file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_const_lt_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.76494\nγ : Type ?u.76497\nδ : Type ?u.76500\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : IsFiniteMeasure μ\nc : ℝ≥0∞\nhc : c ≠ ⊤\n⊢ (∫⁻ (x : α), c ∂μ) < ⊤",
"tactic": "simpa only [Measure.restrict_univ] using set_lintegral_const... | [
196,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finsupp/WellFounded.lean | Finsupp.Lex.acc | [
{
"state_after": "α : Type u_1\nN : Type u_2\ninst✝ : Zero N\nr : α → α → Prop\ns : N → N → Prop\nhbot : ∀ ⦃n : N⦄, ¬s n 0\nhs : WellFounded s\nx : α →₀ N\nh : ∀ (a : α), a ∈ x.support → Acc (rᶜ ⊓ fun x x_1 => x ≠ x_1) a\n⊢ Acc (InvImage (Dfinsupp.Lex r fun x => s) toDfinsupp) x",
"state_before": "α : Type ... | [
45,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_one | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.nodup_Ico | [] | [
36,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.eq_mul_of_div_eq_right | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nH1 : b ∣ a\nH2 : a / b = c\n⊢ a = b * c",
"tactic": "rw [← H2, Nat.mul_div_cancel' H1]"
}
] | [
654,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
11
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_iff_one_lt_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.24947\ninst✝³ : MulOneClass α\ninst✝² : LT α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b : α\n⊢ a < a * b ↔ a * 1 < a * b",
... | [
508,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_add | [
{
"state_after": "case none\ny z : ℝ\nhx : none ≠ 0\nh'x : none ≠ ⊤\n⊢ none ^ (y + z) = none ^ y * none ^ z\n\ncase some\ny z : ℝ\nx : ℝ≥0\nhx : Option.some x ≠ 0\nh'x : Option.some x ≠ ⊤\n⊢ Option.some x ^ (y + z) = Option.some x ^ y * Option.some x ^ z",
"state_before": "x : ℝ≥0∞\ny z : ℝ\nhx : x ≠ 0\nh'x... | [
434,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.prod_mono | [] | [
413,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.length_lt | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : Fintype V\nu v : V\np : Walk G u v\nhp : IsPath p\n⊢ List.length (support p) ≤ Fintype.card V",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : Simp... | [
1027,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.Measure.toENNRealVectorMeasure_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.149284\nm : MeasurableSpace α\nμ ν : Measure α\ni : Set α\nhi : MeasurableSet i\n⊢ ↑(toENNRealVectorMeasure (μ + ν)) i = ↑(toENNRealVectorMeasure μ + toENNRealVectorMeasure ν) i",
"state_before": "α : Type u_1\nβ : Type ?u.149284\nm : MeasurableSpace α\nμ ν : Meas... | [
516,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq | [] | [
344,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
11
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_iff_derivative_ne_zero | [
{
"state_after": "F : Type u\ninst✝¹ : Field F\nK : Type v\ninst✝ : Field K\nf : F[X]\nhf : Irreducible f\nh : ↑derivative f ≠ 0\ng : F[X]\nhg1 : g ∈ nonunits F[X]\n_hg2 : g ≠ 0\nx✝ : g ∣ f\nhg4 : g ∣ ↑derivative f\np : F[X]\nhg3 : f = g * p\nu : F[X]ˣ\nhu : ↑u = p\n⊢ g * ↑u ∣ ↑derivative f",
"state_before"... | [
286,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | tendsto_const_smul_iff₀ | [] | [
299,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.fundamentalInterior | [
{
"state_after": "G : Type u_1\nH : Type ?u.546154\nα : Type u_2\nβ : Type ?u.546160\nE : Type ?u.546163\ninst✝⁶ : Countable G\ninst✝⁵ : Group G\ninst✝⁴ : MulAction G α\ninst✝³ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : IsFundamentalDomain G s\ninst✝² : MeasurableSpace G\ninst✝¹ : MeasurableSMul G α\ni... | [
702,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
11
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | HasCompactMulSupport.comp_smul | [] | [
385,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Topology/SubsetProperties.lean | LocallyFinite.finite_nonempty_of_compact | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι✝ : Type ?u.89027\nπ : ι✝ → Type ?u.89032\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\nι : Type u_1\ninst✝ : CompactSpace α\nf : ι → Set α\nhf : LocallyFinite f\n⊢ Set.Finite {i | Set.Nonempty (f i)}",
"tac... | [
819,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Topology/Separation.lean | ClosedEmbedding.normalSpace | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : NormalSpace β\nf : α → β\nhf : ClosedEmbedding f\ns t : Set α\nhs : IsClosed s\nht : IsClosed t\nhst : Disjoint s t\nH : SeparatedNhds (f '' s) (f '' t)\n⊢ SeparatedNhds s t",
"state_before": "α : Typ... | [
1743,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
11
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.ofBijective_apply | [] | [
969,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Algebra/Group/Units.lean | isUnit_one | [] | [
624,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean | Real.le_tan | [
{
"state_after": "case inl\nh1 : 0 ≤ 0\nh2 : 0 < π / 2\n⊢ 0 ≤ tan 0\n\ncase inr\nx : ℝ\nh1 : 0 ≤ x\nh2 : x < π / 2\nh1' : 0 < x\n⊢ x ≤ tan x",
