file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | MeasureTheory.Measure.ext_of_Ico' | [
{
"state_after": "case intro.intro.intro.intro\nα✝ : Type ?u.682427\nβ : Type ?u.682430\nγ : Type ?u.682433\nγ₂ : Type ?u.682436\nδ : Type ?u.682439\nι : Sort y\ns✝ t u : Set α✝\ninst✝²² : TopologicalSpace α✝\ninst✝²¹ : MeasurableSpace α✝\ninst✝²⁰ : OpensMeasurableSpace α✝\ninst✝¹⁹ : TopologicalSpace β\ninst✝¹⁸... | [
713,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Std/Data/List/Lemmas.lean | List.mem_filter | [
{
"state_after": "no goals",
"state_before": "case nil\nα✝ : Type u_1\nx : α✝\np : α✝ → Bool\n⊢ x ∈ filter p [] ↔ x ∈ [] ∧ p x = true",
"tactic": "simp [filter]"
},
{
"state_after": "case pos\nα✝ : Type u_1\nx : α✝\np : α✝ → Bool\na : α✝\nas : List α✝\nih : x ∈ filter p as ↔ x ∈ as ∧ p x = true\... | [
1129,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1123,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_lf_of_le | [
{
"state_after": "x y z : PGame\nh₁ : ¬y ≤ x\nh₂ : y ≤ z\n⊢ ¬z ≤ x",
"state_before": "x y z : PGame\nh₁ : x ⧏ y\nh₂ : y ≤ z\n⊢ x ⧏ z",
"tactic": "rw [← PGame.not_le] at h₁⊢"
},
{
"state_after": "no goals",
"state_before": "x y z : PGame\nh₁ : ¬y ≤ x\nh₂ : y ≤ z\n⊢ ¬z ≤ x",
"tactic": "exa... | [
569,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Topology/ContinuousFunction/T0Sierpinski.lean | TopologicalSpace.productOfMemOpens_inducing | [
{
"state_after": "case h.e'_3\nX : Type u_1\ninst✝ : TopologicalSpace X\n⊢ inst✝ = ⨅ (i : Opens X), induced (fun x => x ∈ i) inferInstance",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\n⊢ Inducing ↑(productOfMemOpens X)",
"tactic": "convert inducing_iInf_to_pi fun (u : Opens X) (x : X) => ... | [
55,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_pair | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.23294\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns t : Set E\nx✝ y✝ x y : E\n⊢ {x, y} ⊆ segment 𝕜 x y",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.2329... | [
139,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_mul_span_singleton | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n x y : A\n⊢ x ∈ map (↑(LinearMap.flip (LinearMap.mul R A)) y) P ↔ ∃ z, z ∈ P ∧ Mul.mul z y = x",
"tactic": "rfl"
... | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.pow_left | [
{
"state_after": "no goals",
"state_before": "m k n : Nat\nH1 : coprime m k\n⊢ coprime (m ^ n) k",
"tactic": "induction n with\n| zero => exact coprime_one_left _\n| succ n ih => have hm := H1.mul ih; rwa [Nat.pow_succ, Nat.mul_comm]"
},
{
"state_after": "no goals",
"state_before": "case zer... | [
370,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
367,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_le | [
{
"state_after": "case inl\nα : Type u_1\ninst✝ : LinearOrderedField α\na b c : CauSeq α abs\nhb : b ≤ c\nha : a < c\n⊢ a ⊔ b ≤ c\n\ncase inr\nα : Type u_1\ninst✝ : LinearOrderedField α\na b c : CauSeq α abs\nhb : b ≤ c\nha : a ≈ c\n⊢ a ⊔ b ≤ c",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\n... | [
976,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
11
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_toRingHom_apply_toRingHom_apply | [] | [
756,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.divMonomial_mul_monomial | [] | [
93,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_toReal_eq_two_mul | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal (2 • θ) = 2 * toReal θ ↔ toReal θ ∈ Set.Ioc (-π / 2) (π / 2)",
"tactic": "exact_mod_cast nsmul_toReal_eq_mul two_ne_zero"
}
] | [
673,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | lebesgue_number_lemma | [
{
"state_after": "α✝ : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι✝ : Sort ?u.181498\nα : Type u\ninst✝ : UniformSpace α\ns : Set α\nι : Sort u_1\nc : ι → Set α\nhs : IsCompact s\nhc₁ : ∀ (i : ι), IsOpen (c i)\nhc₂ : s ⊆ ⋃ (i : ι), c i\nu : Set (α × α) → Set α := fun n => {x | ∃ i m, m ∈ 𝓤 α ∧ {y | (x, y... | [
1857,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1835,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_bot | [] | [
639,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongTopology.hasBasis_nhds_zero | [] | [
175,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_of_not_mem_closure | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.370490\nδ : Type ?u.370493\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nx : α\nhx : ¬x ∈ closure s\n⊢ ContinuousWithinAt f s x",
"state_before": "α : Type u_... | [
1103,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_iUnion_nat | [
{
"state_after": "case e_f.h\nα : Type u_1\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU✝ :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f ... | [
1387,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_two | [
{
"state_after": "no goals",
"state_before": "⊢ ↑abs 2 = ↑abs ↑2",
"tactic": "rfl"
},
{
"state_after": "no goals",
"state_before": "⊢ 0 ≤ 2",
"tactic": "norm_num"
}
] | [
995,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_neg | [] | [
93,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.map_subtype_embedding_Ico | [] | [
