source":"hn₁ i","source_end":37817,"source_start":37810,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 212 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ed60ba76c83f893921f3db18fec33182a408833c1891323c6d3a1f5cd3daef6 | 7312bc3cf1402ecff3750ab3e4d156f97629ac4f8c23c58aa780ef558a087b12 | 65a0a6bcd04186e53972f1fd101d4c2c248fb48cee7e38510af9cf4f66a8cc03 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 338 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hu'.1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.832267))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV7) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact_mod_cast","sourceEnd":37869,"sourceStart":37855,"tag":"atom"},{"children":[{"contextIndex":34,"semanticRole":"local","source":"hu'","sourceEnd":37873,"sourceStart":37870,"tag":"identifier"},{"source":".","sourceEnd":37874,"sourceStart":37873,"tag":"at... | [] | [{"source":"hu'.1","source_end":37875,"source_start":37870,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 217 | exact | true | 1 | 34 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 83951e505392093c5c31c07c514653c02f0c19eebf41cf0549ade112851bed73 | 7d1c09dac583a8429baa0e59f026c4662a06bcbdd8b21f59488f2ac93c536a93 | d6baa19933f6e4b56dc8be40f5cae3e2068344ecde60d74e2fde8fe2b99c35b7 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 339 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr n^(<a>AkraBazziRecurrence.p</a> a b) * (<a>Finset.Ico</a> (r i n) n).<a>Finset.sum</a> (fun _ => c₂ * g n / ?_) with u hu | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c GE.ge) (: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 Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":37999,"sourceStart":37993,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":21,"semanticRole":"local","source":"n","sourceEnd":38001,"sourceStart":38000,"tag":"identifier"},{"source":"^","sourceEnd":38002,"sourceStart":38001,"tag":"atom"},{"children":[{"sou... | [] | [{"source":"n^(p a b) * (Finset.Ico (r i n) n).sum (fun _ => c₂ * g n / ?_)","source_end":38065,"source_start":38000,"syntax_kind":"«term_*_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 224 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1794f414e05c2ad9e219a9b559a95a0b9c52f7f76f89f1bdee741eff655410d2 | 27149e652f16573bf1e5fd1800a9a8a79f25330633b33a1e36a3c87c3541bc8f | 8ad4c7769dc4bcfba172d71221da2eaa0a90e792b25bcc4178452c3a0e2936cf | 1abfc36753da8cd771690e3298ac2b4da0904ac9e90d3c8178f787eaee70e2fb |
cat-searcher/leandojo-benchmark-4-random | test | 340 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":38094,"sourceStart":38092,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38096,"sourceStart":38095,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":38110,"source_start":38096,"syntax_kind":"ident"},{"source":"hu","source_end":38117,"source_start":38115,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 229 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e4d6b9d657eebc1e1fbb35e3dcb7f01e9627def32b85f1f8ac61d39c8be58759 | d825fe562232b9bc7fc9319d24ef67406661c7b315d392c7ccf37d80372f8b43 | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | 483fa531e330c14d973288318d5d79d0d7e04cde212ef2fd3738324bb661de25 |
cat-searcher/leandojo-benchmark-4-random | test | 341 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have := calc 0 < r i n := hrpos_i _ ≤ u := hu.1 | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"have","sourceEnd":38137,"sourceStart":38133,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"","sourceEnd":38138,"sourceStart":38138,"tag":"identifier"}],"kind":"hygieneInfo","source":"","sourceEnd":38138,"sourceStart":38138,"tag":"node"}],"kind":"Lean.Parser.Term.hav... | [] | [{"source":"calc 0 < r i n := hrpos_i\n _ ≤ u := hu.1","source_end":38209,"source_start":38141,"syntax_kind":"Lean.calc"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 232 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 643ceb781bb8f112756615d2d6fb67db991906ba60b14a006a6c31d4c5ecc9a0 | 483fa531e330c14d973288318d5d79d0d7e04cde212ef2fd3738324bb661de25 | 462b645665503a04f21475c45538d1d18d71544cbf0b328442e8e0cfae0d4e32 | 4a2f070ab51d0df0a205e05847c0024527df8a7726ac0dbb9a72c9090342c12d |
cat-searcher/leandojo-benchmark-4-random | test | 342 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | case h.h.hc
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ... | ((:c LT.lt) (:c Real) ((:c Preorder.toLT) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"positivity","sourceEnd":38235,"sourceStart":38225,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":38235,"sourceStart":38225,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 233 | exact | true | 1 | 34 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f703718f65dcbd4fe3f10903411be79f6315562705816b414930a148524a2684 | 4a2f070ab51d0df0a205e05847c0024527df8a7726ac0dbb9a72c9090342c12d | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 343 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Finset.mem_Ico</a>] at hu | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":38254,"sourceStart":38252,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38256,"sourceStart":38255,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Finset.mem_Ico",... | [] | [{"source":"Finset.mem_Ico","source_end":38270,"source_start":38256,"syntax_kind":"ident"},{"source":"hu","source_end":38277,"source_start":38275,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 238 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 515a0c77569841af6cb54848fe6c903f476309af9c938856d9ecfc5650bc01b5 | f42edbe267298915d42659a3b63e2f031041f5ad15fb6b6feab040f8aae0ba56 | e03ca1855f111f96df0ca3325cc611848b6b63c7d70640ceb137c2cbcd41fce3 | 5b2bebf9ce5ed87ebfe980438d957508a90495420fdbf5a27fddb183d0332a78 |
cat-searcher/leandojo-benchmark-4-random | test | 344 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Real.rpow_le_rpow_of_exponent_nonpos</a> (by positivity) (by exact_mod_cast hu.1) (<a>le_of_lt</a> hp) | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":38298,"sourceStart":38293,"tag":"atom"},{"children":[{"name":"Real.rpow_le_rpow_of_exponent_nonpos","semanticRole":"global","source":"rpow_le_rpow_of_exponent_nonpos","sourceEnd":38330,"sourceStart":38299,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":... | [] | [{"source":"rpow_le_rpow_of_exponent_nonpos (by positivity)\n (by exact_mod_cast hu.1) (le_of_lt hp)","source_end":38402,"source_start":38299,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 241 | exact | true | 1 | 33 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c48b0e2cbc38d7b04299d5ca4a1ab1251b1e2397d49e9e5968bdb9a03a17303b | 5b2bebf9ce5ed87ebfe980438d957508a90495420fdbf5a27fddb183d0332a78 | 5365d410801e16758a503e73f55c3c3632a398aa0d2aec70aef030fe07a3aad0 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 345 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":38345,"sourceStart":38335,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":38345,"sourceStart":38335,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":38345,"sourceStart":383... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 244 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f8eb723bde1a68b0f229b44e1942637f1b2e74ef966eff4d2485982c5685e8cb | 4741386056d6a3b095819c9f734a761962c9481c571c4c608225a068bd4ffc1a | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 346 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact_mod_cast hu.1 | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.852246))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV7) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"exact_mod_cast","sourceEnd":38382,"sourceStart":38368,"tag":"atom"},{"children":[{"contextIndex":33,"semanticRole":"local","source":"hu","sourceEnd":38385,"sourceStart":38383,"tag":"identifier"},{"source":".","sourceEnd":38386,"sourceStart":38385,"tag":"ato... | [] | [{"source":"hu.1","source_end":38387,"source_start":38383,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 249 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a59c726518a4870bafc4abf76422a1f2c86a159bf6fe06242727fe7dd5a53198 | 1a0526fb6b12cab518fdd1411eb6da9e9edcfa16a013f1c94b2e252c3c4e56f5 | 9edea7f92174ff226a0f964b33830d117c0b101f56a83f048532cf6e47460615 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 347 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c GE.ge) (: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 Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":38525,"sourceStart":38519,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":38525,"sourceStart":38519,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 256 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 317eace91c8fbbffa1e8833c130f2588a9efdf096ce50458e44489e97dc31583 | fb32c7b5d077b0152505fe8477a5194bb2552f4ad5c9ac763980bc9c1a69afe4 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | 73018167029920dad20f3fc88ce1115246993e3e2ec8b26dbd6b1d9771a5f32b |
cat-searcher/leandojo-benchmark-4-random | test | 348 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Finset.card_nsmul_le_sum</a> _ _ _ (fun x _ => by rfl) | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c HSMul.hSMul) (:c Nat) (:c Real) (:c Real) ((:c instHSMul) (:c Nat) (:c Real) ((:c AddMonoid.toNatSMul) (:c Real) (:c Real.instAddMonoid))) ((:c Finset.card) (:c Nat) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c Str... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 HSMul.hSMul) (:arg :implicit-type 0 (:c Nat)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HSMul) ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":38532,"sourceStart":38527,"tag":"atom"},{"children":[{"name":"Finset.card_nsmul_le_sum","semanticRole":"global","source":"Finset.card_nsmul_le_sum","sourceEnd":38557,"sourceStart":38533,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":38559,"sourceStart"... | [] | [{"source":"Finset.card_nsmul_le_sum _ _ _ (fun x _ => by rfl)","source_end":38583,"source_start":38533,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 258 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 67bb9839ad0e3cc400812ed766a39fb1f8942f497bf801cacaffe84e8721e0dc | 73018167029920dad20f3fc88ce1115246993e3e2ec8b26dbd6b1d9771a5f32b | 71e5078428783271fe09af98b4d14fac5e0c120a7b1e755def217160e8571502 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 349 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rfl | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c OrderedAddCommMonoid.toPartialOrder) (:c Real) (:c Real.orderedAddCommMonoid)))) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedFiel... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rfl","sourceEnd":38582,"sourceStart":38579,"tag":"atom"}],"kind":"Lean.Parser.Tactic.tacticRfl","source":"rfl","sourceEnd":38582,"sourceStart":38579,"tag":"node"}],"kind":"null","source":"rfl","sourceEnd":38582,"sourceStart":38579,"tag":"node"}],"kind":"Lea... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 261 | exact | true | 1 | 33 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 7c9042a30449279d0c68bc8d7bf8f0e5c9524ac9ca06ca2abb1ce207c2e7c132 | 44c6db898ff5e4418aef1914f1114907f7aea3a96a908e00e2f4bc03a04035c4 | 5a633da644c1afc6f5222be040e6a19d687c01104c0263cce32773e07376dfa8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 350 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>nsmul_eq_mul</a>, <a>mul_assoc</a>] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c AkraBazziRecurrence.p) (:fv _uniq.67230... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":38698,"sourceStart":38696,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":38700,"sourceStart":38699,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"nsmul_eq_mul","source_end":38712,"source_start":38700,"syntax_kind":"ident"},{"source":"mul_assoc","source_end":38723,"source_start":38714,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 266 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 93b29e974c466ac514dd5fa5947fad38dfcc99a12afeda119624105e392d617c | cf037f413e167b1bccff9891c3b5b4f074c5cc50df857211bd0eca31406a8be5 | 662a107411ae853a509cd24106594811cbaf0c555f89cde2110b9b8df430a191 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 351 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr n^(<a>AkraBazziRecurrence.p</a> a b) * (<a>Finset.Ico</a> (r i n) n).<a>Finset.card</a> * (c₂ * g n / ?_) | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ... | ((:c GE.ge) (: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 HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":38848,"sourceStart":38842,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"contextIndex":21,"semanticRole":"local","source":"n","sourceEnd":38850,"sourceStart":38849,"tag":"identifier"},{"source":"^","sourceEnd":38851,"sourceStart":38850,"tag":"atom"},{"chi... | [] | [{"source":"n^(p a b) * (Finset.Ico (r i n) n).card * (c₂ * g n / ?_)","source_end":38908,"source_start":38849,"syntax_kind":"«term_*_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 276 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b89eb3a5a31dbc05d9d80703ace437f37be885e82fdee07053fbcf79ad3a6c19 | 22dbdb8379afeb0c49e32d48ec7769eb7118f73298f56d11cae6c1c3c5c99817 | 23056978ceb87765e675ea6704d3278206bf58d9d07b01f84ce2f42f10bd0ac6 | ac5d717bde65d9ba02debfff56f45a2635765fcbb93399d0a855c8cd26e3a1db |
