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 |
|---|---|---|---|---|---|---|
Std/Data/List/Basic.lean | List.zipWith_eq_zipWithTR | [
{
"state_after": "case h.h.h.h.h.h\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nf : α → β → γ\nas : List α\nbs : List β\n⊢ zipWith f as bs = zipWithTR f as bs",
"state_before": "⊢ @zipWith = @zipWithTR",
"tactic": "funext α β γ f as bs"
},
{
"state_after": "case h.h.h.h.h.h\nα : Type u_3\nβ : Type... | [
185,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
180,
10
] |
Mathlib/Data/List/MinMax.lean | List.minimum_concat | [] | [
371,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Std/Data/Int/DivMod.lean | Int.div_one | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ div -[n+1] 1 = -[n+1]",
"tactic": "simp [Int.div, neg_ofNat_succ]"
}
] | [
122,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
120,
19
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_zero_left | [] | [
82,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_pow | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1304029\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1304035\ninst✝¹² : Semiring R''\nM : Type u_3\nN : Type u_2\nP : Type ?u.1304047\nQ : Type ?u.1304050\nS : Type ?u.1304053\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMon... | [
1163,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsClopen.union | [] | [
1554,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1553,
1
] |
Mathlib/Computability/Partrec.lean | Computable.nat_bodd | [] | [
330,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.comap_id | [] | [
259,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | ball_subset_of_comp_subset | [] | [
631,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Computability/Partrec.lean | Computable.partrec | [] | [
268,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
11
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_isBot | [] | [
2397,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2396,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.toSignedMeasure_injective | [
{
"state_after": "α : Type u_1\nβ : Type ?u.70440\ninst✝ : MeasurableSpace α\nj₁ j₂ : JordanDecomposition α\nhj : toSignedMeasure j₁ = toSignedMeasure j₂\n⊢ j₁ = j₂",
"state_before": "α : Type u_1\nβ : Type ?u.70440\ninst✝ : MeasurableSpace α\n⊢ Injective toSignedMeasure",
"tactic": "intro j₁ j₂ hj"
}... | [
427,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.tunnelAux_injective | [] | [
898,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | Set.Finite.of_summable_const | [] | [
279,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_mul_const_field | [
{
"state_after": "case pos\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type u... | [
241,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.comp_zero | [
{
"state_after": "case a\nF : Type ?u.33482\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝² : NonUnitalNonAssocSemiring α\ninst✝¹ : NonUnitalNonAssocSemiring β\ninst✝ : NonUnitalNonAssocSemiring γ\ng✝ : β →ₙ+* γ\nf : α →ₙ+* β\ng : β →ₙ+* γ\nx✝ : α\n⊢ ↑(comp g 0) x✝ = ↑0 x✝",
"state_before": "F : Type ?u.3... | [
282,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_norm_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22376\nE : Type u_2\nF : Type ?u.22382\nG : Type ?u.22385\nE' : Type ?u.22388\nF' : Type u_3\nG' : Type ?u.22394\nE'' : Type ?u.22397\nF'' : Type ?u.22400\nG'' : Type ?u.22403\nR : Type ?u.22406\nR' : Type ?u.22409\n𝕜 : Type ?u.22412\n... | [
154,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_apply_of_aleph0_le | [] | [
1682,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | le_of_pow_le_pow' | [] | [
323,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.shiftFunctor_obj_apply | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Analysis/Complex/RemovableSingularity.lean | Complex.tendsto_limUnder_of_differentiable_on_punctured_nhds_of_bounded_under | [] | [
137,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Support.lean | Pi.mulSupport_mulSingle_disjoint | [
{
"state_after": "no goals",
"state_before": "A : Type u_2\nB : Type u_1\ninst✝¹ : DecidableEq A\ninst✝ : One B\na : A\nb b' : B\nhb : b ≠ 1\nhb' : b' ≠ 1\ni j : A\n⊢ Disjoint (mulSupport (mulSingle i b)) (mulSupport (mulSingle j b')) ↔ i ≠ j",
"tactic": "rw [mulSupport_mulSingle_of_ne hb, mulSupport_mu... | [