"state_before": "x : ℝ\nh1 : 0 ≤ x\nh2 : x < π / 2\n⊢ x ≤ tan x",
"tactic": "rcases eq_or_lt_of_le h1 with (rfl | h1')"
},
{
"state_after": "no goals",
... | [
126,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.lt_right_of_left_lt | [] | [
822,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.pointed_iff_not_blunt | [] | [
356,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/PFun.lean | PFun.fixInduction'_stop | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.33763\nδ : Type ?u.33766\nε : Type ?u.33769\nι : Type ?u.33772\nC : α → Sort u_1\nf : α →. β ⊕ α\nb : β\na : α\nh : b ∈ fix f a\nfa : Sum.inl b ∈ f a\nhbase : (a_final : α) → Sum.inl b ∈ f a_final → C a_final\nhind : (a₀ a₁ : α) → b ∈ fix f a₁ → Sum.inr ... | [
379,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_add_const' | [] | [
117,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_inv | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.comap_abs_atTop | [
{
"state_after": "ι : Type ?u.201690\nι' : Type ?u.201693\nα : Type u_1\nβ : Type ?u.201699\nγ : Type ?u.201702\ninst✝ : LinearOrderedAddCommGroup α\n⊢ ∀ (i' : α × α), True ∧ True → ∃ i, True ∧ abs ⁻¹' Ici i ⊆ Iic i'.fst ∪ Ici i'.snd",
"state_before": "ι : Type ?u.201690\nι' : Type ?u.201693\nα : Type u_1\n... | [
950,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/List/Sublists.lean | List.nodup_sublists' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ Nodup (sublists' l) ↔ Nodup l",
"tactic": "rw [sublists'_eq_sublists, nodup_map_iff reverse_injective, nodup_sublists, nodup_reverse]"
}
] | [
380,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Topology/Order.lean | singletons_open_iff_discrete | [] | [
325,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.liftOfRightInverse_comp | [] | [
2286,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2283,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mk'_toSubmonoid | [] | [
291,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_pos_of_neg_of_neg | [
{
"state_after": "a b : Int\nha : a < 0\nhb : b < 0\nthis : 0 * b < a * b\n⊢ 0 < a * b",
"state_before": "a b : Int\nha : a < 0\nhb : b < 0\n⊢ 0 < a * b",
"tactic": "have : 0 * b < a * b := Int.mul_lt_mul_of_neg_right ha hb"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nha : a ... | [
1231,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1229,
11
] |
src/lean/Init/Data/List/Basic.lean | List.reverse_nil | [] | [
172,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
171,
9
] |
Mathlib/FieldTheory/Normal.lean | AlgEquiv.transfer_normal | [] | [
154,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurableSet_of_differentiableWithinAt_Ioi | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\ninst✝ : CompleteSpace F\n⊢ MeasurableSet {x | DifferentiableWithinAt ℝ f (Ioi x) x}",
"tactic": "simpa [differentiableWithinAt_Ioi_iff_Ici] using measurableSet_of_di... | [
808,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lowerCentralSeries_map_eq_lcs | [
{
"state_after": "R : 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 : ℕ\nN : LieSubmodule R L M\n⊢ lcs k N ≤ N",
"state_before": "R : Type u\nL : Type v\nM... | [
121,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Filter/Extr.lean | isMaxOn_dual_iff | [] | [
238,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.symm | [] | [
188,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Invertible.lean | IsUnit.nonempty_invertible | [] | [
213,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.fst'' | [] | [
359,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Std/Data/AssocList.lean | Std.AssocList.any_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\np : α → β → Bool\nl : AssocList α β\n⊢ any p l =\n List.any (toList l) fun x =>\n match x with\n | (a, b) => p a b",
"tactic": "induction l <;> simp [any, *]"
}
] | [
134,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
9
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.image_symm_eq_preimage | [] | [
571,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
11
] |
Mathlib/CategoryTheory/Linear/Yoneda.lean | CategoryTheory.whiskering_linearYoneda₂ | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumLexAssoc_symm_apply_inr_inr | [] | [
687,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.contains | [
{
"state_after": "no goals",
"state_before": "l m r : List Char\nc : Char\nx✝ : Substring\nh : ValidFor l m r x✝\n⊢ Substring.contains x✝ c = true ↔ c ∈ m",
"tactic": "simp [Substring.contains, h.any, String.contains]"
}
] | [
935,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
934,
1
] |
Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_conjTranspose | [] | [
320,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Order/LocallyFinite.lean | Prod.uIcc_eq | [] | [