cat-searcher/leandojo-benchmark-4-random | test | 352 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>Real.rpow_le_rpow_of_exponent_nonpos</a> (by positivity) (hn₁ i) (<a>le_of_lt</a> hp) | case h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) ((:c PartialOrder.toPreorder) (:c Real) ((:c StrictOrderedSemiring.toPartialOrder) (:c Real) ((:c LinearOrderedSemiring.toStrictOrderedSemiring) (:c Real) ((:c LinearOrderedCommSemiring.toLinearOrderedSemiring) (:c Real) ((:c LinearOrderedSemifield.toLinearOrderedComm... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HPow.hPow) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HPow) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":38927,"sourceStart":38922,"tag":"atom"},{"children":[{"name":"Real.rpow_le_rpow_of_exponent_nonpos","semanticRole":"global","source":"rpow_le_rpow_of_exponent_nonpos","sourceEnd":38959,"sourceStart":38928,"tag":"identifier"},{"children":[{"children":[{"source":"(","sourceEnd":... | [] | [{"source":"rpow_le_rpow_of_exponent_nonpos (by positivity) (hn₁ i) (le_of_lt hp)","source_end":38999,"source_start":38928,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 277 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 35e8b11125070f8c0b37fc3a0bfc8706a8a4ac1d9d5d78894d4f57ec61c6eb7d | ac5d717bde65d9ba02debfff56f45a2635765fcbb93399d0a855c8cd26e3a1db | 61e5d8246ed6567e0097847e844d8e07cc196bc8489759423595f1c7ae5619c2 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 353 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LT.lt) (:c Real) (:c Real.instLT) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673278) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:lit 0)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":38974,"sourceStart":38964,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":38974,"sourceStart":38964,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":38974,"sourceStart":389... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 280 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1062926fa3ad1f24a8dd274dbc7b51b304e66834aaf70641f9c78c5501d3329e | bfe99ee276ce2f2809e516aa219abbe00bec3d9e20d9ee3d63c90854b8d55ba6 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 354 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | congr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case e_a.e_a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"congr","sourceEnd":39104,"sourceStart":39099,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Lean.Parser.Tactic.congr","source":"congr","sourceEnd":39104,"sourceStart":39099,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 287 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8a3f530ea64677b3106adc6898debd462b485f93e3ad150933023496e35c3414 | dfad2b9390663b6ba469727c21c362dbc7851e4833cd29eccdacbac7ea04d721 | 092b163cac48997cb6cc327c63cda260e694055f56ff3698a70cdfda80ffbb2b | 78138ea806c94095d3100a5d974b63667f0408d0294ccb3511ec190a294791d2 |
cat-searcher/leandojo-benchmark-4-random | test | 355 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Nat.card_Ico</a>, <a>Nat.cast_sub</a> (<a>le_of_lt</a> <| hr_lt_n i)] | case e_a.e_a
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g... | ((:c Eq) (:c Real) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:c Finset.card) (:c Nat) ((:c Finset.Ico) (:c Nat) ((:c PartialOrder.toPreorder) (:c Nat) ((:c StrictOrderedSemiring.toPartialOrder) (:c Nat) (:c Nat.instStrictOrderedSemiring))) (:c Nat.instLocallyFiniteOrder) ((:fv _uniq.672328) (:fv _uniq.685884) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Finset.card) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Finset.Ico) (:a... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":39108,"sourceStart":39106,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":39110,"sourceStart":39109,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Nat.card_Ico","s... | [] | [{"source":"Nat.card_Ico","source_end":39122,"source_start":39110,"syntax_kind":"ident"},{"source":"Nat.cast_sub (le_of_lt <| hr_lt_n i)","source_end":39160,"source_start":39124,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 289 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b16c514251ff83bd1a9d674bdbdc8f92319cd388d08be2858056789c43bc5708 | 78138ea806c94095d3100a5d974b63667f0408d0294ccb3511ec190a294791d2 | 3983a3d60ef8ca39e098470625e9e31be7044d58d4aaf40224a5c9d7e1003998 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 356 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c GE.ge) (: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 HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) (... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":39272,"sourceStart":39266,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":39272,"sourceStart":39266,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 297 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8182b5722b42beec53d88c1096a84306df175d76cd20a38bd2f31c15390ed99e | 81cfd4161dc40377416f647ebf8c737f23a055361af5cb57644b152b17cead02 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | c799493e431c0a69abb5f511a71d7750e5a00969fb0250bf419ac2819bd5e21a |
cat-searcher/leandojo-benchmark-4-random | test | 357 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hn₃ i | case h.h.h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) ((:fv _uniq.672328) (:fv _uniq.685884) (:fv _uniq.685857))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673438) ((:c Nat.cast) (:c Real) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:fv FV7) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":39279,"sourceStart":39274,"tag":"atom"},{"children":[{"contextIndex":24,"semanticRole":"local","source":"hn₃","sourceEnd":39285,"sourceStart":39280,"tag":"identifier"},{"children":[{"contextIndex":28,"semanticRole":"local","source":"i","sourceEnd":39287,"sourceStart":39286,"ta... | [] | [{"source":"hn₃ i","source_end":39287,"source_start":39280,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 299 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8ba75f51b4a3a42d894a7bb53d2d0eb038eda07b161f3edd5ccf4717d1398226 | c799493e431c0a69abb5f511a71d7750e5a00969fb0250bf419ac2819bd5e21a | 48b3eb454f6c66a0aeeed6efeb0f7a0f269c5adab2e24a55ff787c1fa73e3f53 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 358 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"ring","sourceEnd":39381,"sourceStart":39377,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":39381,"sourceStart":39377,"tag":"node"}],"kind":"null","source":"ring","sourceEnd":39381,"sourceStart":39377,"tag":"node"}],"kind":"Le... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 302 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d99bbd1852d7e2f60137f74536fb0243ffb901dd7151bd5535ed4d2d60b5a753 | 6286e1d421b03895fe400cc4abf7d5a9deea6153cb4e9cd87fdd31254bfcca70 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 359 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>Real.mul_rpow</a> (by positivity) (by positivity)] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c R... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":39502,"sourceStart":39500,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":39504,"sourceStart":39503,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"",... | [] | [{"source":"Real.mul_rpow (by positivity) (by positivity)","source_end":39549,"source_start":39504,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 307 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c950dfc4dcf39febf5285c71ae49a5c542f9fa4ea92ef7c93686600372f28c5e | 281508307961a2caf54538d8c6bcd73ac3568b9715e320333cb6d95272d238c5 | 0ecbda284f2be9516bf66221f5eca2250d33345ce708235f9302898a4d1df2b4 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 360 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((: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.673278)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":39532,"sourceStart":39522,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":39532,"sourceStart":39522,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":39532,"sourceStart":395... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 313 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 27fb12381ba3a08aea2f3f3848e0358a042cee655c05fa25ff47a47a8c4d9054 | f2b27514ebb3405edd3878e4af15990f04efbd7c3575e23f972cef4ba8a7a4f6 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 361 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c LE.le) (:c Real) (:c Real.instLE) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero))) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":39548,"sourceStart":39538,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":39548,"sourceStart":39538,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":39548,"sourceStart":395... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 318 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | cf87e273197b91debc8d9ea6a726eb8d5da13846ed41f5efa1391522961dbfaf | 456e19e3f0284f87ba4cec9bf075760562edf5efdba17de3c095c14950a7db57 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 362 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← <a>Real.rpow_add_one</a> (by positivity) (<a>AkraBazziRecurrence.p</a> a b)] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c R... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":39671,"sourceStart":39669,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":39673,"sourceStart":39672,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":39676,"sourceSt... | [] | [{"source":"Real.rpow_add_one (by positivity) (p a b)","source_end":39718,"source_start":39677,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 326 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9e0cc3666f9e28b735f6d2b60fbd291d8acc02916f3315953fa9a5bd283df610 | 5a657080e4b1b157979177db24ae5c3c920d577a3b4487904520c7d3018ee58c | c5e92108013a14e69201b1079e3dc4922b9d84649a49d9b136a80cb30bd363ac | c84b21183314f24ef12d575637dba8440ddff639f2f3c67fb1b19d0702670592 |