52,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.mono_blimsup' | [] | [
866,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Order/Max.lean | IsMin.prod_mk | [] | [
413,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/Group/Units.lean | isUnit_iff_exists_inv' | [
{
"state_after": "α : Type u\nM : Type u_1\nN : Type ?u.58079\ninst✝ : CommMonoid M\na : M\n⊢ (∃ b, a * b = 1) ↔ ∃ b, b * a = 1",
"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.58079\ninst✝ : CommMonoid M\na : M\n⊢ IsUnit a ↔ ∃ b, b * a = 1",
"tactic": "rw [isUnit_iff_exists_inv]"
},
{
"... | [
658,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.refl | [
{
"state_after": "R : Type u_1\ninst✝⁶ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type ?u.7004\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nι : Type ?u.7086\ninst✝¹ : DecidableEq ι\nx✝ y z x : M\ninst✝ : Nontrivial R\n⊢ SameRay R x x",
"state_before": ... | [
82,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_union | [
{
"state_after": "α : Type u_1\nβ : Type ?u.14144\nγ : Type ?u.14147\nr : α → α → Prop\ns✝ t✝ : Multiset α\na✝ : α\ninst✝ : DecidableEq α\ns t : Multiset α\nx✝ : Nodup s ∧ Nodup t\nh₁ : Nodup s\nh₂ : Nodup t\na : α\n⊢ max (count a s) (count a t) ≤ 1",
"state_before": "α : Type u_1\nβ : Type ?u.14144\nγ : Ty... | [
223,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | prod_normalizedFactors_eq_self | [] | [
901,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.rightUnitor_hom_app | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.commonNeighbors_subset_neighborSet_left | [] | [
1034,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_div_iff | [] | [
140,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | eventually_closure_subset_of_isOpen_of_omegaLimit_subset | [] | [
296,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.of_codisjoint_sup_of_le | [] | [
358,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.exists_list_of_mem_closure | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nA : Type ?u.81053\nB : Type ?u.81056\ninst✝ : Monoid M\ns : Set M\nx : M\nhx : x ∈ closure s\n⊢ ∃ l x_1, List.prod l = x",
"tactic": "rwa [← SetLike.mem_coe, closure_eq_image_prod, Set.mem_image_iff_bex] at hx"
}
] | [
373,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.mem_equalizer | [] | [
677,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | AddCommGroupCat.injective_of_mono | [
{
"state_after": "G H : AddCommGroupCat\nf : G ⟶ H\ninst✝ : Mono f\ng₁ g₂ : ↑G\nh : ↑f g₁ = ↑f g₂\nt0 : asHom g₁ ≫ f = asHom g₂ ≫ f\n⊢ g₁ = g₂",
"state_before": "G H : AddCommGroupCat\nf : G ⟶ H\ninst✝ : Mono f\ng₁ g₂ : ↑G\nh : ↑f g₁ = ↑f g₂\n⊢ g₁ = g₂",
"tactic": "have t0 : asHom g₁ ≫ f = asHom g₂ ≫ f ... | [
370,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Algebra/Category/ModuleCat/Images.lean | ModuleCat.imageIsoRange_hom_subtype | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : Ring R\nG✝ H✝ : ModuleCat R\nf✝ : G✝ ⟶ H✝\nG H : ModuleCat R\nf : G ⟶ H\n⊢ (imageIsoRange f).hom ≫ ofHom (Submodule.subtype (LinearMap.range f)) = Limits.image.ι f",
"tactic": "erw [← imageIsoRange_inv_image_ι f, Iso.hom_inv_id_assoc]"
... | [
121,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_bot | [] | [
128,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.separatingLeft_of_det_ne_zero | [] | [
760,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_left_on_Ioo | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\nhgg' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt g (g' x) x\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → g' x ≠ 0\nhfb : Tendsto f (𝓝[Iio b] b) (𝓝 0)\nhgb : Tendsto g (𝓝[Iio b] b) (𝓝 0)\nhdiv : Tends... | [
133,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_left_cancel_iff | [] | [
62,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
61,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.deriv_cosh | [] | [
163,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_of_mem | [] | [
631,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_eq_prod_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.88795\nδ : Type ?u.88798\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\n⊢ s = s₁ ∧ t = t₁ ∨ (s = ∅ ∨ t = ∅) ∧ (s₁ = ∅ ∨ t₁ = ∅) ↔ s ×ˢ t = s₁ ×ˢ t₁",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.88795\nδ : Type ?u.88798\ns s₁ s₂ : Set α... | [
419,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_top_of_mul_ne_top_left | [] | [
591,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_inv | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nf : Cauchy abs\n⊢ (Real.inv' { cauchy := f }).cauchy = { cauchy := f }.cauchy⁻¹",
"tactic": "rw [inv']"
}
] | [
171,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_zero | [] | [
558,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.isPath | [] | [
1279,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
11
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_compContinuousLinearMap_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι)... | [
1151,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_im | [] | [