492,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | mem_piiUnionInter_of_measurableSet | [] | [
498,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.support_eq | [
{
"state_after": "E : Type u_1\nX : Type ?u.84106\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup X\ninst✝¹ : NormedSpace ℝ X\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\n⊢ (fun x => f.rIn⁻¹ • (x - c)) ⁻¹' ball 0 (f.rOut / f.rIn) = ball c f.rOut",
... | [
407,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Combinatorics/Hall/Basic.lean | Fintype.all_card_le_rel_image_card_iff_exists_injective | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq β\nr : α → β → Prop\ninst✝ : (a : α) → Fintype ↑(Rel.image r {a})\nr' : α → Finset β := fun a => Set.toFinset (Rel.image r {a})\n⊢ (∀ (A : Finset α), Finset.card A ≤ card ↑(Rel.image r ↑A)) ↔ ∃ f, Function.Injective f ∧ ∀ (x : α), r x (f x)",
"s... | [
205,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_lt_one_subset_self | [
{
"state_after": "𝕜 : Type ?u.71418\nE : Type u_1\nF : Type ?u.71424\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\nhs : Convex ℝ s\nh₀ : 0 ∈ s\nabsorbs : Absorbent ℝ s\n⊢ (⋃ (r : ℝ) (_ : r ∈ Ioo 0 1), r • s) ⊆ s",
"state_before": "𝕜 : Type ?u.71418\nE : Type u_1\nF : Type ?u.71424\nins... | [
196,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.r_mul_r | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.comp_assoc | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Filter.lean | Filter.HasBasis.nhds | [
{
"state_after": "ι : Sort u_2\nα : Type u_1\nβ : Type ?u.5424\nX : Type ?u.5427\nY : Type ?u.5430\nl : Filter α\np : ι → Prop\ns : ι → Set α\nh : HasBasis l p s\n⊢ HasBasis (Filter.lift' l (Iic ∘ 𝓟)) p fun i => Iic (𝓟 (s i))",
"state_before": "ι : Sort u_2\nα : Type u_1\nβ : Type ?u.5424\nX : Type ?u.542... | [
95,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
11
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_weighted_homogeneous_polynomial | [
{
"state_after": "R : Type u_3\nM : Type u_1\ninst✝² : CommSemiring R\nσ : Type u_2\ninst✝¹ : AddCommMonoid M\nw : σ → M\nn✝ : M\nφ ψ : MvPolynomial σ R\ninst✝ : DecidableEq M\nm n : M\np : MvPolynomial σ R\nh : IsWeightedHomogeneous w p n\n⊢ ↑(weightedHomogeneousComponent w m) p = if m = n then p else 0",
... | [
439,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Topology/Separation.lean | CofiniteTopology.continuous_of | [] | [
503,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Topology/LocalExtr.lean | Filter.EventuallyLE.isLocalMax | [] | [
595,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Order/InitialSeg.lean | wellFounded_iff_wellFounded_subrel | [
{
"state_after": "α : Type ?u.65547\nβ✝ : Type ?u.65550\nγ : Type ?u.65553\nr : α → α → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nβ : Type u_1\ns : β → β → Prop\ninst✝ : IsTrans β s\nwf : ∀ (b : β), WellFounded (Subrel s {b' | s b' b})\nb b' : β\nhb' : s b' b\n⊢ Acc s b'",
"state_before": "α : Type ?u.65... | [
449,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.modEq_iff_not_forall_mem_Ioo_mod | [] | [
647,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_injective | [
{
"state_after": "case ofFinsupp.ofFinsupp\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\np q : AddMonoidAlgebra R ℕ\n⊢ coeff { toFinsupp := p } = coeff { toFinsupp := q } → { toFinsupp := p } = { toFinsupp := q }",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R... | [
660,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.subset_mapRange_neLocus | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nM : Type u_2\nN : Type u_1\nP : Type ?u.8114\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ x ∈ neLocus (mapRange F F0 f) (mapRange F F0 g) →... | [
93,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_Iio | [] | [
594,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.restrict_prod_eq_prod_univ | [
{
"state_after": "α : Type u_1\nα' : Type ?u.4488691\nβ : Type u_2\nβ' : Type ?u.4488697\nγ : Type ?u.4488700\nE : Type ?u.4488703\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
552,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.nat_add_continuum | [] | [
142,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_pow | [] | [
682,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.dom_bool₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.131924\nγ : Type ?u.131927\nδ : Type ?u.131930\nσ : Type ?u.131933\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : Bool → Bool → α\nx✝ : Bool × Bool\na b : Bool... | [
