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/WittVector/Basic.lean | WittVector.ghostFun_nsmul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nS : Type ?u.786921\nT : Type ?u.786924\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.786939\nβ : Type ?u.786942\nx y : 𝕎 R\nm : ℕ\n⊢ WittVector.ghostFun (m • x) = m • WittVector.ghostFun... | [
218,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
9
] |
Mathlib/Algebra/Category/ModuleCat/Colimits.lean | ModuleCat.Colimits.cocone_naturality_components | [
{
"state_after": "R : Type u\ninst✝¹ : Ring R\nJ : Type w\ninst✝ : Category J\nF : J ⥤ ModuleCat R\nj j' : J\nf : j ⟶ j'\nx : ↑(F.obj j)\n⊢ ↑(coconeMorphism F j') (↑(F.map f) x) = ↑(F.map f ≫ coconeMorphism F j') x",
"state_before": "R : Type u\ninst✝¹ : Ring R\nJ : Type w\ninst✝ : Category J\nF : J ⥤ Modul... | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Deprecated/Submonoid.lean | Multiplicative.isSubmonoid | [] | [
76,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.condition_one | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nt : PullbackCone f g\nw :\n ((Functor.const WalkingCospan).obj t.pt).map inl ≫ t.π.app WalkingCospan.one =\n t.π.app WalkingCospan.left ≫ (cospan f g).map inl\n⊢ t.π.app WalkingCospan.one =... | [
541,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_uncurry_prod | [] | [
288,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.add_mod_eq_add_mod_left | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k✝ m n k i : ℕ\nH : m % n = k % n\n⊢ (i + m) % n = (i + k) % n",
"tactic": "rw [add_comm, add_mod_eq_add_mod_right _ H, add_comm]"
}
] | [
763,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_nonpos_of_nonneg_of_nonpos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : MulZeroClass α\ninst✝¹ : Preorder α\ninst✝ : PosMulMono α\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a * b ≤ 0",
"tactic": "simpa only [mul_zero] using mul_le_mul_of_nonneg_left hb ha"
}
] | [
383,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom | [] | [
1577,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_monotone | [] | [
1515,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | nonempty_sections_of_finite_cofiltered_system.init | [
{
"state_after": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsCofilteredOrEmpty J\nF : J ⥤ Type u\nhf : ∀ (j : J), Finite (F.obj j)\nhne : ∀ (j : J), _root_.Nonempty (F.obj j)\nF' : J ⥤ TopCat := F ⋙ TopCat.discrete\n⊢ Set.Nonempty (Functor.sections F)",
"state_before": "J : Type u\ninst✝¹ : SmallCatego... | [
77,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | AddGroupCat.epi_iff_surjective | [
{
"state_after": "A B : AddGroupCat\nf : A ⟶ B\ni1 : Epi f ↔ Epi (groupAddGroupEquivalence.inverse.map f)\n⊢ Epi f ↔ Function.Surjective ↑f",
"state_before": "A B : AddGroupCat\nf : A ⟶ B\n⊢ Epi f ↔ Function.Surjective ↑f",
"tactic": "have i1 : Epi f ↔ Epi (groupAddGroupEquivalence.inverse.map f) := by\... | [
374,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.continuousOn_cos | [] | [
70,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.natPred_strictMono | [] | [
48,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.nndist_le_op_nnnorm | [] | [
487,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_iff_nat_mul_le_aux | [
{
"state_after": "case mp\nα : Type u_3\nβ : Type ?u.46730\nE : Type u_1\nF : Type u_2\nG : Type ?u.46739\nE' : Type ?u.46742\nF' : Type ?u.46745\nG' : Type ?u.46748\nE'' : Type ?u.46751\nF'' : Type ?u.46754\nG'' : Type ?u.46757\nR : Type ?u.46760\nR' : Type ?u.46763\n𝕜 : Type ?u.46766\n𝕜' : Type ?u.46769\nin... | [
262,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.comp_lift | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ V W X Y : C\ninst✝ : HasBinaryProduct X Y\nf : V ⟶ W\ng : W ⟶ X\nh : W ⟶ Y\n⊢ (f ≫ lift g h) ≫ fst = lift (f ≫ g) (f ≫ h) ≫ fst\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ V W X Y : C\ninst✝ : HasBinaryProduct X Y\nf : V ⟶ W\ng : W ⟶ X\nh ... | [
708,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.smul_sup | [] | [
92,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_add | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Computability/Language.lean | Language.mem_add | [] | [
113,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.ι_comp_lift | [
{