cat-searcher/leandojo-benchmark-4-random | test | 363 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Re... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"ring","sourceEnd":39725,"sourceStart":39721,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":39725,"sourceStart":39721,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 335 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 45d6fc295efffd015e9ce9f3d4994ede5f7f34b3901247630197c824e61c47b0 | c84b21183314f24ef12d575637dba8440ddff639f2f3c67fb1b19d0702670592 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 364 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Ne) (:c Real) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c OfNat.ofNat) (:c Real) (:lit 0) ((:c Zero.toOfNat0) (:c Real) (:c Real.instZero)))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c Nat.cast) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c NatCast) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:fv FV21)))) (:arg :explicit 2 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Real)) (:arg :exp... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":39709,"sourceStart":39699,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":39709,"sourceStart":39699,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":39709,"sourceStart":396... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 330 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b2ace3681062e01f123dbd04c85b65129190b1714a852bf2bfbb90f0ff0d4959 | 641b07fa030f98215ce6199050b8e285a5d6017fc05c6cf15ce5b36530f446cf | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 365 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>div_self</a> (by positivity), <a>one_mul</a>] | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"rw","sourceEnd":39804,"sourceStart":39802,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":39806,"sourceStart":39805,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"div... | [] | [{"source":"div_self (by positivity)","source_end":39830,"source_start":39806,"syntax_kind":"Lean.Parser.Term.app"},{"source":"one_mul","source_end":39839,"source_start":39832,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 340 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | fcc84a40a5d7fecabf2c91c3580f1eafe4ce5836de1d352d1042a7b3cf82fb51 | c90329857f5bf8e7fbd7c5464c9bc8d162509717485615d75a6b195628989aa4 | 334cf0435dc8d1375ec04fa0cc3e59d707826cbce4bba4b30bb51f9eb675864f | 9b221e93e1f7bc9c60719e01a78552558b127eb8506e38c98f9fb0b94ab995c3 |
cat-searcher/leandojo-benchmark-4-random | test | 366 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ring | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Eq) (:c Real) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Eq) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HDiv.hDiv) (:arg :implicit-type 0 (:c Real)) (:arg :implicit-type 1 (:c Real)) (:arg :implicit-type 2 (:c Real)) (:arg :instance 3 (:instance-of (:app (:c HDiv) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"ring","sourceEnd":39846,"sourceStart":39842,"tag":"atom"}],"kind":"Mathlib.Tactic.RingNF.ring","source":"ring","sourceEnd":39846,"sourceStart":39842,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 350 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | e6182ceda135c95717c2b7047cffb484c24adfcebf0da92a106d3f4ce9042517 | 9b221e93e1f7bc9c60719e01a78552558b127eb8506e38c98f9fb0b94ab995c3 | 16b974583155fdcb11fb6832a37be09c18c7acecbfb352c25a35512bfd755a33 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 367 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | positivity | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | ((:c Ne) (:c Real) ((:c HPow.hPow) (:c Real) (:c Real) (:c Real) ((:c instHPow) (:c Real) (:c Real) (:c Real.instPow)) ((:c Nat.cast) (:c Real) (:c Real.instNatCast) (:fv _uniq.685857)) ((:c HAdd.hAdd) (:c Real) (:c Real) (:c Real) ((:c instHAdd) (:c Real) (:c Real.instAdd)) ((:c AkraBazziRecurrence.p) (:fv _uniq.67230... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c Ne) (:arg :implicit-type 0 (:c Real)) (:arg :explicit 1 (:app (:c HPow.hPow) (: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 HPow) (:arg :explicit 0 (:c Real)) (:arg :explicit 1 (:c Real)) (:arg :explicit 2 (:c Rea... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"children":[{"children":[{"children":[{"source":"positivity","sourceEnd":39829,"sourceStart":39819,"tag":"atom"}],"kind":"Mathlib.Tactic.Positivity.positivity","source":"positivity","sourceEnd":39829,"sourceStart":39819,"tag":"node"}],"kind":"null","source":"positivity","sourceEnd":39829,"sourceStart":398... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 344 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5215abc927d9cce018d51d4f620bb53fae966a3a9efebb9ae1d9ebd991577d2e | bdce45897d55b9b898e8931b3fb49e97bc7a8c88a01a54d20a78b9b573d82050 | bfac723e90b2b18faaf3a5c655a156ad247487e2d4cd2b4fe44fd8ea9dcad7de | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 368 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | gcongr | α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ g u
c₃ ... | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c GE.ge) (:c Real) (:c Real.instLE) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) ((:c HDiv.hDiv) (:c Real) (:c Real) (:c Real) ((:c instHDiv) (:c Real) ((:c LinearOrderedField.toDiv) (:c Real) (:c Real.instLinearOrderedField))) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (:app (:c GE.ge) (: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.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"gcongr","sourceEnd":39957,"sourceStart":39951,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"}],"kind":"Mathlib.Tactic.GCongr.tacticGcongr__With__","source":"gcongr","sourceEnd":39957,"sourceStart":39951,"tag":"node"} | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 355 | exact | true | 1 | 31 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62b89a02df83f380f751ea2a7f9704c93f0de640cc385cd49376ea25edde799e | a8a96e7bca9341f084f419eceb6ee61ff3fd3e8ffc7fcf26a7df4d9b312101c3 | 7681489794c20ff221cf115a6d6f5e4351c46b6ec8b1f901575d361640dc6cdf | f1b084afa785d8b64749c38a17a1629cfd95aeb25700f50c63e4d28b3e91ce79 |
cat-searcher/leandojo-benchmark-4-random | test | 369 | AkraBazziRecurrence.eventually_atTop_sumTransform_ge | Mathlib/Computability/AkraBazzi/AkraBazzi.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>min_le_right</a> _ _ | case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : Nonempty α
T : ℕ → ℝ
g : ℝ → ℝ
a b : α → ℝ
r : α → ℕ → ℕ
R : AkraBazziRecurrence T g a b r
c₁ : ℝ
hc₁_mem : c₁ ∈ Set.Ioo 0 1
hc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)
c₂ : ℝ
hc₂_mem : c₂ > 0
hc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c₂ * g ↑n ≤ ... | ((:c LE.le) (:c Real) ((:c Preorder.toLE) (:c Real) (:c Real.instPreorder)) ((:c Min.min) (:c Real) ((:c LinearOrderedRing.toMin) (:c Real) (:c Real.instLinearOrderedRing)) ((:c HMul.hMul) (:c Real) (:c Real) (:c Real) ((:c instHMul) (:c Real) (:c Real.instMul)) (:fv _uniq.673364) ((:c HSub.hSub) (:c Real) (:c Real) (:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝¹","sexp":"((:c Fintype) (:fv _uniq.672300))"},{"name":"inst✝","sexp":"((:c Nonempty) (:fv _uniq.672300))"},{"name":"T","sexp":"(:forall _ (:c Nat) (:c Real))"},{"name":"g","sexp":"(:forall _ (:c Real) (:c Real))"},{"name":"a","sexp":"(:forall _ (:fv _uniq.672300) ... | (: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 Min.min) (:arg :implicit-type 0 (:c Real)) (:arg :instance 1 (:instance-of (:app (:c Min) (:arg :explicit 0 (:c Real))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"name":"inst✝¹","sexp":"(:app (:c Fintype) (:arg :expli... | {"children":[{"source":"exact","sourceEnd":39964,"sourceStart":39959,"tag":"atom"},{"children":[{"name":"min_le_right","semanticRole":"global","source":"min_le_right","sourceEnd":39977,"sourceStart":39965,"tag":"identifier"},{"children":[{"children":[{"source":"_","sourceEnd":39979,"sourceStart":39978,"tag":"atom"}],"k... | [] | [{"source":"min_le_right _ _","source_end":39981,"source_start":39965,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.672300","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.672303","is_instance":true,"is_let":false,"user_name":"inst✝¹"},{"binder_role":":instance-implicit","context_index... | 86 | 357 | exact | true | 1 | 31 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9f3e00087b22d0f9748aa4691d5175d3a12153b292ef6ea9840687aa0e88df21 | f1b084afa785d8b64749c38a17a1629cfd95aeb25700f50c63e4d28b3e91ce79 | dec4ce9aae6e4bd4a4fb2c8e13ecde19ae010bf57bafd2a68612e4041785afa6 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 370 | iSup₂_disjoint_iff | Mathlib/Order/CompleteBooleanAlgebra.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>iSup_disjoint_iff</a>] | α : Type u
β : Type v
ι : Sort w
κ : ι → Sort w'
inst✝ : Frame α
s t : Set α
a b : α
f : (i : ι) → κ i → α
⊢ Disjoint (⨆ i, ⨆ j, f i j) a ↔ ∀ (i : ι) (j : κ i), Disjoint (f i j) a | ((:c Iff) ((:c Disjoint) (:fv _uniq.29149) ((:c CompleteSemilatticeInf.toPartialOrder) (:fv _uniq.29149) ((:c CompleteLattice.toCompleteSemilatticeInf) (:fv _uniq.29149) ((:c Order.Frame.toCompleteLattice) (:fv _uniq.29149) (:fv _uniq.29160)))) ((:c BoundedOrder.toOrderBot) (:fv _uniq.29149) ((:c Preorder.toLE) (:fv _u... | [{"name":"α","sexp":"(:sort (+ u 1))"},{"name":"β","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort w)"},{"name":"κ","sexp":"(:forall _ (:fv _uniq.29153) (:sort w'))"},{"name":"inst✝","sexp":"((:c Order.Frame) (:fv _uniq.29149))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.29149))"},{"name":"t","sexp":"((:c Set) (:fv... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Disjoint) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c PartialOrder) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 2 (:instance-of (:app (:c OrderBot) (:arg :explicit 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29149","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29151","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp_rw","sourceEnd":10424,"sourceStart":10417,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":10426,"sourceStart":10425,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source... | [] | [{"source":"iSup_disjoint_iff","source_end":10443,"source_start":10426,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.29149","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.29151","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 46 | 2 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4a4ac1f15589083a75573ffcaef77a9917e0e712f700907b319493bdac3b7f5a | c91b5d452d8cd550dfed8b6cecde33140a41f6a2f3c12f654d524374544d5cb6 | fbf92ff9576e77dbb639dbdbb2d593c0627c2164849a94d1ef205c231f7dcd95 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 371 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rcases <a>eq_or_ne</a> p 0 with h|h | R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 ∨ p = 0 | case inl
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p = 0
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 ∨ p = 0
case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R ... | ((:c Iff) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.55274) (:fv _uniq.55311) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799))) ((:c Polynomial.degree) (:fv _uniq.55272) (:fv _uniq.55287) (:fv _uniq.55799))) ((:c O... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Polynomi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rcases","sourceEnd":13303,"sourceStart":13297,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"eq_or_ne","semanticRole":"global","source":"eq_or_ne","sourceEnd":13312,"sourceStart":13304,"tag":"identifier"},{"children":[{"contex... | [] | [{"source":"eq_or_ne p 0","source_end":13316,"source_start":13304,"syntax_kind":"Lean.Parser.Term.app"},{"source":"h|h","source_end":13325,"source_start":13322,"syntax_kind":"Lean.Parser.Tactic.rcasesPatMed"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 4 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 5d1933c6185ebf6bd95703623fdfc98dea4d0b64a5f818530fdf9473e13f829c | 6e8305e38a4e95ad9a84ef92f30bf2891c411820b0038f8745b7b841f466ffcf | ce559bc5ed835039575546fef41394e203d0a1683098b20498cd66d2ae83593a | 7e712d5998952b67ff695068a8f7c2c9befc57a9ccd2df3227f5ee10b2da98dd |
cat-searcher/leandojo-benchmark-4-random | test | 372 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [h, <a>or_false</a>] | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 ∨ p = 0 | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 | ((:c Iff) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.55274) (:fv _uniq.55311) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799))) ((:c Polynomial.degree) (:fv _uniq.55272) (:fv _uniq.55287) (:fv _uniq.55799))) ((:c O... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Polynomi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp","sourceEnd":13346,"sourceStart":13342,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":13351,"sourceStart":13347,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":133... | [] | [{"source":"h","source_end":13354,"source_start":13353,"syntax_kind":"ident"},{"source":"or_false","source_end":13364,"source_start":13356,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 10 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3047c3e223641727f0f777897f1d3687a990b29bb94c68cd41496f4cf8cb5dd6 | 416f2d44e2de9a61b0f677f843b9a3ed0949fa9a740806cfa0385deb1bb1f192 | cc19c7136f11d28978da2fdbcd44430069d24accfc92c2b0eee8f8975cb3330e | ff6016071da3534614b3272cd6011c0f12b084b17ca1e371ee0e2cbeeb95610c |
