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/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_prime | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI : Ideal α\np : α\nhp : p ≠ 0\n⊢ IsPrime (span {p}) ↔ Prime p",
"tactic": "simp [isPrime_iff, Prime, span_singleton_eq_top, hp, mem_span_singleton]"
}
] | [
526,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.generate_empty | [] | [
535,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_ne_one | [] | [
187,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monic_X | [] | [
832,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.814548\nβ : Type ?u.814551\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nhp : 0 ≤ p\n⊢ ENNReal.ofReal (p * q) = ENNReal.ofReal p * ENNReal.ofReal q",
"tactic": "simp only [ENNReal.ofReal, ← coe_mul, Real.toNNReal_mul hp]"
}
] | [
2169,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2167,
1
] |
Mathlib/Data/Multiset/Range.lean | Multiset.range_add | [] | [
66,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal | [
{
"state_after": "n : Type u_1\np : Type ?u.319321\nR : Type u₂\n𝕜 : Type u_2\ninst✝⁵ : Field 𝕜\ninst✝⁴ : DecidableEq n\ninst✝³ : DecidableEq p\ninst✝² : CommRing R\nr : ℕ\nM✝ : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\ninst✝¹ : Fintype n\ninst✝ : Fintype p\nM : Matrix n n 𝕜\ne : n ≃ Fin (Fintype.card n)\n⊢ ∃... | [
677,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Topology/Constructions.lean | nhds_ofDual | [] | [
181,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.map_one₂ | [] | [
154,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | cauchySeq_finset_of_norm_bounded_eventually | [
{
"state_after": "ι : Type u_1\nα : Type ?u.3377\nE : Type u_2\nF : Type ?u.3383\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : SeminormedAddCommGroup F\nf : ι → E\ng : ι → ℝ\nhg : Summable g\nh : ∀ᶠ (i : ι) in cofinite, ‖f i‖ ≤ g i\nε : ℝ\nhε : ε > 0\n⊢ ∃ s, ∀ (t : Finset ι), Disjoint t s → ‖∑ i in t, f i‖ < ε",
... | [
70,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/MetricSpace/CantorScheme.lean | CantorScheme.Antitone.closureAntitone | [] | [
97,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
11
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_congr | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9864\nι : Type ?u.9867\nM : Type u_2\nN : Type ?u.9873\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g : α → M\na : α\nh : EqOn f g s\nx : α\n⊢ (if x ∈ s then f x else 1) = if x ∈ s then g x else 1",
"state_before": "α : Type u_1\nβ : Type ?u.9864\nι : Type ?u.98... | [
196,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/PNat/Basic.lean | OrderIso.pnatIsoNat_symm_apply | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.dTo_eq | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\nj : ι\nr : ComplexShape.Rel c (ComplexShape.prev c j) j\n⊢ dTo C j = (xPrevIso C r).hom ≫ d C (ComplexShape.prev c j) j",
"state_before": "ι : Type u_1\nV : Type u\nin... | [
412,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasFDerivAt.comp_hasDerivWithinAt | [] | [
252,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.c_mk | [] | [
86,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_const_mul | [] | [
270,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_def | [] | [
541,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Iso.apply_mem_neighborSet_iff | [] | [
1929,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.Nondegenerate.toMatrix' | [] | [
583,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Data/Set/Basic.lean | Set.symmDiff_nonempty | [] | [
2111,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2110,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_left_cancel_iff' | [] | [
186,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
11
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.rank_prime_pow_ramificationIdx | [
{
"state_after": "R : Type u\ninst✝⁵ : CommRing R\nS : Type v\ninst✝⁴ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhfp : NeZero e\ninst✝³ : IsDomain S\ninst✝² : IsDedekindDomain S\ninst✝¹ : IsMaximal p\ninst✝ : IsPrime P\nhP0 : P ≠ ⊥\nhe : e ≠ 0\nthis : NeZero e := { out := he }\n⊢ Module.rank (R ⧸ p) (... | [
662,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.coe_fun_mk | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.continuousAt | [] | [
854,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneous_span | [
{
"state_after": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.93837\nA : Type u_1\ninst✝⁵ : Semiring A\ninst✝⁴ : SetLike σ A\ninst✝³ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : GradedRing 𝒜\nI : Ideal A\ns : Set A\nh : ∀ (x : A), x ∈ s → Homogeneous 𝒜 x\ni : ι\nr : A... | [
181,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.815243\nβ : Type ?u.815246\na b c d : ℝ≥0∞\nr p✝ q : ℝ≥0\np : ℝ\nhp : 0 ≤ p\nn : ℕ\n⊢ ENNReal.ofReal (p ^ n) = ENNReal.ofReal p ^ n",
"tactic": "rw [ofReal_eq_coe_nnreal hp, ← coe_pow, ← ofReal_coe_nnreal, NNReal.coe_pow, NNReal.coe_mk]"
}
] | [