"state_after": "case H\nV : Type u_2\nW : Type u_3\nV₁ : Type u_1\nV₂ : Type ?u.506724\nV₃ : Type ?u.506727\ninst✝⁷ : SeminormedAddCommGroup V\ninst✝⁶ : SeminormedAddCommGroup W\ninst✝⁵ : SeminormedAddCommGroup V₁\ninst✝⁴ : SeminormedAddCommGroup V₂\ninst✝³ : SeminormedAddCommGroup V₃\nf : NormedAddGroupHom V... | [
926,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.leadingCoeff_isUnit | [] | [
171,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.mem_Lp | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.9151247\nG : Type ?u.9151250\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpace α\ninst✝... | [
1601,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1598,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.coe_one | [] | [
141,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.right_of_add_measure | [] | [
208,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.isSpanning_iff | [] | [
158,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_inclusion | [
{
"state_after": "case mk\nG : Type u_1\nG' : Type ?u.156101\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.156110\ninst✝ : AddGroup A\nH✝ K✝ H K : Subgroup G\nh : H ≤ K\nval✝ : G\nproperty✝ : val✝ ∈ H\n⊢ ↑(↑(inclusion h) { val := val✝, property := property✝ }) = ↑{ val := val✝, property := property✝ }",
... | [
816,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.const_eq | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\na : α\n⊢ ∀ (n : ℕ), nth (const a) n = nth (a :: const a) n",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\na : α\n⊢ const a = a :: const a",
"tactic": "apply Stream'.ext"
},
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ :... | [
244,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.countp_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.336299\nγ : Type ?u.336302\np : α → Prop\ninst✝ : DecidablePred p\ns : Multiset α\n_l : List α\n⊢ countp p (Quot.mk Setoid.r _l) = 0 ↔ ∀ (a : α), a ∈ Quot.mk Setoid.r _l → ¬p a",
"tactic": "simp"
}
] | [
2305,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2304,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | piiUnionInter_mono_right | [] | [
473,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Topology/Basic.lean | Dense.inter_of_open_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns t : Set α\nhs : Dense s\nht : Dense t\nhso : IsOpen s\nx : α\n⊢ x ∈ closure (s ∩ closure t)",
"tactic": "simp [hs.closure_eq, ht.closure_eq]"
... | [
1419,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_zero | [
{
"state_after": "case a.h\nl : Type ?u.923940\nm : Type u_1\nn : Type u_2\no : Type ?u.923949\nm' : o → Type ?u.923954\nn' : o → Type ?u.923959\nR : Type ?u.923962\nS : Type ?u.923965\nα : Type v\nβ : Type w\nγ : Type ?u.923972\ninst✝ : Zero α\ni✝ : n\nx✝ : m\n⊢ 0ᵀ i✝ x✝ = OfNat.ofNat 0 i✝ x✝",
"state_befo... | [
1975,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1973,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.of_le_add | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nK : ℝ≥0\ns : Set α\nf✝ : α → β\nf : α → ℝ\nh : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → f x ≤ f y + dist x y\n⊢ ∀ (x : α), x ∈ s... | [
563,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
11
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_upperSemicontinuousOn_antitone | [] | [
873,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_lt_re | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | a < z.re} = {z | z.re = a}",
"tactic": "simpa only [frontier_Ioi] using frontier_preimage_re (Ioi a)"
}
] | [
168,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.imageToKernel_isIso_of_image_eq_kernel | [
{
"state_after": "V : Type u\ninst✝³ : Category V\ninst✝² : HasImages V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasKernels V\nA B C : V\nf : A ⟶ B\ng : B ⟶ C\np : imageSubobject f = kernelSubobject g\n⊢ imageToKernel f g (_ : f ≫ g = 0) ≫\n Subobject.ofLE (kernelSubobject g) (imageSubobject f) (_ : kernelS... | [
153,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LieSubalgebra.ad_comp_incl_eq | [
{
"state_after": "case h\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nK : LieSubalgebra R L\nx y : { x // x ∈ K }\n⊢ ↑(LinearMap.comp (↑(ad R L) ↑x) ↑(incl... | [