712,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp₃ | [] | [
865,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | upperCentralSeries_zero | [] | [
150,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.surjective | [] | [
2026,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2025,
11
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_iInf | [
{
"state_after": "case h\nι✝ : Type ?u.15394\nα : Type u_2\nβ : Type ?u.15400\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nι : Sort u_1\ns : ι → Closeds α\nx✝ : α\n⊢ x✝ ∈ ↑(⨅ (i : ι), s i) ↔ x✝ ∈ ⋂ (i : ι), ↑(s i)",
"state_before": "ι✝ : Type ?u.15394\nα : Type u_2\nβ : Type ?u.15400\ninst✝¹ : ... | [
170,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/List/Count.lean | List.countp_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\np q : α → Bool\nl₁ l₂ : List α\n⊢ countp p (l₁ ++ l₂) = countp p l₁ + countp p l₂",
"tactic": "simp only [countp_eq_length_filter, filter_append, length_append]"
}
] | [
93,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_updateColumn_add_self | [
{
"state_after": "m : Type ?u.1683272\nn : Type u_1\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix n n R\ni j : n\nhij : i ≠ j\n⊢ det (updateRow Aᵀ i fun k => A k i + A k j) = det Aᵀ",
"state_before": "m : Type ?u.1683272\n... | [
457,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.mul_right | [
{
"state_after": "S : Type u_1\ninst✝ : Semigroup S\na b x y z x' y' : S\nh : SemiconjBy a x y\nh' : SemiconjBy a x' y'\n⊢ a * (x * x') = y * y' * a",
"state_before": "S : Type u_1\ninst✝ : Semigroup S\na b x y z x' y' : S\nh : SemiconjBy a x y\nh' : SemiconjBy a x' y'\n⊢ SemiconjBy a (x * x') (y * y')",
... | [
62,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.cons_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.10730\nδ : Type ?u.10733\na : α\ns t : Multiset α\nf g : α → Multiset β\n⊢ bind (a ::ₘ s) f = f a + bind s f",
"tactic": "simp [bind]"
}
] | [
111,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.le_def' | [
{
"state_after": "a b c p q : ℚ\n⊢ p.num /. ↑p.den ≤ q.num /. ↑q.den ↔\n (p.num /. ↑p.den).num * ↑(q.num /. ↑q.den).den ≤ (q.num /. ↑q.den).num * ↑(p.num /. ↑p.den).den",
"state_before": "a b c p q : ℚ\n⊢ p ≤ q ↔ p.num * ↑q.den ≤ q.num * ↑p.den",
"tactic": "rw [← @num_den q, ← @num_den p]"
},
{
... | [
225,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
11
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.gcd_eq | [
{
"state_after": "m n a b c d : ℕ\nh : a ≡ b [MOD m]\nh1 : gcd a m ∣ m\n⊢ gcd a m = gcd b m",
"state_before": "m n a b c d : ℕ\nh : a ≡ b [MOD m]\n⊢ gcd a m = gcd b m",
"tactic": "have h1 := gcd_dvd_right a m"
},
{
"state_after": "m n a b c d : ℕ\nh : a ≡ b [MOD m]\nh1 : gcd a m ∣ m\nh2 : gcd b ... | [
260,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.transpose | [] | [
93,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_eq_integral_of_support_subset | [
{
"state_after": "case inl\nι : Type ?u.16437814\n𝕜 : Type ?u.16437817\nE : Type u_1\nF : Type ?u.16437823\nA : Type ?u.16437826\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na✝ b✝ c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\na b : ℝ\nh : support f ⊆ Ioc a b\nhab : a ... | [
983,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.neg_pf | [] | [
43,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_copy | [
{
"state_after": "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⊢ length (Walk.copy p (_ : u' = u') (_ : v' = v')) = length p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\... | [
397,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Topology/ContinuousOn.lean | ite_inter_closure_eq_of_inter_frontier_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.398357\nγ : Type ?u.398360\nδ : Type ?u.398363\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ns s' t : Set α\nht : s ∩ frontier t = s' ∩ frontier t\n⊢ Set.ite t s s' ∩... | [
1231,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.homCongr_refl | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf : X ⟶ Y\n⊢ ↑(homCongr (refl X) (refl Y)) f = f",
"tactic": "simp"
}
] | [
62,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Ring/Regular.lean | isRegular_of_ne_zero' | [] | [