1163,
44
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1161,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | TotallyBounded.exists_subset | [
{
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473,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
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Mathlib/Data/Finset/Powerset.lean | Finset.coe_powerset | [
{
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{
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47,
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44,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_apply | [] | [
2035,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2034,
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.wellFounded_of_noetherian | [] | [
589,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
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Mathlib/Order/Basic.lean | Eq.not_gt | [] | [
242,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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Mathlib/Analysis/Convex/Between.lean | Wbtw.left_ne_right_of_ne_left | [
{
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325,
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322,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | norm_iteratedFDerivWithin_fderivWithin | [
{
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95
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863,
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Mathlib/LinearAlgebra/Dimension.lean | rank_subsingleton | [
{
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487,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.not_mem_support_iff | [] | [
1142,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.eq_top_of_isUnit_mem | [] | [
93,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapSMul_def | [] | [
1433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
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Mathlib/GroupTheory/GroupAction/Pi.lean | Pi.single_smul | [] | [
185,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/RingTheory/Ideal/Basic.lean | mul_mem_nonunits_right | [] | [
834,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.pair_obj_right | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Data/Fin/Basic.lean | Fin.one_succAbove_one | [
{
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},
{
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2254,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2251,
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Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.continuous_comp_right | [] | [
379,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.isDiag_transpose_iff | [] | [
125,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Data/Finset/Basic.lean | Multiset.mem_toFinset | [] | [
3138,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3137,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | UniformSpace.Completion.inner_coe | [] | [
2325,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2323,
1
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Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ioo | [
{
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}
] | [
163,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Sheaf.Hom.add_app | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/Data/Set/Image.lean | Set.subsingleton_range | [] | [
1242,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
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Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.map_neg | [
{
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},
{
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113,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Analysis/Convex/Star.lean | StarConvex.union | [
{
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127,
35
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123,
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Mathlib/Data/Multiset/Basic.lean | Multiset.erase_le | [] | [
1069,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_cos | [] | [
960,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Data/Set/Function.lean | Function.invFunOn_apply_mem | [] | [
1232,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
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Mathlib/Topology/LocalExtr.lean | IsExtrOn.localize | [] | [
141,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Set/Pairwise/Lattice.lean | Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion | [
{
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123,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Data/Int/Basic.lean | Int.sign_coe_add_one | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.CompactSpace.isFiniteMeasure | [] | [
3972,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3970,
1
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Mathlib/Topology/Order/Basic.lean | orderTopology_of_nhds_abs | [
{