298,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_eq_sdiff_fromEdgeSet | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.154730\n𝕜 : Type ?u.154733\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\ns : Set (Sym2 V)\nx✝¹ x✝ : V\n⊢ Adj (deleteEdges G s) x✝¹ x✝ ↔ Adj (G \\ fromEdgeSet s) x✝¹ x✝",
"state_before": "ι : Sort ?u.154... | [
1123,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/Order/CompleteLattice.lean | toDual_sSup | [] | [
425,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.preimage_emetric_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.652149\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nh : α ≃ᵢ β\nx : β\nr : ℝ≥0∞\n⊢ ↑h ⁻¹' EMetric.ball x r = EMetric.ball (↑(IsometryEquiv.symm h) x) r",
"tactic"... | [
481,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_option | [] | [
445,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_smul_index_addMonoidHom | [] | [
1642,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/Order/Bounds/Basic.lean | bddBelow_Ioc | [] | [
676,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.exists_unique | [] | [
193,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.liftAux_map_smul | [] | [
192,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.induction | [
{
"state_after": "R : Type u_1\ninst✝ : CommSemiring R\nX : Type u_2\nC : FreeAlgebra R X → Prop\nh_grade0 : ∀ (r : R), C (↑(algebraMap R (FreeAlgebra R X)) r)\nh_grade1 : ∀ (x : X), C (ι R x)\nh_mul : ∀ (a b : FreeAlgebra R X), C a → C b → C (a * b)\nh_add : ∀ (a b : FreeAlgebra R X), C a → C b → C (a + b)\na ... | [
508,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Real.lean | dist_le_tsum_dist_of_tendsto | [] | [
93,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/Connected.lean | Sum.isPreconnected_iff | [
{
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51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
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Mathlib/Data/Set/List.lean | Set.range_list_nthLe | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.905\nl : List α\n⊢ (range fun k => nthLe l ↑k (_ : ↑k < length l)) = {x | x ∈ l}",
"tactic": "ext x"
},
{
... | [
46,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Std/Data/Int/Lemmas.lean | Int.sign_ofNat_of_nonzero | [] | [
209,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
207,
1
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.toSet_sUnion | [
{
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"state_before": "x : PSet\n⊢ toSet (⋃₀ x) = ⋃₀ (toSet '' toSet x)",
"tactic": "ext"
},
{
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499,
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497,
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Mathlib/Order/LocallyFinite.lean | WithTop.Ico_coe_coe | [] | [
1125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
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Mathlib/RingTheory/PolynomialAlgebra.lean | matPolyEquiv_symm_apply_coeff | [
{
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281,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Algebra/Order/Field/Power.lean | zpow_bit0_pos_iff | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedField α\nb c d : α\nn : ℤ\nhn : n ≠ 0\nh : 0 < 0 ^ bit0 n\n⊢ False",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhn : n ≠ 0\n⊢ 0 < a ^ bit0 n → a ≠ 0",
"tactic": "rintro h rfl"
},
{
"state_after": "α : Type... | [
155,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_toSubtype_subtype | [
{
"state_after": "case w\nJ : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nf : J → C\ninst✝¹ : HasBiproduct f\np : J → Prop\ninst✝ : HasBiproduct (Subtype.restrict p f)\nj : Subtype p\n⊢ ∀ (j_1 : Subtype p),\n (ι f ↑j ≫ toSubtype f p) ≫ π (Subtype.restrict p f) j_1 = ι (Subtype.restr... | [
641,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
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Mathlib/ModelTheory/Order.lean | FirstOrder.Language.relMap_leSymb | [
{
"state_after": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝³ : IsOrdered L\ninst✝² : Structure L M\ninst✝¹ : LE M\ninst✝ : OrderedStructure L M\na b : M\n⊢ RelMap leSymb ![a, b] ↔ a ≤ b",
"state_before": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝³ : IsOrdered L\ninst✝² : Structure L M\ni... | [
211,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_comap | [] | [
534,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.length_toList | [
{
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}