cat-searcher/leandojo-benchmark-4-random | test | 373 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨fun h2 ↦ ?_, <a>Polynomial.degree_map_eq_of_leadingCoeff_ne_zero</a> f⟩ | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
⊢ f p.leadingCoeff ≠ 0 | ((:c Iff) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.55274) (:fv _uniq.55311) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799))) ((:c Polynomial.degree) (:fv _uniq.55272) (:fv _uniq.55287) (:fv _uniq.55799))) ((:c N... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Polynomi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"refine","sourceEnd":13374,"sourceStart":13368,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13378,"sourceStart":13375,"tag":"atom"},{"children":[{"children":[{"source":"fun","sourceEnd":13381,"sourceStart":13378,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","sourc... | [] | [{"source":"⟨fun h2 ↦ ?_, degree_map_eq_of_leadingCoeff_ne_zero f⟩","source_end":13435,"source_start":13375,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 11 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f3b3e20fc48a3bcf8bd4843bfae5e7cada9ed75c9ac64ce5eee200fb488c80d3 | ff6016071da3534614b3272cd6011c0f12b084b17ca1e371ee0e2cbeeb95610c | 4ec40bdba89262457d22d6136ace21cc4f4a9f08b127b2174834979808ae6cf5 | 64d0fe5d1b998617c8d6688f8e9e92e2776513c79539b5c93f4692c911e8b10c |
cat-searcher/leandojo-benchmark-4-random | test | 374 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h3 : <a>Polynomial.natDegree</a> (<a>Polynomial.map</a> f p) = <a>Polynomial.natDegree</a> p := by simp_rw [<a>Polynomial.natDegree</a>, h2] | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
⊢ f p.leadingCoeff ≠ 0 | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
h3 : (map f p).natDegree = p.natDegree
⊢ f p.leadingCoeff ≠ 0 | ((:c Ne) (:fv _uniq.55274) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.55272) (:fv _uniq.55274) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55272) (:fv _uniq.55287)) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55274) (:fv _uniq.55311))) (:fv _uniq.55272) (:lambda _ (:fv _uniq.55272) (:fv _uniq.55274)) ((:c RingHom.in... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13442,"sourceStart":13438,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h3","sourceEnd":13445,"sourceStart":13443,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h3","sourceEnd":13445,"sourceStart":13443,"tag":"nod... | [] | [{"source":"natDegree (map f p) = natDegree p","source_end":13481,"source_start":13448,"syntax_kind":"«term_=_»"},{"source":"natDegree","source_end":13506,"source_start":13497,"syntax_kind":"ident"},{"source":"h2","source_end":13510,"source_start":13508,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 12 | exact | true | 1 | 16 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9df312fb568ee2d1844c388bfe67637aabe2e8ac8f52b141c35c64441bdc2d68 | 64d0fe5d1b998617c8d6688f8e9e92e2776513c79539b5c93f4692c911e8b10c | e432060dfa86598f90016120053c342ecd0ebd3bf3cc287ac38742b0daa4f984 | 1005f46d67f3c12648bbc6ccea9be52bd9ddf804d6fa4b6573890cd2c8a2e68a |
cat-searcher/leandojo-benchmark-4-random | test | 375 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h4 : <a>Polynomial.map</a> f p ≠ 0 := by rwa [<a>ne_eq</a>, ← <a>Polynomial.degree_eq_bot</a>, h2, <a>Polynomial.degree_eq_bot</a>] | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
h3 : (map f p).natDegree = p.natDegree
⊢ f p.leadingCoeff ≠ 0 | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
h3 : (map f p).natDegree = p.natDegree
h4 : map f p ≠ 0
⊢ f p.leadingCoeff ≠ 0 | ((:c Ne) (:fv _uniq.55274) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.55272) (:fv _uniq.55274) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55272) (:fv _uniq.55287)) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55274) (:fv _uniq.55311))) (:fv _uniq.55272) (:lambda _ (:fv _uniq.55272) (:fv _uniq.55274)) ((:c RingHom.in... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"have","sourceEnd":13518,"sourceStart":13514,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h4","sourceEnd":13521,"sourceStart":13519,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h4","sourceEnd":13521,"sourceStart":13519,"tag":"nod... | [] | [{"source":"map f p ≠ 0","source_end":13537,"source_start":13524,"syntax_kind":"«term_≠_»"},{"source":"ne_eq","source_end":13558,"source_start":13553,"syntax_kind":"ident"},{"source":"degree_eq_bot","source_end":13577,"source_start":13564,"syntax_kind":"ident"},{"source":"h2","source_end":13581,"source_start":13579,"sy... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 18 | exact | true | 1 | 17 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 72817206d3efb5058bd9dfac8e2831d1449e939194fb58f8dadb1090b2dcbf83 | 1005f46d67f3c12648bbc6ccea9be52bd9ddf804d6fa4b6573890cd2c8a2e68a | 2eee40d2fad673a10b5a8552b0ce4283e711893e67dfc0b4f84872edc163f42c | 28a1578d8b6ae199b976e8e2cf30a1d194b433182107631bdd568236cab690e1 |
cat-searcher/leandojo-benchmark-4-random | test | 376 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>Polynomial.coeff_natDegree</a>, ← <a>Polynomial.coeff_map</a>, ← h3, <a>Polynomial.coeff_natDegree</a>, <a>ne_eq</a>, <a>Polynomial.leadingCoeff_eq_zero</a>] | case inr
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
h3 : (map f p).natDegree = p.natDegree
h4 : map f p ≠ 0
⊢ f p.leadingCoeff ≠ 0 | ((:c Ne) (:fv _uniq.55274) ((:c DFunLike.coe) ((:c RingHom) (:fv _uniq.55272) (:fv _uniq.55274) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55272) (:fv _uniq.55287)) ((:c Semiring.toNonAssocSemiring) (:fv _uniq.55274) (:fv _uniq.55311))) (:fv _uniq.55272) (:lambda _ (:fv _uniq.55272) (:fv _uniq.55274)) ((:c RingHom.in... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Ne) (:arg :implicit-type 0 (:fv FV1)) (:arg :explicit 1 (:app (:c DFunLike.coe) (:arg :implicit-type 0 (:app (:c RingHom) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:app (:c NonAssocSemiring) (:arg :explicit 0 (:fv FV0))))) (:arg :instance 3 (:instance-of (:app ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":13603,"sourceStart":13600,"tag":"atom"},{"children":[{"source":"[","sourceEnd":13605,"sourceStart":13604,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":13608,"sourceStart":13605,"tag":"atom"}],"kind":"token.«← »","source"... | [] | [{"source":"coeff_natDegree","source_end":13624,"source_start":13609,"syntax_kind":"ident"},{"source":"coeff_map","source_end":13639,"source_start":13630,"syntax_kind":"ident"},{"source":"h3","source_end":13647,"source_start":13645,"syntax_kind":"ident"},{"source":"coeff_natDegree","source_end":13664,"source_start":136... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 26 | exact | true | 1 | 18 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6fa12ab20f544637dd171420ad0e3507adc2794d1530bcc6ec5f30a3b7805a8b | 28a1578d8b6ae199b976e8e2cf30a1d194b433182107631bdd568236cab690e1 | 08b1166f5b018bd2c637c0d27eebca73849f1f39eddb4bfd7a81519b6207a548 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 377 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [h] | case inl
R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p = 0
⊢ (map f p).degree = p.degree ↔ f p.leadingCoeff ≠ 0 ∨ p = 0 | ((:c Iff) ((:c Eq) ((:c WithBot) (:c Nat)) ((:c Polynomial.degree) (:fv _uniq.55274) (:fv _uniq.55311) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799))) ((:c Polynomial.degree) (:fv _uniq.55272) (:fv _uniq.55287) (:fv _uniq.55799))) ((:c O... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Eq) (:arg :implicit-type 0 (:app (:c WithBot) (:arg :explicit 0 (:c Nat)))) (:arg :explicit 1 (:app (:c Polynomial.degree) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Polynomi... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":13335,"sourceStart":13331,"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":13338,"source_start":13337,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 7 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d93b61bab9611f44c1fd70ac65cdc5d6b08b20b505d5fef28045d037ce503e0e | 09f0f39efcf866b6ec5e322975b6efcbcbae8fa3fd5d37f15b6d6a3c09381b24 | 80b5426f4cd8afb2daab5c530b5abbdb5bd333c6b56653091017c22104b3e089 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 378 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp_rw [<a>Polynomial.natDegree</a>, h2] | R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
⊢ (map f p).natDegree = p.natDegree | ((:c Eq) (:c Nat) ((:c Polynomial.natDegree) (:fv _uniq.55274) (:fv _uniq.55311) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799))) ((:c Polynomial.natDegree) (:fv _uniq.55272) (:fv _uniq.55287) (:fv _uniq.55799))) | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Eq) (:arg :implicit-type 0 (:c Nat)) (:arg :explicit 1 (:app (:c Polynomial.natDegree) (:arg :implicit-type 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))) (:arg :explicit 2 (:app (:c Polynomial.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"simp_rw","sourceEnd":13495,"sourceStart":13488,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":13497,"sourceStart":13496,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Polynomial.... | [] | [{"source":"natDegree","source_end":13506,"source_start":13497,"syntax_kind":"ident"},{"source":"h2","source_end":13510,"source_start":13508,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 14 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4ea8266fb3402a0c703ff78d31131f5f95f287db1941b3fe23a6c75d67296d4c | 15776806dd8925db3630712d4d114c4d4784cd1cbd0d657c30be4e5701a3c712 | a7d66cd4a8eef4272236d6c3698247cee83d222589e7897ef27c1655c6e4580b | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 379 | Polynomial.degree_map_eq_iff | Mathlib/Algebra/Polynomial/Degree/Lemmas.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>ne_eq</a>, ← <a>Polynomial.degree_eq_bot</a>, h2, <a>Polynomial.degree_eq_bot</a>] | R : Type u
S : Type v
ι : Type w
a b : R
m n : ℕ
inst✝¹ : Semiring R
p✝ q r : R[X]
inst✝ : Semiring S
f : R →+* S
p : R[X]
h : p ≠ 0
h2 : (map f p).degree = p.degree
h3 : (map f p).natDegree = p.natDegree
⊢ map f p ≠ 0 | ((:c Ne) ((:c Polynomial) (:fv _uniq.55274) (:fv _uniq.55311)) ((:c Polynomial.map) (:fv _uniq.55272) (:fv _uniq.55274) (:fv _uniq.55287) (:fv _uniq.55311) (:fv _uniq.55798) (:fv _uniq.55799)) ((:c OfNat.ofNat) ((:c Polynomial) (:fv _uniq.55274) (:fv _uniq.55311)) (:lit 0) ((:c Zero.toOfNat0) ((:c Polynomial) (:fv _uni... | [{"name":"R","sexp":"(:sort (+ u 1))"},{"name":"S","sexp":"(:sort (+ v 1))"},{"name":"ι","sexp":"(:sort (+ w 1))"},{"name":"a","sexp":"(:fv _uniq.55272)"},{"name":"b","sexp":"(:fv _uniq.55272)"},{"name":"m","sexp":"(:c Nat)"},{"name":"n","sexp":"(:c Nat)"},{"name":"inst✝¹","sexp":"((:c Semiring) (:fv _uniq.55272))"},{"... | (:app (:c Ne) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV1)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV1))))))) (:arg :explicit 1 (:app (:c Polynomial.map) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :instance 2 (:instance-of (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"name":"S","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"source":"rwa","sourceEnd":13551,"sourceStart":13548,"tag":"atom"},{"children":[{"source":"[","sourceEnd":13553,"sourceStart":13552,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"ne_eq","semanticRole":"global","source":"ne_eq","sourceEnd":13558,"sou... | [] | [{"source":"ne_eq","source_end":13558,"source_start":13553,"syntax_kind":"ident"},{"source":"degree_eq_bot","source_end":13577,"source_start":13564,"syntax_kind":"ident"},{"source":"h2","source_end":13581,"source_start":13579,"syntax_kind":"ident"},{"source":"degree_eq_bot","source_end":13596,"source_start":13583,"synt... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.55272","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.55274","is_instance":false,"is_let":false,"user_name":"S"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 63 | 20 | exact | true | 1 | 17 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | df9727fafd9fe00afac727fee6eaa5ccb3085fb2709d8ed2e553a6ec7605cdb3 | a5a7fdee9dc0c8e305e094dce5fe0e151ee0d858c495b2d516c58ca9d9b4b758 | fc5e46fb5cb395311b920bc34f12b791f0a8a04466b1d84f7024213274d4518a | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 380 | prodXSubSMul.smul | Mathlib/Algebra/Polynomial/GroupRingAction.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [<a>MulAction.ofQuotientStabilizer_smul</a>, <a>smul_sub</a>, <a>Polynomial.smul_X</a>, <a>Polynomial.smul_C</a>] | M : Type u_1