42,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_mul | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ (a - b) * c = a * c - b * c",
"tactic": "simp [Int.sub_eq_add_neg, Int.add_mul]"
}
] | [
481,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
480,
11
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.mem_range_self | [] | [
1221,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexRange_repr | [] | [
513,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.le_log_of_pow_le | [
{
"state_after": "case inl\nb x y : ℕ\nhb : 1 < b\nh : b ^ x ≤ y\nhy : y ≠ 0\n⊢ x ≤ log b y\n\ncase inr\nb x : ℕ\nhb : 1 < b\nh : b ^ x ≤ 0\n⊢ x ≤ log b 0",
"state_before": "b x y : ℕ\nhb : 1 < b\nh : b ^ x ≤ y\n⊢ x ≤ log b y",
"tactic": "rcases ne_or_eq y 0 with (hy | rfl)"
},
{
"state_after": ... | [
119,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Iio_iff_exists_Ioo_subset' | [] | [
1697,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1695,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.graph_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5629\nγ : Type ?u.5632\nι : Type ?u.5635\nM : Type u_2\nM' : Type ?u.5641\nN : Type ?u.5644\nP : Type ?u.5647\nG : Type ?u.5650\nH : Type ?u.5653\nR : Type ?u.5656\nS : Type ?u.5659\ninst✝ : Zero M\n⊢ graph 0 = ∅",
"tactic": "simp [... | [
118,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.smul | [] | [
1001,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.map_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nf : α → β\np : Pmf α\nb : β\ng : β → γ\n⊢ map g (map f p) = map (g ∘ f) p",
"tactic": "simp [map, Function.comp]"
}
] | [
71,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.exists_fin_zero_pi | [] | [
208,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.ext_of_direction_eq | [
{
"state_after": "case h\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns1 s2 : AffineSubspace k P\nhd : direction s1 = direction s2\nhn : Set.Nonempty (↑s1 ∩ ↑s2)\np : P\n⊢ p ∈ s1 ↔ p ∈ s2",
"state_before": "k : Type u_1\nV... | [
381,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Icc_of_Ico | [] | [
264,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.equiv_iff | [] | [
159,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.top_sub_coe | [] | [
856,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Logic/Encodable/Basic.lean | ULower.up_down | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Encodable α\na : α\n⊢ up (down a) = a",
"tactic": "simp [up, down,Equiv.left_inv _ _, Equiv.symm_apply_apply]"
}
] | [
530,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_eq_self_of_mem_closed | [] | [
393,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.forall_of_forall_mem_ball | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nX : Type ?u.45910\nι : Type ?u.45913\ninst✝ : PseudoMetricSpace α\nx✝ y✝ z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\np : α → Prop\nx : α\nH : ∃ᶠ (R : ℝ) in atTop, ∀ (y : α), y ∈ ball x R → p y\ny : α\nR : ℝ\nhR : R > dist y x\nh : ∀ (z : α), z ∈ ball x R → p z\n⊢... | [
688,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.ι_coconeMorphism | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F : J ⥤ C\ninst✝ : HasColimit F\nc : Cocone F\nj : J\n⊢ ι F j ≫ (coconeMorphism c).Hom = c.ι.app j",
"tactic": "simp"
}
] | [
792,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_pi_closedBall | [] | [
694,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_mul_of_apply_of_not_le | [
{
"state_after": "ι : Type u_1\nσ : Type u_3\nS : Type ?u.309265\nR : Type u_2\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Semiring R\ninst✝³ : SetLike σ R\ninst✝² : AddSubmonoidClass σ R\nA : ι → σ\ninst✝¹ : CanonicallyOrderedAddMonoid ι\ninst✝ : SetLike.GradedMonoid A\nr : ⨁ (i : ι), { x // x ∈ A i }\ni : ι\nr' : { x /... | [
251,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Logic/Function/Basic.lean | cast_bijective | [
{
"state_after": "case refl\nα : Sort u_1\n⊢ Bijective (cast (_ : α = α))",
"state_before": "α β : Sort u_1\nh : α = β\n⊢ Bijective (cast h)",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "case refl\nα : Sort u_1\n⊢ Bijective (cast (_ : α = α))",
"tactic": "refine ... | [
1014,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_precompR_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type ?u.1605174\n𝕜₃ : Type ?u.1605177\nE : Type u_2\nEₗ : Type u_5\nF : Type ?u.1605186\nFₗ : Type u_4\nG : Type ?u.1605192\nGₗ : Type u_3\n𝓕 : Type ?u.1605198\ninst✝¹⁸ : SeminormedAddCommGroup E\ninst✝¹⁷ : SeminormedAddCommGroup Eₗ\ninst✝... | [