] | [
726,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_zero | [] | [
783,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.neg_comp_neg | [
{
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}
] | [
166,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_range_reflect | [
{
"state_after": "case zero\nα : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f✝ : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\n⊢ ∏ j in range zero, f (zero - 1 - j) = ∏ j in range zero, f j\n\ncase succ\nα : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f✝ : α → β\ninst✝ : CommMonoid ... | [
178,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.le_mul_of_ediv_le | [
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b c : ℤ\nH1 : 0 ≤ b\nH2 : b ∣ a\nH3 : a / b ≤ c\n⊢ a / b * b ≤ c * b",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b c : ℤ\nH1 : 0 ≤ b\nH2 : b ∣ a\nH3 : a / b ≤ c\n⊢ a ≤ c * b",
"tactic": "rw [← Int.ediv_mul_cancel H2]"
},
{
"state_after": "no goals",
"state_be... | [
463,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
11
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.prod_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.155993\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.156014\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\ns : Submonoid M\nt : Submonoid N\n⊢ prod s t = ⊤ ↔ ... | [
1331,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
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Mathlib/Algebra/Order/WithZero.lean | mul_le_mul_left₀ | [
{
"state_after": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nha : a ≠ 0\n⊢ b * a ≤ c * a ↔ b ≤ c",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nha : a ≠ 0\n⊢ a * b ≤ a * c ↔ b ≤ c",
"tactic": "simp only [mul_comm a]"
},
{... | [
237,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_subgroup | [] | [
571,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_iSup_directed | [
{
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1163,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
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Mathlib/Data/Finset/MulAntidiagonal.lean | Finset.swap_mem_mulAntidiagonal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedCancelCommMonoid α\ns t : Set α\nhs : Set.IsPwo s\nht : Set.IsPwo t\na : α\nu : Set α\nhu : Set.IsPwo u\nx : α × α\n⊢ Prod.swap x ∈ mulAntidiagonal hs ht a ↔ x ∈ mulAntidiagonal ht hs a",
"tactic": "simp only [mem_mulAntidiagonal... | [
99,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/Order/WellFoundedSet.lean | Set.Finite.isWf | [] | [
468,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
11
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.enum_zero_le' | [
{
"state_after": "no goals",
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"tactic": "rwa [type_lt]"
},
{
"state_after": "α : Ty... | [
1174,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_le_bit1 | [] | [
199,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
11
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Mathlib/Data/Finset/Prod.lean | Finset.disjUnion_product | [] | [
269,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | LinearMap.toAffineMap_linear | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Hom/Basic.lean | map_inv_lt_iff | [
{
"state_after": "F : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.32188\nδ : Type ?u.32191\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : OrderIsoClass F α β\nf : F\na : α\nb : β\n⊢ ↑f (EquivLike.inv f b) < ↑f a ↔ b < ↑f a",
"state_before": "F : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.32... | [
208,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.neg_one_right | [] | [
77,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Order/BoundedOrder.lean | eq_bot_mono | [] | [
377,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.single_mul_left | [] | [
528,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.extend_unique_at | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nδ : Type ?u.8623\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ni : α → β\ndi✝ : DenseInducing i\ninst✝² : TopologicalSpace δ\nf✝ : γ → α\ng✝ : γ → δ\nh : δ → β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space γ\nb : β\nf : α → γ\ng : β → γ\nd... | [
188,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Data/Nat/Cast/Basic.lean | Commute.ofNat_left | [] | [