inst✝⁴ : Monoid M
G : Type u_2
inst✝³ : Group G
inst✝² : Fintype G
R : Type u_3
inst✝¹ : CommRing R
inst✝ : MulSemiringAction G R
x : R
g : G
this : DecidableEq R := Classical.decEq R
g' : G ⧸ stabilizer G x
⊢ g • (X - C (ofQuotientStabilizer G x g')) = X - C (ofQuotientStabilizer G x (g • g')) | ((:c Eq) ((:c Polynomial) (:fv _uniq.45338) ((:c CommSemiring.toSemiring) (:fv _uniq.45338) ((:c CommRing.toCommSemiring) (:fv _uniq.45338) (:fv _uniq.45341)))) ((:c HSMul.hSMul) (:fv _uniq.45329) ((:c Polynomial) (:fv _uniq.45338) ((:c CommSemiring.toSemiring) (:fv _uniq.45338) ((:c CommRing.toCommSemiring) (:fv _uniq... | [{"name":"M","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝⁴","sexp":"((:c Monoid) (:fv _uniq.45323))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝³","sexp":"((:c Group) (:fv _uniq.45329))"},{"name":"inst✝²","sexp":"((:c Fintype) (:fv _uniq.45329))"},{"name":"R","sexp":"(:sort (+ u_3 1))"},{"name":"inst✝¹","sexp... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5)) (:arg :instance 1 (:instance-of (:app (:c Semiring) (:arg :explicit 0 (:fv FV5))))))) (:arg :explicit 1 (:app (:c HSMul.hSMul) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Polynomial) (:arg :explicit 0 (:fv FV5... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.45323","is_instance":false,"is_let":false,"name":"M","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.45326","is_instance":true,"is_let":false,"name":"inst✝⁴","sexp":"(:app (:c Monoid) (:arg :explicit... | {"children":[{"children":[{"children":[{"children":[{"source":"rw","sourceEnd":4174,"sourceStart":4172,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":4176,"sourceStart":4175,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag... | [] | [{"source":"ofQuotientStabilizer_smul","source_end":4201,"source_start":4176,"syntax_kind":"ident"},{"source":"smul_sub","source_end":4211,"source_start":4203,"syntax_kind":"ident"},{"source":"Polynomial.smul_X","source_end":4230,"source_start":4213,"syntax_kind":"ident"},{"source":"Polynomial.smul_C","source_end":4249... | [{"binder_role":":explicit","context_index":0,"internal_name":"_uniq.45323","is_instance":false,"is_let":false,"user_name":"M"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.45326","is_instance":true,"is_let":false,"user_name":"inst✝⁴"},{"binder_role":":explicit","context_index":2,"intern... | 35 | 2 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f5a253293b606cd0c427e48b288df56db9f668cebeb924251a7a534df145a18c | b66c73cc0e3aba258c6550e56b536b8f793ac9eaa63cdfae316d7fc144505237 | 6385d0756e91157ecaa68e12de705c21f653d5badc42cd9a999c401e053402d8 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 381 | OreLocalization.mul_div_one | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp [<a>OreLocalization.oreDiv_mul_char</a> p r s 1 p 1 (by simp)] | R : Type u_1
inst✝² : Monoid R
S : Submonoid R
inst✝¹ : OreSet S
X : Type ?u.113376
inst✝ : MulAction R X
p r : R
s : ↥S
⊢ p /ₒ s * (r /ₒ 1) = p * r /ₒ s | ((:c Eq) ((:c OreLocalization) (:fv _uniq.113218) (:fv _uniq.113221) (:fv _uniq.113332) (:fv _uniq.113371) (:fv _uniq.113218) ((:c Monoid.toMulAction) (:fv _uniq.113218) (:fv _uniq.113221))) ((:c HMul.hMul) ((:c OreLocalization) (:fv _uniq.113218) (:fv _uniq.113221) (:fv _uniq.113332) (:fv _uniq.113371) (:fv _uniq.1132... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.113218))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.113218) ((:c Monoid.toMulOneClass) (:fv _uniq.113218) (:fv _uniq.113221)))"},{"name":"inst✝¹","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.113218) (:fv _uniq.113221) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c OreLocalization) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c Monoid) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV2)) (:arg :instance 3 (:instance-of (:app (:c OreLocalization.OreSet) (:arg :implicit-type 0 (:fv FV0)) (:arg :inst... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113218","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.113221","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":20547,"sourceStart":20543,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","source... | [] | [{"source":"oreDiv_mul_char p r s 1 p 1 (by simp)","source_end":20586,"source_start":20549,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113218","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.113221","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte... | 87 | 2 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | b730c989d9b288326f1fd67638a3bef7e94565c32642033e4f23cbb5cbf3922c | 6798e6fa0ee5623313757e1b532a09867c7cb668f7a30c6b9027c79241c6234f | 37ab0de5ddbd9d0b39b17485dab1e5c94af92e3da5fd732b38e1c3034167d405 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 382 | OreLocalization.mul_div_one | Mathlib/RingTheory/OreLocalization/Basic.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | R : Type u_1
inst✝² : Monoid R
S : Submonoid R
inst✝¹ : OreSet S
X : Type ?u.113376
inst✝ : MulAction R X
p r : R
s : ↥S
⊢ ↑1 * p = p * ↑1 | ((:c Eq) (:fv _uniq.113218) ((:c HMul.hMul) (:fv _uniq.113218) (:fv _uniq.113218) (:fv _uniq.113218) ((:c instHMul) (:fv _uniq.113218) ((:c MulOneClass.toMul) (:fv _uniq.113218) ((:c Monoid.toMulOneClass) (:fv _uniq.113218) (:fv _uniq.113221)))) ((:c Subtype.val) (:fv _uniq.113218) (:lambda x (:fv _uniq.113218) ((:c Me... | [{"name":"R","sexp":"(:sort (+ u_1 1))"},{"name":"inst✝²","sexp":"((:c Monoid) (:fv _uniq.113218))"},{"name":"S","sexp":"((:c Submonoid) (:fv _uniq.113218) ((:c Monoid.toMulOneClass) (:fv _uniq.113218) (:fv _uniq.113221)))"},{"name":"inst✝¹","sexp":"((:c OreLocalization.OreSet) (:fv _uniq.113218) (:fv _uniq.113221) (:f... | (:app (:c Eq) (:arg :implicit-type 0 (:fv FV0)) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV0)) (:arg :implicit-type 2 (:fv FV0)) (:arg :instance 3 (:instance-of (:app (:c HMul) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv FV0)) (:arg :explicit 2 (:fv FV... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113218","is_instance":false,"is_let":false,"name":"R","sexp":"(:sort Type)"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.113221","is_instance":true,"is_let":false,"name":"inst✝²","sexp":"(:app (:c Monoid) (:arg :explic... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":20585,"sourceStart":20581,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","sour... | [] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.113218","is_instance":false,"is_let":false,"user_name":"R"},{"binder_role":":instance-implicit","context_index":1,"internal_name":"_uniq.113221","is_instance":true,"is_let":false,"user_name":"inst✝²"},{"binder_role":":implicit","context_index":2,"inte... | 87 | 7 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 9c605907f754c4070175555b5bc63731cb7361d7e032231d817ad821ceb11f43 | 2fcf1a449653d8531f4bdb3e57efd01251372a023a6c7e141ca585f73dec6b72 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 383 | Submonoid.coe_mul_self_eq | Mathlib/Algebra/Group/Submonoid/Pointwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | ext x | α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
⊢ ↑s * ↑s = ↑s | case h
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
x : M
⊢ x ∈ ↑s * ↑s ↔ x ∈ ↑s | ((:c Eq) ((:c Set) (:fv _uniq.2998)) ((:c HMul.hMul) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c instHMul) ((:c Set) (:fv _uniq.2998)) ((:c Set.mul) (:fv _uniq.2998) ((:c MulOneClass.toMul) (:fv _uniq.2998) ((:c Monoid.toMulOneClass) (:fv _uniq.2998) (:fv _uniq.3007))))) ((:... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"A","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.2998))"},{"name":"inst✝","sexp":"((:c AddMonoid) (:fv _uniq.3004))"},{... | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :explicit 1 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :implicit-type 2 (:app (:c Set) (:arg :explicit 0 (:fv... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"ext","sourceEnd":2431,"sourceStart":2428,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"x","sourceEnd":2433,"sourceStart":2432,"tag":"identifier"}],"kind":"Lean.Parser.Tactic.rcasesPat.one","source":"x","sourceEnd":2433,"sourceStart":2432,"tag":"nod... | [{"role":"fresh_name","source":"x","source_end":2433,"source_start":2432,"syntax_kind":"ident"}] | [] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 4 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 1f8a946fc5497a2fd66b3628917e24ea9df3f8140a9708c9acfa7d674fd40cf7 | 73ba43f669a3db457cb1a13ce2dcd3153f6e0fd16f40ec48a6a4989ad0704498 | ee522618587c4a8062e9541e92fad69d5c6e7dbdf5366e9d82c63ebe3c1e08c5 | 8301e83c6d474be36b5374953edbae527255172bbeb2ab16e75abd9de564afa3 |
cat-searcher/leandojo-benchmark-4-random | test | 384 | Submonoid.coe_mul_self_eq | Mathlib/Algebra/Group/Submonoid/Pointwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨?_, fun h => ⟨x, h, 1, s.one_mem, <a>mul_one</a> x⟩⟩ | case h
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
x : M
⊢ x ∈ ↑s * ↑s ↔ x ∈ ↑s | case h
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
x : M
⊢ x ∈ ↑s * ↑s → x ∈ ↑s | ((:c Iff) ((:c Membership.mem) (:fv _uniq.2998) ((:c Set) (:fv _uniq.2998)) ((:c Set.instMembership) (:fv _uniq.2998)) (:fv _uniq.4102) ((:c HMul.hMul) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c instHMul) ((:c Set) (:fv _uniq.2998)) ((:c Set.mul) (:fv _uniq.2998) ((:c MulOn... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"A","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.2998))"},{"name":"inst✝","sexp":"((:c AddMonoid) (:fv _uniq.3004))"},{... | (:app (:c Iff) (:arg :explicit 0 (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :e... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"refine","sourceEnd":2442,"sourceStart":2436,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":2446,"sourceStart":2443,"tag":"atom"},{"children":[{"children":[{"source":"?","sourceEnd":2447,"sourceStart":2446,"tag":"atom"},{"children":[{"source":"_","sourceEnd":2448,"sourceStart":2447,"tag":"a... | [] | [{"source":"⟨?_, fun h => ⟨x, h, 1, s.one_mem, mul_one x⟩⟩","source_end":2497,"source_start":2443,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 5 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 54839eac3d9f8ed98fbbae23bd35ad76b6d3dcd218fff76ddb27efdadefbc1b2 | 8301e83c6d474be36b5374953edbae527255172bbeb2ab16e75abd9de564afa3 | 6c51e9c6ffb2a841394daf282b1b672b3b1fadcf8e358ffb430b5422f024d553 | affb2d214a8fbfde9849b9757ccbeae4fa88e31552f3dc63744c8f29f359dbb2 |
cat-searcher/leandojo-benchmark-4-random | test | 385 | Submonoid.coe_mul_self_eq | Mathlib/Algebra/Group/Submonoid/Pointwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rintro ⟨a, ha, b, hb, rfl⟩ | case h
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
x : M
⊢ x ∈ ↑s * ↑s → x ∈ ↑s | case h.intro.intro.intro.intro
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
a : M
ha : a ∈ ↑s
b : M
hb : b ∈ ↑s
⊢ (fun x x_1 => x * x_1) a b ∈ ↑s | (:forall _ ((:c Membership.mem) (:fv _uniq.2998) ((:c Set) (:fv _uniq.2998)) ((:c Set.instMembership) (:fv _uniq.2998)) (:fv _uniq.4102) ((:c HMul.hMul) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c Set) (:fv _uniq.2998)) ((:c instHMul) ((:c Set) (:fv _uniq.2998)) ((:c Set.mul) (:fv _uniq.2998) ((:c MulO... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"A","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.2998))"},{"name":"inst✝","sexp":"((:c AddMonoid) (:fv _uniq.3004))"},{... | (:forall _ :explicit (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"rintro","sourceEnd":2506,"sourceStart":2500,"tag":"atom"},{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":2510,"sourceStart":2507,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"a","sourceEnd":2511,"sourceSt... | [{"role":"fresh_name","source":"a","source_end":2511,"source_start":2510,"syntax_kind":"ident"},{"role":"fresh_name","source":"ha","source_end":2515,"source_start":2513,"syntax_kind":"ident"},{"role":"fresh_name","source":"b","source_end":2518,"source_start":2517,"syntax_kind":"ident"},{"role":"fresh_name","source":"hb... | [{"source":"⟨a, ha, b, hb, rfl⟩","source_end":2530,"source_start":2507,"syntax_kind":"Lean.Parser.Tactic.rcasesPat.tuple"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 6 | exact | true | 1 | 12 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | c588c0d10560d92317a7f08d1cf6f97a777bceadf9371b2c29342b70c5a70560 | affb2d214a8fbfde9849b9757ccbeae4fa88e31552f3dc63744c8f29f359dbb2 | a73e3a6960af335666ec53e78c4cc3320bc481eb4d6c699e3a0f37631dbc9aca | 13c87d8cd9992958c638c4c03586b80b2bdaa70be7c25c07d869e784bab4ddc1 |