2178,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2177,
1
] |
Mathlib/Topology/Paracompact.lean | ClosedEmbedding.paracompactSpace | [
{
"state_after": "ι : Type u\nX : Type v\nY : Type w\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : ParacompactSpace Y\ne : X → Y\nhe : ClosedEmbedding e\nα : Type v\ns : α → Set X\nho : ∀ (a : α), IsOpen (s a)\nhu : (⋃ (a : α), s a) = univ\nU : α → Set Y\nhUo : ∀ (a : α), IsOpen (U a)\nhU :... | [
128,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/List/Zip.lean | List.length_zip | [] | [
79,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_pmap | [
{
"state_after": "case nil\nα : Type u_2\nβ : Type u_1\nR S T : α → α → Prop\na : α\nl✝ : List α\np : β → Prop\nf : (b : β) → p b → α\nl : List β\nh✝ : ∀ (x : β), x ∈ l → p x\nh : ∀ (x : β), x ∈ [] → p x\n⊢ Pairwise R (pmap f [] h) ↔ Pairwise (fun b₁ b₂ => ∀ (h₁ : p b₁) (h₂ : p b₂), R (f b₁ h₁) (f b₂ h₂)) []\n\... | [
242,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_add_left | [
{
"state_after": "a b c : Int\nH : a ∣ c\nh : a ∣ b + c\nthis : a ∣ b + c - c\n⊢ a ∣ b",
"state_before": "a b c : Int\nH : a ∣ c\nh : a ∣ b + c\n⊢ a ∣ b",
"tactic": "have := Int.dvd_sub h H"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nH : a ∣ c\nh : a ∣ b + c\nthis : a ∣ b ... | [
622,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
621,
11
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_set_eq | [] | [
212,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Data/List/Lemmas.lean | List.get_set_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\ni : Nat\na : α\nh : i < length (set l i a)\n⊢ get (set l i a) { val := i, isLt := h } = a",
"tactic": "rw [← Option.some_inj, ← get?_eq_get, get?_set_eq, get?_eq_get] <;> simp_all"
}
] | [
837,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
835,
9
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | differentiable_inner | [] | [
72,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_one_one_zmod_p | [
{
"state_after": "case intro.intro.intro\nR : Type ?u.256583\nS : Type ?u.256586\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nk : ℕ\na : R\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nK : Type\nw✝¹ : Field K\nw✝ : CharP K p\nH : Infinite K\n⊢ dickson 1 1 p = X ^ p",
"state_before": "R : Type ?u.256583\nS : Type ?u.256... | [
268,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/Algebra/Order/LeftRight.lean | nhds_left'_sup_nhds_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2014\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : TopologicalSpace β\na : α\n⊢ 𝓝[Iio a] a ⊔ 𝓝[Ici a] a = 𝓝 a",
"tactic": "rw [← nhdsWithin_union, Iio_union_Ici, nhdsWithin_univ]"
}
] | [
66,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/Option/Lemmas.lean | Option.getD_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\nx : α\no : Option α\n⊢ getD (Option.map f o) (f x) = f (getD o x)",
"tactic": "cases o <;> rfl"
}
] | [
198,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
197,
9
] |
Mathlib/Data/Part.lean | Part.Dom.toOption | [] | [
306,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
11
] |
Mathlib/GroupTheory/Schreier.lean | Subgroup.exists_finset_card_le_mul | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\nR S✝ : Set G\ninst✝ : FiniteIndex H\nS : Finset G\nhS : closure ↑S = ⊤\nthis : Fintype (G ⧸ H) := fintypeQuotientOfFiniteIndex H\n⊢ ∃ T, Finset.card T ≤ index H * Finset.card S ∧ closure ↑T = ⊤",
"state_before": "G : Type u_1\ninst✝¹ : Group ... | [
127,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.interior | [] | [
235,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
11
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ioo_bot_coe | [] | [
1180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.coe_pureMulHom | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_inter_le | [] | [
695,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_nsmulRec | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.935054\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : PseudoMetricSpace β\ninst✝¹ : AddMonoid β\ninst✝ : LipschitzAdd β\nf g : α →ᵇ β\nx : α\nC : ℝ\n⊢ ↑(nsmulRec 0 f) = 0 • ↑f",
"tactic": "rw [nsmulRec, zero_smul, coe_... | [
704,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Algebra/AddTorsor.lean | Prod.fst_vsub | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/LinearAlgebra/Ray.lean | eq_zero_of_sameRay_neg_smul_right | [
{
"state_after": "case inl\nR : Type u_1\ninst✝⁵ : StrictOrderedCommRing R\nM : Type u_2\nN : Type ?u.147146\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\ny : M\ninst✝ : NoZeroSMulDivisors R M\nr : R\nhr : r < 0\n⊢ 0 = 0\n\ncase inr.inl\nR : Type u_1\ninst✝⁵ : Stri... | [
416,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Deprecated/Subfield.lean | Field.closure.isSubmonoid | [
{
"state_after": "case intro.intro.intro.intro.refl.intro.intro.intro.intro.refl\nF : Type u_1\ninst✝ : Field F\nS : Set F\np : F\nhp : p ∈ Ring.closure S\nq : F\nhq : q ∈ Ring.closure S\nr : F\nhr : r ∈ Ring.closure S\ns : F\nhs : s ∈ Ring.closure S\n⊢ p / q * (r / s) ∈ closure S",