75,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.aEStronglyMeasurable_on_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nH : Type ?u.308154\nα : Type u_3\nβ✝ : Type ?u.308160\nE : Type ?u.308163\ninst✝¹² : Group G\ninst✝¹¹ : Group H\ninst✝¹⁰ : MulAction G α\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : MulAction H β✝\ninst✝⁷ : MeasurableSpace β✝\ninst✝⁶ : NormedAddCommGroup ... | [
382,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
11
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Std/Data/String/Lemmas.lean | String.toString_toSubstring | [] | [
471,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
9
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kronecker_diagonal | [] | [
332,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.smul_val | [
{
"state_after": "no goals",
"state_before": "d n x y : ℤ\n⊢ ↑n * { re := x, im := y } = { re := n * x, im := n * y }",
"tactic": "simp [ext]"
}
] | [
316,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_gt_Ioo | [] | [
246,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.disjoint_left_ordSeparatingSet | [] | [
181,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsAdjointPair.add | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.311393\nR₂ : Type ?u.311396\nR₃ : Type ?u.311399\nM : Type u_2\nM₁ : Type u_3\nM₂ : Type ?u.311408\nMₗ₁ : Type ?u.311411\nMₗ₁' : Type ?u.311414\nMₗ₂ : Type ?u.311417\nMₗ₂' : Type ?u.311420\nK : Type ?u.311423\nK₁ : Type ?u.311426\nK₂ :... | [
455,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
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Mathlib/Topology/Maps.lean | IsOpenMap.mapsTo_interior | [] | [
370,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_of_forall_row_eq_smul_add_pred | [] | [
560,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_vsub | [] | [
1460,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.closure_univ | [] | [
772,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toMul_neg | [] | [
306,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.mul_le_iff_le_one_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.87676\ninst✝² : LE α\ninst✝¹ : MulOneClass α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\nha : MulLECancellable a\n⊢ a * b ≤ a ↔ a * b ≤ a * 1",
"tactic": "rw [mul_one]"
}
] | [
1658,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1655,
11
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.symm_bijective | [] | [
527,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_add_of_degree_eq | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.652536\nh : degree p = degree q\nhlc : leadingCoeff p + leadingCoeff q ≠ 0\nthis : natDegree (p + q) = natDegree p\n⊢ leadingCoeff (p + q) = leadingCoeff p + leadingCoeff q",
"state_before": "R : Type... | [
887,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_empty | [] | [
208,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | hasSum_cauchyPowerSeries_integral | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nR : ℝ\nw : ℂ\nhf : CircleIntegrable f c R\nhw : ↑Complex.abs w < R\n⊢ HasSum (fun n => (2 * ↑π * I)⁻¹ • ∮ (z : ℂ) in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z)\n ((2 * ↑π * I... | [
620,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.coe_copy | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Associates.finset_prod_mk | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.34497\nδ : Type ?u.34500\ninst✝ : CommMonoid α\np : Finset β\nf : β → α\nthis : (fun i => Associates.mk (f i)) = Associates.mk ∘ f\n⊢ ∏ i in p, Associates.mk (f i) = Associates.mk (∏ i in p, f i)",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Typ... | [
121,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/SetTheory/Cardinal/SchroederBernstein.lean | Function.Embedding.antisymm | [] | [
86,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Init/Algebra/Classes.lean | trans_of | [] | [
300,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.ofBijective_apply_symm_apply | [] | [
1413,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.is_pow_of_dvd_count | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\nk : ℕ\na0 : α\nhz : a0 ≠ 0\nha : Associates.mk a0 ≠... | [
1832,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
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