cat-searcher/leandojo-benchmark-4-random | test | 386 | Submonoid.coe_mul_self_eq | Mathlib/Algebra/Group/Submonoid/Pointwise.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact s.mul_mem ha hb | case h.intro.intro.intro.intro
α : Type u_1
G : Type u_2
M : Type u_3
R : Type u_4
A : Type u_5
inst✝¹ : Monoid M
inst✝ : AddMonoid A
s✝ t u : Set M
s : Submonoid M
a : M
ha : a ∈ ↑s
b : M
hb : b ∈ ↑s
⊢ (fun x x_1 => x * x_1) a b ∈ ↑s | ((:c Membership.mem) (:fv _uniq.2998) ((:c Set) (:fv _uniq.2998)) ((:c Set.instMembership) (:fv _uniq.2998)) ((:lambda _ (:fv _uniq.2998) (:lambda _ (:fv _uniq.2998) ((:c HMul.hMul) (:fv _uniq.2998) (:fv _uniq.2998) (:fv _uniq.2998) ((:c instHMul) (:fv _uniq.2998) ((:c MulOneClass.toMul) (:fv _uniq.2998) ((:c Monoid.to... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"G","sexp":"(:sort (+ u_2 1))"},{"name":"M","sexp":"(:sort (+ u_3 1))"},{"name":"R","sexp":"(:sort (+ u_4 1))"},{"name":"A","sexp":"(:sort (+ u_5 1))"},{"name":"inst✝¹","sexp":"((:c Monoid) (:fv _uniq.2998))"},{"name":"inst✝","sexp":"((:c AddMonoid) (:fv _uniq.3004))"},{... | (:app (:c Membership.mem) (:arg :implicit-type 0 (:fv FV2)) (:arg :implicit-type 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2)))) (:arg :instance 2 (:instance-of (:app (:c Membership) (:arg :explicit 0 (:fv FV2)) (:arg :explicit 1 (:app (:c Set) (:arg :explicit 0 (:fv FV2))))))) (:arg :explicit 3 (:app (:lambda _ :expli... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"name":"G","sexp":"(:sort Type)"},{"binder_role":":implicit","conte... | {"children":[{"source":"exact","sourceEnd":2538,"sourceStart":2533,"tag":"atom"},{"children":[{"source":"s.mul_mem","sourceEnd":2548,"sourceStart":2539,"tag":"identifier"},{"children":[{"contextIndex":13,"semanticRole":"local","source":"ha","sourceEnd":2551,"sourceStart":2549,"tag":"identifier"},{"contextIndex":15,"sem... | [] | [{"source":"s.mul_mem ha hb","source_end":2554,"source_start":2539,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.2992","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.2995","is_instance":false,"is_let":false,"user_name":"G"},{"binder_role":":implicit","context_index":2,"internal_name":"_uniq... | 14 | 7 | exact | true | 1 | 15 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 44e0e2cb08f3d8b673f72668faca963a3ceab14766ab9e7a51c9b47db7d34e55 | 13c87d8cd9992958c638c4c03586b80b2bdaa70be7c25c07d869e784bab4ddc1 | 27de5909fb2760fccb104ea82b30f73f9384c4f5f9223a98a77c16c457f5c054 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 387 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have h₂ : <a>Order.succ</a> (1 : <a>Ordinal</a>) = 2 := by simp | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
⊢ (fun x x_1 => x * x_1) a b < 2 | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
h₂ : succ 1 = 2
⊢ (fun x x_1 => x * x_1) a b < 2 | ((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:lambda _ (:c Ordinal) (:lambda _ (:c Ordinal) ((:c HMul.hMul) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHMul) (:c Ordinal) ((:c MulZeroClass.toMul) (:c Ordinal) ((:c MulZeroOneClass.... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Ordinal) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:lambda _ :explicit (:c Ordinal) (:lambda _ :explicit (:c Ordinal) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Ordinal)) (:arg :implicit-type 1 (:c Ordinal)... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"have","sourceEnd":11932,"sourceStart":11928,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"h₂","sourceEnd":11937,"sourceStart":11933,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"h₂","sourceEnd":11937,"sourceStart":11933,"tag":"nod... | [] | [{"source":"succ (1 : Ordinal) = 2","source_end":11962,"source_start":11940,"syntax_kind":"«term_=_»"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 4 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 4733e9a39d68f8a31a498f197e3d4bb27ccbf59bdcd0ef3207f5a6225e6a7188 | f4f0a1d88c049b7cabd12e4e4ff18af311498cad392be3af90276d46838b7c59 | 8fc99a6f852fe483c2a103d4e550e89b98c8a13d55413720dd3964f6a40f08b3 | 586341f8a5b9a16c8c8e3a11872600e6963828cf6409a39d7f878cc1f1381c15 |
cat-searcher/leandojo-benchmark-4-random | test | 388 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | dsimp only | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
h₂ : succ 1 = 2
⊢ (fun x x_1 => x * x_1) a b < 2 | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
h₂ : succ 1 = 2
⊢ a * b < 2 | ((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:lambda _ (:c Ordinal) (:lambda _ (:c Ordinal) ((:c HMul.hMul) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHMul) (:c Ordinal) ((:c MulZeroClass.toMul) (:c Ordinal) ((:c MulZeroOneClass.... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Ordinal) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:lambda _ :explicit (:c Ordinal) (:lambda _ :explicit (:c Ordinal) (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Ordinal)) (:arg :implicit-type 1 (:c Ordinal)... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"dsimp","sourceEnd":11981,"sourceStart":11976,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":11986,"sourceStart":11982,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":11... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 7 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88e9f963880992919c0dfb6235f331f2b8b409fd1a8328fb7206361c492e27ea | 586341f8a5b9a16c8c8e3a11872600e6963828cf6409a39d7f878cc1f1381c15 | a4e0c85d6bda4413b7728099944a8f316bd66db76d368a5fb7af15b2a8905273 | 90a58692861224617d475d21f63724e1304c02268f8c8bc7256c18ff1ead155e |
cat-searcher/leandojo-benchmark-4-random | test | 389 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rw [← h₂, <a>Order.lt_succ_iff</a>] at ha hb ⊢ | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
h₂ : succ 1 = 2
⊢ a * b < 2 | a b : Ordinal.{u_1}
ha : a ≤ 1
hb : b ≤ 1
h₂ : succ 1 = 2
⊢ a * b ≤ 1 | ((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c HMul.hMul) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHMul) (:c Ordinal) ((:c MulZeroClass.toMul) (:c Ordinal) ((:c MulZeroOneClass.toMulZeroClass) (:c Ordinal) ((:c MonoidWithZero.... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Ordinal) (:... | (:app (:c LT.lt) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LT) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Ordinal)) (:arg :implicit-type 1 (:c Ordinal)) (:arg :implicit-type 2 (:c Ordinal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"rw","sourceEnd":11991,"sourceStart":11989,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"[","sourceEnd":11993,"sourceStart":11992,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":11996,"sourceSt... | [] | [{"source":"h₂","source_end":12001,"source_start":11997,"syntax_kind":"ident"},{"source":"ha","source_end":12021,"source_start":12019,"syntax_kind":"ident"},{"source":"hb","source_end":12024,"source_start":12022,"syntax_kind":"ident"},{"source":"lt_succ_iff","source_end":12014,"source_start":12003,"syntax_kind":"ident"... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 8 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a9898572f2d98baa8fa0d218616ba1b905d6afcd43d0caf8d9a314788277808 | 90a58692861224617d475d21f63724e1304c02268f8c8bc7256c18ff1ead155e | ec4166ba2c82d5854f6f8830ed612408b61b9ab9eacd0d549b983682a77190b6 | 33776d55e48b228340caa02410914d490478af0ff1d90aabba14d3d7f40015dc |
cat-searcher/leandojo-benchmark-4-random | test | 390 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | convert <a>mul_le_mul'</a> ha hb | a b : Ordinal.{u_1}
ha : a ≤ 1
hb : b ≤ 1
h₂ : succ 1 = 2
⊢ a * b ≤ 1 | case h.e'_4
a b : Ordinal.{u_1}
ha : a ≤ 1
hb : b ≤ 1
h₂ : succ 1 = 2
⊢ 1 = 1 * 1 | ((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) ((:c HMul.hMul) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHMul) (:c Ordinal) ((:c MulZeroClass.toMul) (:c Ordinal) ((:c MulZeroOneClass.toMulZeroClass) (:c Ordinal) ((:c MonoidWithZero.... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordin... | (:app (:c LE.le) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c LE) (:arg :explicit 0 (:c Ordinal))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :implicit-type 0 (:c Ordinal)) (:arg :implicit-type 1 (:c Ordinal)) (:arg :implicit-type 2 (:c Ordinal)) (:arg :instance 3 (:instance-of (:a... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"convert","sourceEnd":12038,"sourceStart":12031,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"name":"mul_le_mul'","semanticRole":"global","source":"mul_le_mul'","sourceEnd":12050,"sourceStart":12039,"tag"... | [] | [{"source":"mul_le_mul' ha hb","source_end":12056,"source_start":12039,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 12 | exact | true | 1 | 5 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 6114f41f962907142ccff4fc5f4e4d58b47b06f1d1de96df654bd7904a1b56ac | 33776d55e48b228340caa02410914d490478af0ff1d90aabba14d3d7f40015dc | a6f8274f17e292adcce52beb5e52afcc8b8050c6856c24523a66aaee0c09c2be | 6d1f71cc40c1a7451c14bd0f42080216dcac1e694303c00f2b0b2bcd900baa21 |
cat-searcher/leandojo-benchmark-4-random | test | 391 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact (<a>mul_one</a> 1).<a>Eq.symm</a> | case h.e'_4
a b : Ordinal.{u_1}
ha : a ≤ 1
hb : b ≤ 1
h₂ : succ 1 = 2
⊢ 1 = 1 * 1 | ((:c Eq) (:c Ordinal) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordinal.one))) ((:c HMul.hMul) (:c Ordinal) (:c Ordinal) (:c Ordinal) ((:c instHMul) (:c Ordinal) ((:c MulZeroClass.toMul) (:c Ordinal) ((:c MulZeroOneClass.toMulZeroClass) (:c Ordinal) ((:c MonoidWithZero.toMulZeroOneClas... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LE.le) (:c Ordinal) ((:c Preorder.toLE) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordin... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c OfNat.ofNat) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:lit 1)) (:arg :instance 2 (:instance-of (:app (:c OfNat) (:arg :explicit 0 (:c Ordinal)) (:arg :explicit 1 (:lit 1))))))) (:arg :explicit 2 (:app (:c HMul.hMul) (:arg :imp... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"exact","sourceEnd":12064,"sourceStart":12059,"tag":"atom"},{"children":[{"children":[{"source":"(","sourceEnd":12066,"sourceStart":12065,"tag":"atom"},{"children":[{"name":"mul_one","semanticRole":"global","source":"mul_one","sourceEnd":12073,"sourceStart":12066,"tag":"identifier"},{"children":[... | [] | [{"source":"(mul_one 1).symm","source_end":12081,"source_start":12065,"syntax_kind":"Lean.Parser.Term.proj"}] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 13 | exact | true | 1 | 5 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | feecb5086e6fb195d3a0accee874174809e2a7e29fedd56ce2ff325c914640af | 6d1f71cc40c1a7451c14bd0f42080216dcac1e694303c00f2b0b2bcd900baa21 | c6d8bec62e3644ef309591f25b1baa0a1f51c7746807f919e6d90e2012e52e5f | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 392 | Ordinal.principal_mul_two | Mathlib/SetTheory/Ordinal/Principal.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp | a b : Ordinal.{u_1}
ha : a < 2
hb : b < 2