"state_before": "F : Typ... | [
101,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_powers_iff | [] | [
441,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_apply_le' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.151856\nι : Type ?u.151859\nM : Type u_2\nN : Type ?u.151865\ninst✝¹ : One M\ns t : Set α\nf g : α → M\na : α\ny : M\ninst✝ : LE M\nhfg : a ∈ s → f a ≤ y\nhg : ¬a ∈ s → 1 ≤ y\nha : a ∈ s\n⊢ mulIndicator s f a ≤ y\n\ncase neg\nα : Type u_1\nβ : Type ?u.151856... | [
761,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.toGlue_commute | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝³ : Nonempty Z\ninst✝² : MetricSpace Z\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nhΦ : Isometry Φ\nhΨ : Isometry Ψ\ni : PseudoMetricSpace (X ⊕ Y) := gluePremetric hΦ hΨ\n⊢ toGlueL hΦ hΨ ∘ Φ = toGlueR hΦ hΨ ∘ Ψ",
"st... | [
516,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_C_mul | [] | [
1504,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1503,
1
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Mathlib/Order/SymmDiff.lean | bihimp_of_ge | [
{
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"tactic": "rw [bihimp, himp_eq_top_iff.2 h, top_inf_eq]"
}
] | [
267,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/Algebra/Hom/Aut.lean | AddAut.conj_apply | [] | [
289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.exists_prime_dvd_of_not_inf_one | [
{
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1655,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
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Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.rightInverse_of_injective | [] | [
371,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_add_cons | [
{
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"tactic": "simp"
}
] | [
472,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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Mathlib/Order/Bounds/Basic.lean | bddBelow_Icc | [] | [
660,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
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Mathlib/Algebra/Module/Basic.lean | Nat.noZeroSMulDivisors | [
{
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641,
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637,
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Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_of_eq | [
{
"state_after": "no goals",
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"tactic": "rw [cycleRange_of_le h.le, if_pos h]"
}
] | [
211,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.not_one_mem_div_iff | [] | [
1122,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
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Mathlib/Order/Heyting/Basic.lean | himp_bot | [] | [
781,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.contDiffWithinAt_extend_coord_change' | [
{
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1017,
39
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1012,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.isConnected_setOf_wSameSide | [
{
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872,
51
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861,
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Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_int_eq_if_mod_four | [
{
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"tactic": "have help : ∀ m : ℤ... | [
74,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.exists_subset_real_measurableEquiv | [
{
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821,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
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Mathlib/Algebra/Order/Group/Defs.lean | le_mul_inv_iff_le | [
{
"state_after": "no goals",
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"tactic": "rw [← mul_le_mul_iff_right b, one_mul, inv_mul_cancel_right]"
}
] | [
265,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.pairwise_disjoint_fundamentalInterior | [
{
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"state_... | [
637,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.not_ne_id | [] | [
139,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.NatTrans.Equifibered.whiskerRight | [] | [
518,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
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Mathlib/Analysis/Convex/Segment.lean | openSegment_subset_iff | [] | [
104,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_of_tendsto_ae | [
{
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1647,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1631,
1
] |
Mathlib/Topology/GDelta.lean | Set.Countable.isGδ_compl | [
{
"state_after": "α : Type u_1\nβ : Type ?u.11615\nγ : Type ?u.11618\nι : Type ?u.11621\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns : Set α\nhs : Set.Countable s\n⊢ IsGδ (⋂ (i : α) (_ : i ∈ s), {i}ᶜ)",
"state_before": "α : Type u_1\nβ : Type ?u.11615\nγ : Type ?u.11618\nι : Type ?u.11621\ninst✝¹ : To... | [