1003,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Data/Fintype/Perm.lean | mem_perms_of_finset_iff | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.50561\nγ : Type ?u.50564\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nval✝ : Multiset α\nl : List α\nhs : Multiset.Nodup (Quot.mk Setoid.r l)\nf : Equiv.Perm α\n⊢ f ∈ permsOfFinset { val := Quot.mk Setoid.r l, nodup := hs } ↔\n ∀ {x : α}, ↑f x ≠ x → ... | [
145,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_fderiv | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_2\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.247750\ninst✝... | [
253,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.continuousOn | [] | [
895,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
11
] |
Std/Control/ForInStep/Lemmas.lean | ForInStep.bind_bindList_assoc | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nβ : Type u_1\nα : Type u_3\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : β → m (ForInStep β)\ng : α → β → m (ForInStep β)\ns : ForInStep β\nl : List α\n⊢ (do\n let x ← ForInStep.bind s f\n bindList g l x) =\n ForInStep.bind ... | [
38,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
35,
9
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.powerlt_min | [] | [
2307,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2306,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_zero | [] | [
490,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.pi_eval | [] | [
340,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.Fin.circulant_inj | [] | [
80,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/Convex/Hull.lean | IsLinearMap.convexHull_image | [] | [
176,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/Order/Kleene.lean | Prod.snd_kstar | [] | [
322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioc_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.211771\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioc a c ∪ Ioc b c = Ioc (min a b) c",
"tactic": "rw [Ioc_union_Ioc, max_self] <;> exact (min_le_right _ _).trans (le_max_right _ _)"
}
] | [
1847,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1846,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_prime_factors | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : UniqueFactorizationMonoid α\na : α\n⊢ a ≠ 0 → ∃ f, (∀ (b : α), b ∈ f → Irreducible b) ∧ Multiset.prod f ~ᵤ a",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : UniqueFactorizationMonoid α\na : α\n⊢ a ≠ 0 ... | [
206,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/CategoryTheory/Limits/FullSubcategory.lean | CategoryTheory.Limits.ClosedUnderColimitsOfShape.colimit | [] | [
56,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Init/CcLemmas.lean | and_eq_of_eq_false_left | [] | [
28,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Control/Applicative.lean | Functor.Comp.seq_pure | [] | [
101,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.EventuallyEq.comp_tendsto | [] | [
72,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofSubmodule'_apply | [] | [
2082,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2080,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_injective | [] | [
253,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.symm_comp | [
{
"state_after": "case H\nR : Type u\nA₁ : Type v\nA₂ : Type w\nA₃ : Type u₁\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A₁\ninst✝⁴ : Semiring A₂\ninst✝³ : Semiring A₃\ninst✝² : Algebra R A₁\ninst✝¹ : Algebra R A₂\ninst✝ : Algebra R A₃\ne✝ e : A₁ ≃ₐ[R] A₂\nx✝ : A₁\n⊢ ↑(AlgHom.comp ↑(symm e) ↑e) x✝ = ↑(AlgHom.id... | [
429,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.surjOn_iUnion_iUnion | [] | [
1592,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1590,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.continuous_fderiv_apply | [] | [
1701,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.symm_iff | [] | [
491,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_toIocMod | [] | [
736,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.vanishingIdeal_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : ProjectiveSpectrum 𝒜\n⊢ vanishingIdeal {x} = x.asHomogeneousIdeal",
"tactic": "simp [vanishingIdeal]"
}
] | [
121,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/Order/Basic.lean | isClosed_le' | [] | [
135,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean | AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nX : SimplicialObject C\n⊢ Γ₂N₁.natTrans.app X =\n (compatibility_Γ₂N₁_Γ₂N₂.app X).inv ≫\n (N₂ ⋙ Γ₂).map (Karoubi.decompId_i ((toKaroubi (SimplicialObject C)).obj X)) ≫\n (compatibility_Γ₂N₁... | [
225,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_toDeleteEdges_eq | [
{
"state_after": "case hp'\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nv w : V\ns : Set (Sym2 V)\np : Walk G v w\nhp : ∀ (e : Sym2 V), e ∈ edges p → ¬e ∈ s\n⊢ ∀ (e : Sym2 V),\n e ∈ edges (Walk.transfer p (deleteEdges G s) (_ : ∀ (e : Sym2 V), e ∈ edg... | [
1811,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1806,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.collinear | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.589540\nP : Type u_3\nP' : Type ?u.589546\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y z : P\nh : Wbtw R x y z\n⊢ ∃ p₀ v, ∀ (p : P), p ∈ {x, y, z} → ∃ r, p = r • v +ᵥ p₀",