⊢ succ 1 = 2 | ((:c Eq) (:c Ordinal) ((:c Order.succ) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder)) (:c Ordinal.succOrder) ((:c OfNat.ofNat) (:c Ordinal) (:lit 1) ((:c One.toOfNat1) (:c Ordinal) (:c Ordinal.one)))) ((:c OfNat.ofNat) (:c Ordinal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Ordinal) (:li... | [{"name":"a","sexp":"(:c Ordinal)"},{"name":"b","sexp":"(:c Ordinal)"},{"name":"ha","sexp":"((:c LT.lt) (:c Ordinal) ((:c Preorder.toLT) (:c Ordinal) ((:c PartialOrder.toPreorder) (:c Ordinal) (:c Ordinal.partialOrder))) (:fv _uniq.21473) ((:c OfNat.ofNat) (:c Ordinal) (:lit 2) ((:c instOfNatAtLeastTwo) (:c Ordinal) (:... | (:app (:c Eq) (:arg :implicit-type 0 (:c Ordinal)) (:arg :explicit 1 (:app (:c Order.succ) (:arg :implicit-type 0 (:c Ordinal)) (:arg :instance 1 (:instance-of (:app (:c Preorder) (:arg :explicit 0 (:c Ordinal))))) (:arg :instance 2 (:instance-of (:app (:c SuccOrder) (:arg :explicit 0 (:c Ordinal)) (:arg :instance 1 (:... | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"name":"a","sexp":"(:c Ordinal)"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"name":"b","sexp":"(:c Ordinal)"},{"binder_role":":explicit","con... | {"children":[{"source":"simp","sourceEnd":11973,"sourceStart":11969,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"ki... | [] | [] | [{"binder_role":":explicit","context_index":1,"internal_name":"_uniq.21473","is_instance":false,"is_let":false,"user_name":"a"},{"binder_role":":explicit","context_index":2,"internal_name":"_uniq.21476","is_instance":false,"is_let":false,"user_name":"b"},{"binder_role":":explicit","context_index":3,"internal_name":"_un... | 59 | 6 | exact | true | 1 | 4 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a49249eb64cff919c2d60b88307eccea1612e8cc10891588ebf0620932bb4f1b | 78188764ed793e1c89cce20935ce704fd4a57629c8fe1204b6163f3bb0305916 | 8563d0d12f13ad2504d0835aa3485f7f7185b02656621ae540a1b0d58b8d6a48 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 393 | Rel.preimage_top | Mathlib/Data/Rel.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [← <a>Rel.inv_top</a>, <a>Rel.preimage</a>, <a>Rel.inv_inv</a>, <a>Rel.image_top</a>] | α : Type u_1
β : Type u_2
γ : Type u_3
r : Rel α β
s : Set β
h : s.Nonempty
⊢ ⊤.preimage s = Set.univ | ((:c Eq) ((:c Set) (:fv _uniq.19156)) ((:c Rel.preimage) (:fv _uniq.19156) (:fv _uniq.19159) ((:c Top.top) ((:c Rel) (:fv _uniq.19156) (:fv _uniq.19159)) ((:c CompleteLattice.toTop) ((:c Rel) (:fv _uniq.19156) (:fv _uniq.19159)) ((:c instCompleteLatticeRel) (:fv _uniq.19156) (:fv _uniq.19159)))) (:fv _uniq.19269)) ((:c... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"γ","sexp":"(:sort (+ u_3 1))"},{"name":"r","sexp":"((:c Rel) (:fv _uniq.19156) (:fv _uniq.19159))"},{"name":"s","sexp":"((:c Set) (:fv _uniq.19159))"},{"name":"h","sexp":"((:c Set.Nonempty) (:fv _uniq.19159) (:fv _uniq.19269))"}] | (:app (:c Eq) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:app (:c Rel.preimage) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:fv FV1)) (:arg :explicit 2 (:app (:c Top.top) (:arg :implicit-type 0 (:app (:c Rel) (:arg :explicit 0 (:fv FV0)) (:arg :explicit 1 (:fv ... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19156","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19159","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"rwa","sourceEnd":9442,"sourceStart":9439,"tag":"atom"},{"children":[{"source":"[","sourceEnd":9444,"sourceStart":9443,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"source":"←","sourceEnd":9447,"sourceStart":9444,"tag":"ato... | [] | [{"source":"inv_top","source_end":9455,"source_start":9448,"syntax_kind":"ident"},{"source":"preimage","source_end":9465,"source_start":9457,"syntax_kind":"ident"},{"source":"inv_inv","source_end":9474,"source_start":9467,"syntax_kind":"ident"},{"source":"image_top","source_end":9485,"source_start":9476,"syntax_kind":"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.19156","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.19159","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 87 | 2 | exact | true | 1 | 6 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 62675a6fd93ac96458c41148f248ae9f00b71d848f1619f623e5b8860d2caf2b | 8301aba3d47491c9ec2eca98fcd6fafc7f9ee0d964ccda8b4a2d448bccb85364 | b2a318debc10edef3824a5ecfd5f3b10d34ab21924806fd7b77b1ff392b44f77 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 394 | aemeasurable_union_iff | Mathlib/MeasureTheory/Measure/AEMeasurable.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.union_eq_iUnion</a>, <a>aemeasurable_iUnion_iff</a>, <a>Bool.forall_bool</a>, <a>cond</a>, <a>and_comm</a>] | ι : Type u_1
α : Type u_2
β : Type u_3
γ : Type u_4
δ : Type u_5
R : Type u_6
m0 : MeasurableSpace α
inst✝² : MeasurableSpace β
inst✝¹ : MeasurableSpace γ
inst✝ : MeasurableSpace δ
f g : α → β
μ ν : Measure α
s t : Set α
⊢ AEMeasurable f (μ.restrict (s ∪ t)) ↔ AEMeasurable f (μ.restrict s) ∧ AEMeasurable f (μ.restrict ... | ((:c Iff) ((:c AEMeasurable) (:fv _uniq.16566) (:fv _uniq.16569) (:fv _uniq.16584) (:fv _uniq.16581) (:fv _uniq.16594) ((:c MeasureTheory.Measure.restrict) (:fv _uniq.16566) (:fv _uniq.16581) (:fv _uniq.16606) ((:c Union.union) ((:c Set) (:fv _uniq.16566)) ((:c Set.instUnion) (:fv _uniq.16566)) (:fv _uniq.16699) (:fv _... | [{"name":"ι","sexp":"(:sort (+ u_1 1))"},{"name":"α","sexp":"(:sort (+ u_2 1))"},{"name":"β","sexp":"(:sort (+ u_3 1))"},{"name":"γ","sexp":"(:sort (+ u_4 1))"},{"name":"δ","sexp":"(:sort (+ u_5 1))"},{"name":"R","sexp":"(:sort (+ u_6 1))"},{"name":"m0","sexp":"((:c MeasurableSpace) (:fv _uniq.16566))"},{"name":"inst✝²... | (:app (:c Iff) (:arg :explicit 0 (:app (:c AEMeasurable) (:arg :implicit-type 0 (:fv FV1)) (:arg :implicit-type 1 (:fv FV2)) (:arg :instance 2 (:instance-of (:app (:c MeasurableSpace) (:arg :explicit 0 (:fv FV2))))) (:arg :implicit 3) (:arg :explicit 4 (:fv FV10)) (:arg :explicit 5 (:app (:c MeasureTheory.Measure.restr... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16563","is_instance":false,"is_let":false,"name":"ι","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16566","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","con... | {"children":[{"children":[{"children":[{"children":[{"source":"simp","sourceEnd":6624,"sourceStart":6620,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":6629,"sourceStart":6625,"tag":"atom"}],"kind":"nu... | [] | [{"source":"union_eq_iUnion","source_end":6646,"source_start":6631,"syntax_kind":"ident"},{"source":"aemeasurable_iUnion_iff","source_end":6671,"source_start":6648,"syntax_kind":"ident"},{"source":"Bool.forall_bool","source_end":6689,"source_start":6673,"syntax_kind":"ident"},{"source":"cond","source_end":6695,"source_... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.16563","is_instance":false,"is_let":false,"user_name":"ι"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.16566","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":2,"internal_name":"_un... | 39 | 2 | exact | true | 1 | 16 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | d561c41d15d28b37cbf8c0f33b84f30d3b8e9e9720f2947fdcd8e28967dcc427 | b98e0944f58311c2f5e501e2fdb9979cc74f60e0e231b1023fe61ddcf7260f7e | dcd27ef2d2e5054564932b6afcd56e1fd63ec7b9115e5c3077c1c272b0a29b67 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 395 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let ι : <a>Set</a> (<a>Set</a> α) := <a>irreducibleComponents</a> α \ {Z} | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"let","sourceEnd":11889,"sourceStart":11886,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"ι","sourceEnd":11892,"sourceStart":11890,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"children":[{"source":":","sourceEnd":1189... | [] | [{"source":"Set (Set α)","source_end":11907,"source_start":11895,"syntax_kind":"Lean.Parser.Term.app"},{"source":"irreducibleComponents α \\ {Z}","source_end":11941,"source_start":11911,"syntax_kind":"«term_\\_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 7 | exact | true | 1 | 7 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 88dbb7c8e9ab97040dafb6fc2484ea44089f9134895eca6102113b83eb014358 | 949fa7c67bd2273ee8ee1a4734ebefa3b781599cbbd37fbef7dbf92b493975d7 | 7bb107aced8310e8310d490e460b70564a2884b7970a38f323b376458f56faad | 8f1070681d0258142cc85ca7d39d2181a06653278fbc7aad6e901ff6d5bdcd20 |
cat-searcher/leandojo-benchmark-4-random | test | 396 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hι : ι.Finite := NoetherianSpace.finite_irreducibleComponents.subset <a>Set.diff_subset</a> | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":11948,"sourceStart":11944,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hι","sourceEnd":11952,"sourceStart":11949,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hι","sourceEnd":11952,"sourceStart":11949,"tag":"nod... | [] | [{"source":"ι.Finite","source_end":11964,"source_start":11955,"syntax_kind":"ident"},{"source":"NoetherianSpace.finite_irreducibleComponents.subset Set.diff_subset","source_end":12035,"source_start":11968,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 8 | exact | true | 1 | 8 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 15062000141eba0d003751a3d91e956c7f83fa4b88499a591e70699f67bc48df | 8f1070681d0258142cc85ca7d39d2181a06653278fbc7aad6e901ff6d5bdcd20 | 02202dca7309952ba950c50c5181ac4225ff9cf43d34850fcd9479c34f50cc60 | 8566ced39d5290f2b1b760570352c13ec916f21be8827898fac36c672b89618c |
cat-searcher/leandojo-benchmark-4-random | test | 397 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hι' : <a>Finite</a> ι := by rwa [<a>Set.finite_coe_iff</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":12042,"sourceStart":12038,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hι'","sourceEnd":12047,"sourceStart":12043,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hι'","sourceEnd":12047,"sourceStart":12043,"tag":"n... | [] | [{"source":"Finite ι","source_end":12059,"source_start":12050,"syntax_kind":"Lean.Parser.Term.app"},{"source":"Set.finite_coe_iff","source_end":12089,"source_start":12071,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 9 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | db7452728f22513c6de40eeb577a2b6a24e2024fd617ef3d7ba5eb682f8ad1f4 | 8566ced39d5290f2b1b760570352c13ec916f21be8827898fac36c672b89618c | 6a1452ad0fc5e4df2ec576b47a51ffdbdc93e1b5d148f173bd94b63ebc6e7e58 | cec63cdc48ab98d8265001071d4ecec4f75b6818ac77da9b675523920c6437f3 |
cat-searcher/leandojo-benchmark-4-random | test | 398 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | let U := Z \ ⋃ (x : ι), x | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"let","sourceEnd":12097,"sourceStart":12094,"tag":"atom"},{"children":[{"children":[{"semanticRole":"scoped_local","source":"U","sourceEnd":12099,"sourceStart":12098,"tag":"identifier"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{... | [] | [{"source":"Z \\ ⋃ (x : ι), x","source_end":12122,"source_start":12103,"syntax_kind":"«term_\\_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 14 | exact | true | 1 | 10 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 280ee50238da175045671d96afb7360d6695a51af0981fa5404b894a5ef3a19c | cec63cdc48ab98d8265001071d4ecec4f75b6818ac77da9b675523920c6437f3 | 987128bcbd3369844bc79e63f8117248361b6f8740f61ceaa649af803612cb7b | d4af1c1e115fc2648d8da759081b9549ecca994ba25b2fa4dcb3bb30d305ff1c |
cat-searcher/leandojo-benchmark-4-random | test | 399 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | have hU0 : U ≠ ∅ := fun r ↦ by obtain ⟨Z', hZ'⟩ := isIrreducible_iff_sUnion_closed.mp H.1 hι.toFinset (fun z hz ↦ by simp only [<a>Set.Finite.mem_toFinset</a>, <a>Set.mem_diff</a>, <a>Set.mem_singleton_iff</a>] at hz exact <a>isClosed_of_mem_irreducibleComponents</a> _ hz.1) (by rw [<a>Set.Finite.coe_toFinset</a>, <a>S... | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"have","sourceEnd":12129,"sourceStart":12125,"tag":"atom"},{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"hU0","sourceEnd":12133,"sourceStart":12130,"tag":"identifier"}],"kind":"Lean.Parser.Term.haveId","source":"hU0","sourceEnd":12133,"sourceStart":12130,"tag":"n... | [] | [{"source":"U ≠ ∅","source_end":12145,"source_start":12136,"syntax_kind":"«term_≠_»"},{"source":"fun r ↦ by\n obtain ⟨Z', hZ'⟩ := isIrreducible_iff_sUnion_closed.mp H.1 hι.toFinset\n (fun z hz ↦ by\n simp only [Set.Finite.mem_toFinset, Set.mem_diff, Set.mem_singleton_iff] at hz\n exact isClosed_of... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 15 | exact | true | 1 | 11 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3a7d3f63342b7d429fa26f8d3a1e8c3742f203894325b6cb6d5c0da3a29da924 | d4af1c1e115fc2648d8da759081b9549ecca994ba25b2fa4dcb3bb30d305ff1c | 2c3d07ec3a3b2fe5ec0c7e9c70016bb5dd4596b257c4468a87232173ca08290e | 11e904cd6c6e2ab027827bf7b7c1758dab10d8d570bdfda30c87a56941e7f318 |