1001,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essInf_const | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝ : ConditionallyCompleteLattice β\nc : β\nhμ : NeBot (Measure.ae μ)\n⊢ essInf (fun x => c) μ = c",
"state_before": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝... | [
82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.star_def | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.mem_avoid | [
{
"state_after": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\n⊢ (∃ x, x ∈ P.parts ∧ ¬c = ⊥ ∧ x \\ b = c) ↔ ∃ d, d ∈ P.parts ∧ ¬d ≤ b ∧ d \\ b = c",
"state_before": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b c ... | [
450,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisor_le | [
{
"state_after": "case zero\nn : ℕ\n⊢ n ∈ divisors zero → n ≤ zero\n\ncase succ\nn m : ℕ\n⊢ n ∈ divisors (succ m) → n ≤ succ m",
"state_before": "n m : ℕ\n⊢ n ∈ divisors m → n ≤ m",
"tactic": "cases' m with m"
},
{
"state_after": "no goals",
"state_before": "case zero\nn : ℕ\n⊢ n ∈ divisors ... | [
142,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.refl | [] | [
324,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
322,
9
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Embedding.map_apply | [] | [
1829,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.card_fin | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.10624\nβ : Type ?u.10627\nγ : Type ?u.10630\nn : ℕ\n⊢ card univ = n",
"tactic": "rw [Finset.card_univ, Fintype.card_fin]"
}
] | [
307,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_restrict₀' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.290469\nγ : Type ?u.290472\nδ : Type ?u.290475\nι : Type ?u.290478\nR : Type ?u.290481\nR' : Type ?u.290484\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1650,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1648,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.pred'_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.308729\nn : PosNum\n⊢ Nat.succ ↑(pred' n) = ↑n",
"tactic": "rw [pred'_to_nat n, Nat.succ_pred_eq_of_pos (to_nat_pos n)]"
},
{
"state_after": "α : Type ?u.308729\nn : PosNum\nthis : Nat.succ ↑(pred' n) = ↑n\nh : ↑1 = ↑n\n⊢ ↑(Num.casesOn 0 ... | [
545,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Order/Lattice.lean | sup_sup_sup_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na✝ b✝ c✝ d✝ a b c d : α\n⊢ a ⊔ b ⊔ (c ⊔ d) = a ⊔ c ⊔ (b ⊔ d)",
"tactic": "rw [sup_assoc, sup_left_comm b, ← sup_assoc]"
}
] | [
282,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.closure_mul_le | [] | [
88,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.map_id | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.prop | [] | [
473,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.285080\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA B : Matrix n n α\nk : α\ninst✝ : Invertible k\nh : IsUnit (det A)\n⊢ (⅟k • A⁻¹) ⬝ (k • A) = 1",
"tactic": "simp [h, smul_smul]"
}
] | [
505,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.toMulHom_injective | [] | [
1232,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.eq_adjoint_iff_basis | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\nG : Type ?u.1971189\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : FiniteDim... | [
439,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.mono_of_mono_map | [] | [
64,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart' | [
{
"state_after": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.29422\ninst✝⁸ : TopologicalSpace H\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : ChartedSpace H M\ninst✝⁵ : TopologicalSpace H'\ninst✝⁴ : TopologicalSpace M'\ninst✝³ : ChartedSpace H' M'\ninst✝² : TopologicalSpace X\nG : StructureG... | [
352,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_eq_mk'_iff | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_3\nM' : Type u_2\nM'' : Type ?u.853060\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : IsL... | [
980,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Computability/Reduce.lean | transitive_oneOneReducible | [] | [
126,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.lift_π | [] | [
196,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.