146,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftMonoidWithZeroHom_apply_div' | [
{
"state_after": "no goals",
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895,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
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Std/Data/Int/DivMod.lean | Int.fmod_zero | [] | [
261,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
258,
9
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Mathlib/Topology/SubsetProperties.lean | IsCompact.prod | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.96853\nπ : ι → Type ?u.96858\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t✝ s : Set α\nt : Set β\nhs : ∀ (f : Ultrafilter α), ↑f ≤ 𝓟 s → ∃ a, a ∈ s ∧ ↑f ≤ 𝓝 a\nht : ∀ (f : Ultrafilter β), ↑f ≤ 𝓟 t → ∃ a, a ∈ t ∧ ↑f ≤ 𝓝 a\n⊢ ∀ (f : Ultraf... | [
954,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.uniformContinuous_infDist_pt | [] | [
569,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | Commute.zpow_left₀ | [] | [
128,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_mem | [] | [
88,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_iSup | [] | [
1227,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_eq_Ico_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.69074\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh : a₁ < b₁ ∨ a₂ < b₂\ne : Ico a₁ b₁ ⊆ Ico a₂ b₂ ∧ Ico a₂ b₂ ⊆ Ico a₁ b₁\n⊢ a₁ = a₂ ∧ b₁ = b₂",
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1164,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.zag_of_zag_obj | [] | [
296,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_eq_two_iff | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ (∃ x, ¬x ∈ H ∧ ∀ (x_1 : G), ¬x_1 ∈ H → x_1⁻¹ * x ∈ H) ↔ ∃ a, ∀ (b : G), b * a ∈ H ↔ ¬b ∈ H",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ index H = 2 ↔ ∃ a, ∀ (b : G), Xor' (b * a ∈ H) (b ∈ H)",
"tactic": "si... | [
194,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_lt_3141593 | [
{
"state_after": "no goals",
"state_before": "⊢ π < 3.141593",
"tactic": "pi_upper_bound\n [27720 / 19601, 56935 / 30813, 49359 / 25163, 258754 / 130003, 113599 / 56868,\n 1101994 / 551163, 8671537 / 4336095, 3877807 / 1938940, 52483813 / 26242030,\n 56946167 / 28473117, 23798415 / 11899211... | [
202,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | convexOn_univ_of_deriv2_nonneg | [] | [
1256,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.bot_prod_bot | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.100408\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.100429\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\n⊢ ↑(prod ⊥ ⊥) = ↑⊥",
"tactic": "simp [coe_prod,... | [
891,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_congr | [] | [
92,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_ne_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : 0 ≤ x\n⊢ sqrt x ≠ 0 ↔ x ≠ 0",
"tactic": "rw [not_iff_not, sqrt_eq_zero h]"
}
] | [
344,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isNoetherian_coeIdeal | [
{
"state_after": "R : Type ?u.1753199\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type ?u.1753406\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝³ : CommRing R₁\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\nfrac : IsFractionRing R₁ K\ninst✝ : IsNoetherianRing ... | [
1571,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_lt_iff | [] | [
1014,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsRefl.flip_isRefl_iff | [] | [
193,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.sec_spec | [] | [
604,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_restrict_of_antitoneOn | [] | [
1189,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/Algebra/CharP/Algebra.lean | charP_of_injective_algebraMap' | [] | [
49,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.coe_continuous | [] | [
103,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_eq_iff_eq_inv_smul | [] | [
178,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_inf_le | [] | [
435,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Logic/IsEmpty.lean | IsEmpty.forall_iff | [] | [
120,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_anti | [] | [
97,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.norm_snd | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NonUnitalNormedRing A\ninst✝⁴ : NormedSpace 𝕜 A\ninst✝³ : SMulCommClass 𝕜 A A\ninst✝² : IsScalarTower 𝕜 A A\ninst✝¹ : StarRing A\ninst✝ : CstarRing A\na : 𝓜(𝕜, A)\n⊢ ‖a.snd‖ = ‖a‖",
... | [
648,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.toLaurent_support | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\ns : Finset ℕ\nhd : Polynomial.support f = s\n⊢ (↑toLaurent f).support = Finset.map Nat.castEmbedding s",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\n⊢ (↑toLaurent f).support = Finset.map Nat.castEmbedding (Polynomial.support f)",... | [
469,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
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