cat-searcher/leandojo-benchmark-4-random | test | 400 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | refine ⟨U, hU1 ▸ isOpen_compl_iff.mpr ?_, hU0, <a>sdiff_le</a>⟩ | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
hU1 : U = (⋃ x, ↑x)ᶜ
⊢ ∃ o, IsOpen o ∧ o ≠ ∅ ∧ o ≤ Z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
hU1 : U = (⋃ x, ↑x)ᶜ
⊢ IsClosed (⋃ x, ↑x) | ((:c Exists) ((:c Set) (:fv _uniq.25970)) (:lambda o ((:c Set) (:fv _uniq.25970)) ((:c And) ((:c IsOpen) (:fv _uniq.25970) (:fv _uniq.25976) 0) ((:c And) ((:c Ne) ((:c Set) (:fv _uniq.25970)) 0 ((:c EmptyCollection.emptyCollection) ((:c Set) (:fv _uniq.25970)) ((:c Set.instEmptyCollection) (:fv _uniq.25970)))) ((:c LE.... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Exists) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:lambda o :explicit (:app (:c Set) (:arg :explicit 0 (:fv FV0))) (:app (:c And) (:arg :explicit 0 (:app (:c IsOpen) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:ar... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"refine","sourceEnd":13540,"sourceStart":13534,"tag":"atom"},{"children":[{"source":"⟨","sourceEnd":13544,"sourceStart":13541,"tag":"atom"},{"children":[{"contextIndex":11,"semanticRole":"local","source":"U","sourceEnd":13545,"sourceStart":13544,"tag":"identifier"},{"source":",","sourceEnd":13546... | [] | [{"source":"⟨U, hU1 ▸ isOpen_compl_iff.mpr ?_, hU0, sdiff_le⟩","source_end":13596,"source_start":13541,"syntax_kind":"Lean.Parser.Term.anonymousCtor"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 88 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | a1d802dc91086febaeea789a1d1ad28e5cfdd703979d367f9475508954fd89c9 | d4403a1bc6813512253928cb1961aabe8c259188a28a99cec667991cff9d7385 | 78d3a9abcc723bab0f5b01e81a1d5bbd99c54f4c950c30f6efc44a2e24330c8e | a5706b9953388e233e593bb87966205729fdefc33f9cb1927dc4a8d36684b47b |
cat-searcher/leandojo-benchmark-4-random | test | 401 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact <a>isClosed_iUnion_of_finite</a> fun i ↦ <a>isClosed_of_mem_irreducibleComponents</a> i.1 i.2.1 | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
hU0 : U ≠ ∅
hU1 : U = (⋃ x, ↑x)ᶜ
⊢ IsClosed (⋃ x, ↑x) | ((:c IsClosed) (:fv _uniq.25970) (:fv _uniq.25976) ((:c Set.iUnion) (:fv _uniq.25970) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) (:lambda x ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195)) ((:c Subtype.val) ((:c Set) (:fv _uniq.25970)) (:lambda x ((:c Set) (:fv _uniq.25970)) ((:c Membe... | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c IsClosed) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:app (:c Set.iUnion) (:arg :implicit-type 0 (:fv FV0)) (:arg :implicit-type 1 (:app (:c Set.Elem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":13604,"sourceStart":13599,"tag":"atom"},{"children":[{"name":"isClosed_iUnion_of_finite","semanticRole":"global","source":"isClosed_iUnion_of_finite","sourceEnd":13630,"sourceStart":13605,"tag":"identifier"},{"children":[{"children":[{"source":"fun","sourceEnd":13634,"sourceSt... | [] | [{"source":"isClosed_iUnion_of_finite fun i ↦ isClosed_of_mem_irreducibleComponents i.1 i.2.1","source_end":13688,"source_start":13605,"syntax_kind":"Lean.Parser.Term.app"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 89 | exact | true | 1 | 13 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | f9a74122c272d2562d4b466965c2b0100b1f5df11f4b9194bab916505c3ae6d1 | a5706b9953388e233e593bb87966205729fdefc33f9cb1927dc4a8d36684b47b | c1ac358d6b89554164e8cd0539712b9f5e69829d51b2bf54f10fd7e915cc1122 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 402 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | rwa [<a>Set.finite_coe_iff</a>] | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
⊢ Finite ↑ι | ((:c Finite) ((:c Set.Elem) ((:c Set) (:fv _uniq.25970)) (:fv _uniq.26195))) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c Finite) (:arg :explicit 0 (:app (:c Set.Elem) (:arg :implicit-type 0 (:app (:c Set) (:arg :explicit 0 (:fv FV0)))) (:arg :explicit 1 (:fv FV8))))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"rwa","sourceEnd":12069,"sourceStart":12066,"tag":"atom"},{"children":[{"source":"[","sourceEnd":12071,"sourceStart":12070,"tag":"atom"},{"children":[{"children":[{"children":[],"kind":"null","source":"","tag":"node"},{"name":"Set.finite_coe_iff","semanticRole":"global","source":"Set.finite_coe_i... | [] | [{"source":"Set.finite_coe_iff","source_end":12089,"source_start":12071,"syntax_kind":"ident"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 11 | exact | true | 1 | 9 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 3de461fc4e06d4e7365c507317caf08f97694abe4f57883b501c49ddff3daf87 | 077945ace27d563e565ba79cec1df4d821fec4d697202cbd6b81c571073abb79 | 133ea3213782ec919b795d0852b5282407cf89275dcc29bc8b2d649aa7697e94 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 403 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | obtain ⟨Z', hZ'⟩ := isIrreducible_iff_sUnion_closed.mp H.1 hι.toFinset (fun z hz ↦ by simp only [<a>Set.Finite.mem_toFinset</a>, <a>Set.mem_diff</a>, <a>Set.mem_singleton_iff</a>] at hz exact <a>isClosed_of_mem_irreducibleComponents</a> _ hz.1) (by rw [<a>Set.Finite.coe_toFinset</a>, <a>Set.sUnion_eq_iUnion</a>] rw [<a... | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
⊢ False | case intro
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
Z' : Set α
hZ' : Z' ∈ hι.toFinset ∧ Z ⊆ Z'
⊢ ... | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"obtain","sourceEnd":12172,"sourceStart":12166,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"source":"⟨","sourceEnd":12176,"sourceStart":12173,"tag":"atom"},{"children":[{"children":[{"children":[{"children":[{"children":[{"semanticRole":"scoped_local","source":"Z'","sourceE... | [] | [{"source":"isIrreducible_iff_sUnion_closed.mp H.1 hι.toFinset\n (fun z hz ↦ by\n simp only [Set.Finite.mem_toFinset, Set.mem_diff, Set.mem_singleton_iff] at hz\n exact isClosed_of_mem_irreducibleComponents _ hz.1)\n (by\n rw [Set.Finite.coe_toFinset, Set.sUnion_eq_iUnion]\n rw [Se... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 20 | exact | true | 1 | 12 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | ab30e677a6c176c5d2dec7471e439b96cfeb74cb96976834da28aefc9cb28475 | e3d8726beff9dc8a9da522ab0428ac5bc024cba0ef67fa55688af38cc94083b2 | ad32abb1a3bc817936601d59193a0299f3447946f1184cc4d53ce6d35421a4a5 | 6a4445ca2f08705e34a0005bb96c9e8ac278809e7f18661574a58ebee2fccab4 |
cat-searcher/leandojo-benchmark-4-random | test | 404 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.Finite.mem_toFinset</a>, <a>Set.mem_diff</a>, <a>Set.mem_singleton_iff</a>] at hZ' | case intro
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
Z' : Set α
hZ' : Z' ∈ hι.toFinset ∧ Z ⊆ Z'
⊢ ... | case intro
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
Z' : Set α
hZ' : Z' ∈ ι ∧ Z ⊆ Z'
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":12542,"sourceStart":12538,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12547,"sourceStart":12543,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":125... | [] | [{"source":"Set.Finite.mem_toFinset","source_end":12572,"source_start":12549,"syntax_kind":"ident"},{"source":"Set.mem_diff","source_end":12586,"source_start":12574,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":12609,"source_start":12588,"syntax_kind":"ident"},{"source":"hZ'","source_end":12617,... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 39 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 8fe1fe438a0bb537e5de366aca451241659d3bcf2ce0ad51f00c6a445529c8b6 | 6a4445ca2f08705e34a0005bb96c9e8ac278809e7f18661574a58ebee2fccab4 | 72319056e13a4a89fe265d97d31c8a73d131a88febfd1009ed9aa4f924df36a7 | ca30d61d2997a2b445b5d6c7b56c665dd6233cdf545af6163155fcccaceda314 |
cat-searcher/leandojo-benchmark-4-random | test | 405 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | exact hZ'.1.2 <| <a>le_antisymm</a> (H.2 hZ'.1.1.1 hZ'.2) hZ'.2 | case intro
α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
Z' : Set α
hZ' : Z' ∈ ι ∧ Z ⊆ Z'
⊢ False | (:c False) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:c False) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"exact","sourceEnd":12627,"sourceStart":12622,"tag":"atom"},{"children":[{"children":[{"children":[{"contextIndex":14,"semanticRole":"local","source":"hZ'","sourceEnd":12631,"sourceStart":12628,"tag":"identifier"},{"source":".","sourceEnd":12632,"sourceStart":12631,"tag":"atom"},{"children":[{"so... | [] | [{"source":"hZ'.1.2 <| le_antisymm (H.2 hZ'.1.1.1 hZ'.2) hZ'.2","source_end":12678,"source_start":12628,"syntax_kind":"«term_<|_»"}] | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 40 | exact | true | 1 | 14 | false | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 39c86e2dab00994f08ca9fafb9c8b87f3901782acd8bc52accea8f2f22670f6c | ca30d61d2997a2b445b5d6c7b56c665dd6233cdf545af6163155fcccaceda314 | 26c049caed8eb5e87fde0e1775772b53538b915ca9f2234a0fb0fca5647b6536 | d7064e63adc3d44cf9cf59b8d4bc453382f705da6e9d1ad9cc82503563a0a981 | |
cat-searcher/leandojo-benchmark-4-random | test | 406 | TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent | Mathlib/Topology/NoetherianSpace.lean | https://github.com/leanprover-community/mathlib4 | 29dcec074de168ac2bf835a77ef68bbe069194c5 | simp only [<a>Set.Finite.mem_toFinset</a>, <a>Set.mem_diff</a>, <a>Set.mem_singleton_iff</a>] at hz | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
z : Set α
hz : z ∈ hι.toFinset
⊢ IsClosed z | α : Type u_1
β : Type u_2
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
inst✝ : NoetherianSpace α
Z : Set α
H : Z ∈ irreducibleComponents α
ι : Set (Set α) := irreducibleComponents α \ {Z}
hι : ι.Finite
hι' : Finite ↑ι
U : Set α := Z \ ⋃ x, ↑x
r : U = ∅
z : Set α
hz : z ∈ ι
⊢ IsClosed z | ((:c IsClosed) (:fv _uniq.25970) (:fv _uniq.25976) (:fv _uniq.26729)) | [{"name":"α","sexp":"(:sort (+ u_1 1))"},{"name":"β","sexp":"(:sort (+ u_2 1))"},{"name":"inst✝²","sexp":"((:c TopologicalSpace) (:fv _uniq.25970))"},{"name":"inst✝¹","sexp":"((:c TopologicalSpace) (:fv _uniq.25973))"},{"name":"inst✝","sexp":"((:c TopologicalSpace.NoetherianSpace) (:fv _uniq.25970) (:fv _uniq.25976))"}... | (:app (:c IsClosed) (:arg :implicit-type 0 (:fv FV0)) (:arg :instance 1 (:instance-of (:app (:c TopologicalSpace) (:arg :explicit 0 (:fv FV0))))) (:arg :explicit 2 (:fv FV13))) | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"name":"α","sexp":"(:sort Type)"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"name":"β","sexp":"(:sort Type)"},{"binder_role":":instance-impli... | {"children":[{"source":"simp","sourceEnd":12277,"sourceStart":12273,"tag":"atom"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[],"kind":"null","source":"","tag":"node"},{"children":[{"source":"only","sourceEnd":12282,"sourceStart":12278,"tag":"atom"}],"kind":"null","source":"only","sourceEnd":122... | [] | [{"source":"Set.Finite.mem_toFinset","source_end":12307,"source_start":12284,"syntax_kind":"ident"},{"source":"Set.mem_diff","source_end":12321,"source_start":12309,"syntax_kind":"ident"},{"source":"Set.mem_singleton_iff","source_end":12344,"source_start":12323,"syntax_kind":"ident"},{"source":"hz","source_end":12351,"... | [{"binder_role":":implicit","context_index":0,"internal_name":"_uniq.25970","is_instance":false,"is_let":false,"user_name":"α"},{"binder_role":":implicit","context_index":1,"internal_name":"_uniq.25973","is_instance":false,"is_let":false,"user_name":"β"},{"binder_role":":instance-implicit","context_index":2,"internal_n... | 49 | 25 | exact | true | 1 | 14 | true | 4 | source-invocation-v4 | 2 | lean-model-sexp-v2 | 3 | lean-action-trace-v3 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 73781c2d58456e4bf369dadd4a501e1b78a0b177 | 87531c67e00f84430303baf3cc7ecde179e5f2809efa036da1f5c4687d3475c7 | 80824477dd9ecaadcbcac6968d5585cbde6932ebcc303f03da905129ad53abb1 | 105882dd5484eb1576e1ef3bf8edb1e54a3be805b96c57508070fb70ef922336 | 9915551c83f3b21c95fe9232a123855af4309ba8c356e92f669bfcc97bbe9a7e |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.