"state_before": "... | [
860,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Data/Int/NatPrime.lean | Int.not_prime_of_int_mul | [] | [
24,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Faithful.of_comp | [] | [
288,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.tensor_sum | [
{
"state_after": "C : Type u_3\ninst✝³ : Category C\ninst✝² : Preadditive C\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalPreadditive C\nP Q R S : C\nJ : Type u_1\ns : Finset J\nf : P ⟶ Q\ng : J → (R ⟶ S)\n⊢ (f ⊗ 𝟙 R) ≫ (𝟙 Q ⊗ ∑ j in s, g j) = ∑ j in s, f ⊗ g j",
"state_before": "C : Type u_3\ninst✝³ : Ca... | [
105,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.le_iff_derivBFamily | [
{
"state_after": "o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal → Ordinal\nH : ∀ (i : Ordinal) (hi : i < o), IsNormal (f i hi)\na : Ordinal\n⊢ (∀ (i : Ordinal) (hi : i < o), f i hi a ≤ a) ↔ ∃ b, derivFamily (familyOfBFamily o f) b = a",
"state_before": "o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal → ... | [
384,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radical | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\nf : R\n⊢ (∀ (x : PrimeSpectrum R), x ∈ zeroLocus ↑I → f ∈ x.asIdeal) ↔\n ∀ (p : Submodule R R), p ∈ {J | I ≤ J ∧ Ideal.IsPrime J} → f ∈ p",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ :... | [
226,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_map_of_comap_le_of_surjective | [] | [
1610,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1609,
1
] |
src/lean/Init/Data/Nat/Gcd.lean | Nat.gcd_zero_right | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ gcd n 0 = n",
"tactic": "cases n with\n| zero => simp [gcd_succ]\n| succ n =>\n rw [gcd_succ]\n exact gcd_zero_left _"
},
{
"state_after": "no goals",
"state_before": "case zero\n\n⊢ gcd zero 0 = zero",
"tactic": "simp [gcd_succ]... | [
36,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
30,
9
] |
Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.MonoidalFunctor.ε_inv_hom_id | [] | [
262,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Reachable.symm | [] | [
1877,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1876,
11
] |
Mathlib/Data/Finset/Prod.lean | Finset.diag_empty | [] | [
355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_div_self' | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sqrt x / x = 1 / sqrt x",
"tactic": "rw [← div_sqrt, one_div_div, div_sqrt]"
}
] | [
426,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_comap_of_surjective | [
{
"state_after": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G' →* G\nhf : Function.Surjective ↑f\nthis : Setoid G := QuotientGroup.leftRel H\n⊢ index (comap f H) = index H",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\nins... | [
78,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.natDegree_map | [] | [
284,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | lt_add_of_tsub_lt_left | [] | [
368,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Topology/Sequences.lean | CompactSpace.tendsto_subseq | [] | [
313,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_setCoe | [] | [
1481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_lt_add_right | [] | [
691,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
11
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_div_summable | [] | [
594,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.inf_toSubsemiring | [] | [
851,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.ι_post | [
{
"state_after": "J : Type u₁\ninst✝⁵ : Category J\nK : Type u₂\ninst✝⁴ : Category K\nC : Type u\ninst✝³ : Category C\nF : J ⥤ C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasColimit F\nG : C ⥤ D\ninst✝ : HasColimit (F ⋙ G)\nj : J\n⊢ (G.mapCocone (cocone F)).ι.app j = G.map (ι F j)",
"state_before": "J : T... | [
1031,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.top_sub_coe | [] | [
149,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | AddCommGroupCat.int_hom_ext | [] | [
358,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.centralizer_univ | [] | [
791,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/LinearAlgebra/Ray.lean | exists_pos_left_iff_sameRay_and_ne_zero | [
{
"state_after": "case mp\nR : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhx : x ≠ 0\n⊢ (∃ r, 0 < r ∧ r • x = y) → SameRay R x y ∧ y ≠ 0\n\ncase mpr\nR : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Modu... | [
724,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.congr_mono | [] | [
904,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₈_nat_mod_eight | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑χ₈ ↑n = ↑χ₈ ↑(n % 8)",
"tactic": "rw [← ZMod.nat_cast_mod n 8]"
}
] | [
154,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
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