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1864,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1859,
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Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | mem_fixingSubgroup_iff | [] | [
123,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | Differentiable.clog | [] | [
150,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.lift_symm_apply | [
{
"state_after": "R : Type u_1\ninst✝² : CommSemiring R\nX : Type u_2\nA : Type u_3\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nF : FreeAlgebra R X →ₐ[R] A\n⊢ ↑{ toFun := FreeAlgebra.liftAux R, invFun := fun F => ↑F ∘ ι R,\n left_inv := (_ : ∀ (f : X → A), (fun F => ↑F ∘ ι R) (FreeAlgebra.liftAux R f)... | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.scalingScaleOf_pos | [] | [
160,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_sup_right | [
{
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169,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Order/SymmDiff.lean | Disjoint.symmDiff_right | [] | [
564,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
11
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Mathlib/Order/Filter/Extr.lean | IsMaxFilter.add | [] | [
462,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Control/Traversable/Instances.lean | List.naturality | [
{
"state_after": "no goals",
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100,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
11
] |
Mathlib/Algebra/Star/Module.lean | IsSelfAdjoint.skewAdjointPart_apply | [
{
"state_after": "no goals",
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156,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.atEnd | [
{
"state_after": "no goals",
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"tactic... | [
905,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
904,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_pure | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44252\nδ : Type ?u.44255\nι : Sort ?u.44258\ns : Set α\nt : Set β\nf✝ : Filter α\ng : Filter β\nf : Filter α\nb : β\n⊢ map ((fun g => g b) ∘ Prod.mk) f = map (fun a => (a, b)) f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44252\nδ : Ty... | [
417,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.lift_map | [
{
"state_after": "case h₁\nC : Type u\ninst✝² : Category C\nX✝ Y✝ V W X Y Z : C\ninst✝¹ : HasBinaryProduct W X\ninst✝ : HasBinaryProduct Y Z\nf : V ⟶ W\ng : V ⟶ X\nh : W ⟶ Y\nk : X ⟶ Z\n⊢ (lift f g ≫ map h k) ≫ fst = lift (f ≫ h) (g ≫ k) ≫ fst\n\ncase h₂\nC : Type u\ninst✝² : Category C\nX✝ Y✝ V W X Y Z : C\nin... | [
740,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Order/WithBot.lean | WithTop.exists | [] | [
593,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
11
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_nat_eq_ascFactorial | [
{
"state_after": "no goals",
"state_before": "S : Type u\ninst✝ : Semiring S\nn : ℕ\n⊢ eval (n + 1) (pochhammer ℕ 0) = Nat.ascFactorial n 0",
"tactic": "rw [pochhammer_zero, eval_one, Nat.ascFactorial_zero]"
},
{
"state_after": "S : Type u\ninst✝ : Semiring S\nn t : ℕ\n⊢ Nat.ascFactorial n t * e... | [
152,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_lowerSemicontinuousOn_antitone | [] | [
358,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Topology/Covering.lean | IsCoveringMap.isCoveringMapOn | [] | [
149,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
] |
Mathlib/ModelTheory/Definability.lean | Set.definable_univ | [
{
"state_after": "case h\nM : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.10107\nB : Set M\ns : Set (α → M)\nx✝ : α → M\n⊢ x✝ ∈ univ ↔ x✝ ∈ setOf (Formula.Realize ⊤)",
"state_before": "M : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.1... | [
89,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_nonempty | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ u ∈ {w | w ∈ support p}",
"tactic": "simp"
}
] | [
584,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Compatibility.lean | AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eq | [
{
"state_after": "case w.w.h\nA : Type u_1\nA' : Type u_5\nB : Type ?u.21378\nB' : Type u_4\ninst✝³ : Category A\ninst✝² : Category A'\ninst✝¹ : Category B\ninst✝ : Category B'\neA : A ≌ A'\neB : B ≌ B'\ne' : A' ≌ B'\nF : A ⥤ B'\nhF : eA.functor ⋙ e'.functor ≅ F\nG : B ⥤ A\nhG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA... | [
115,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.decomp' | [
{
"state_after": "k : Type u_1\nV1 : Type u_2\nP1 : Type ?u.607898\nV2 : Type u_3\nP2 : Type ?u.607904\nV3 : Type ?u.607907\nP3 : Type ?u.607910\nV4 : Type ?u.607913\nP4 : Type ?u.607916\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ : AddCommGroup V2\nin... | [
677,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_mono_measure | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.1987947\nF : Type u_2\nG : Type ?u.1987953\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nhμν : ν ≤ μ\nhp0 : p = 0\n⊢ snorm f p ν ≤ snorm f p... | [
592,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
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