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/Data/Nat/Basic.lean | Nat.mul_dvd_of_dvd_div | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nhab : c ∣ b\nh : a ∣ b / c\nh1 : ∃ d, b / c = a * d\nd : ℕ\nhd : b / c = a * d\nh3 : b = a * d * c\n⊢ b = c * a * d",
"tactic": "rwa [mul_comm, ←mul_assoc] at h3"
}
] | [
774,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subtype_injective | [] | [
802,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.congr_const | [] | [
323,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | SubmonoidClass.coe_finset_prod | [] | [
66,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.bit0_apply_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nι : Type ?u.2610\ninst✝¹ : Semiring R\ninst✝ : CharP R 2\nx : R\n⊢ bit0 x = 0",
"tactic": "simp"
}
] | [
46,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_min | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.801740\nβ : Type ?u.801743\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\nhr : a ≠ ⊤\nhp : b ≠ ⊤\nh : a ≤ b\n⊢ ENNReal.toReal (min a b) = min (ENNReal.toReal a) (ENNReal.toReal b)",
"tactic": "simp only [h, (ENNReal.toReal_le_toReal hr hp).2 h, min_... | [
2056,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2053,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_le_mul_iff_left | [] | [
825,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_div_atTop_eq_nat | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.345892\nι' : Type ?u.345895\nα : Type ?u.345898\nβ : Type ?u.345901\nγ : Type ?u.345904\nk : ℕ\nhk : 0 < k\na b : ℕ\nx✝ : b ≥ 1\n⊢ a / k ≤ b ↔ a ≤ (fun b => b * k + (k - 1)) b",
"tactic": "simp only [← Nat.lt_succ_iff, Nat.div_lt_iff_lt_mul hk, N... | [
1671,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1663,
1
] |
Mathlib/Init/Data/Ordering/Lemmas.lean | cmpUsing_eq_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u\nlt : α → α → Prop\ninst✝ : DecidableRel lt\na b : α\n⊢ (cmpUsing lt a b = Ordering.lt) = lt a b",
"tactic": "simp"
}
] | [
51,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_monotone | [] | [
221,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearIndependent.set_finite_of_isNoetherian | [] | [
314,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.extendDomain | [
{
"state_after": "case intro.intro.intro.intro\nι : Type ?u.2071598\nα : Type u_2\nβ : Type u_1\nf✝ g : Perm α\ns t : Set α\na✝ b✝ x y : α\np : β → Prop\ninst✝ : DecidablePred p\nf : α ≃ Subtype p\nh : IsCycleOn g s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\n⊢ SameCycle (Perm.extendDomain g f) ((Subtype.val ∘ ↑f) a... | [
941,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Equalizers.lean | CategoryTheory.Limits.map_π_preserves_coequalizer_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\nw : f ≫ h = g ≫ h\ninst✝² : HasCoequalizer f g\ninst✝¹ : HasCoequalizer (G.map f) (G.map g)\ninst✝ : PreservesColimit (parallelPair f g) G\n⊢ G.map ... | [
209,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/Concept.lean | Concept.fst_injective | [] | [
207,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Combinatorics/Derangements/Finite.lean | card_derangements_eq_numDerangements | [
{
"state_after": "α✝ : Type ?u.21453\ninst✝³ : DecidableEq α✝\ninst✝² : Fintype α✝\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\n⊢ card ↑(derangements (Fin (card α))) = numDerangements (card α)",
"state_before": "α✝ : Type ?u.21453\ninst✝³ : DecidableEq α✝\ninst✝² : Fintype α✝\nα : Type u_1\nins... | [
116,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_mul_right | [
{
"state_after": "d : Nat\nn : Int\na : Nat\nd0 : d ≠ 0\na0 : a ≠ 0\n⊢ normalize (n * ↑a) (d * a) = normalize (↑a * n) (a * d)",
"state_before": "d : Nat\nn : Int\na : Nat\nd0 : d ≠ 0\na0 : a ≠ 0\n⊢ normalize (n * ↑a) (d * a) = normalize n d",
"tactic": "rw [← normalize_mul_left (d0 := d0) a0]"
},
{... | [
44,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
42,
1
] |
Mathlib/RingTheory/Localization/AtPrime.lean | Localization.localRingHom_id | [] | [
257,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.union_left | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nl t₁ t₂ : List α\nh : t₁ ~ t₂\n⊢ List.union l t₁ ~ List.union l t₂",
"tactic": "induction l <;> simp [*, Perm.insert]"
}
] | [
999,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.gcdB_zero_left | [
{
"state_after": "s : ℕ\n⊢ (xgcd 0 s).snd = 1",
"state_before": "s : ℕ\n⊢ gcdB 0 s = 1",
"tactic": "unfold gcdB"
},
{
"state_after": "no goals",
"state_before": "s : ℕ\n⊢ (xgcd 0 s).snd = 1",
"tactic": "rw [xgcd, xgcd_zero_left]"
}
] | [
92,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_pos_of_pos_of_nonneg | [] | [
826,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
825,
11
] |
Mathlib/Order/Heyting/Basic.lean | sup_compl_le_himp | [] | [
807,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | sSup_inv | [
{
"state_after": "α : Type u_1\ninst✝³ : CompleteLattice α\ninst✝² : Group α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ns✝ t s : Set α\n⊢ (⨆ (a : α) (_ : a ∈ s), a⁻¹) = (sInf s)⁻¹",
"state_before": "α... | [
66,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.WellFoundedOn.union | [
{
"state_after": "ι : Type ?u.29184\nα : Type u_1\nβ : Type ?u.29190\nr r' : α → α → Prop\ninst✝ : IsStrictOrder α r\ns t : Set α\nhs : ∀ (f : (fun x x_1 => x > x_1) ↪r r), ¬∀ (n : ℕ), ↑f n ∈ s\nht : ∀ (f : (fun x x_1 => x > x_1) ↪r r), ¬∀ (n : ℕ), ↑f n ∈ t\n⊢ ∀ (f : (fun x x_1 => x > x_1) ↪r r), ¬∀ (n : ℕ), ↑f... | [
166,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_addEquiv_lpBcf | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.neg_def | [] | [
848,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
11
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.beth_one | [
{
"state_after": "no goals",
"state_before": "⊢ beth 1 = 𝔠",
"tactic": "simpa using beth_succ 0"
}
] | [
87,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/List/Nodup.lean | List.get_indexOf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na b : α\ninst✝ : DecidableEq α\nl : List α\nH : Nodup l\ni : Fin (length l)\n⊢ get l { val := indexOf (get l i) l, isLt := (_ : indexOf (get l i) l < length l) } = get l i",
"tactic": "simp"
}
] | [
172,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.bind | [] | [
822,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Algebra/Order/Kleene.lean | mul_kstar_le_kstar | [] | [
207,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasFDerivWithinAt.clog | [] | [
121,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakDual.coeFn_continuous | [] | [
280,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.dim_ne_zero | [] | [
123,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_mul | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.118109\nι : Type ?u.118112\nM : Type u_2\nN : Type ?u.118118\ninst✝ : MulZeroClass M\ns✝ t : Set α\nf✝ g✝ : α → M\na : α\ns : Set α\nf g : α → M\nx✝ : α\n⊢ indicator s (fun a => f a * g a) x✝ = indicator s f x✝ * indicator s g x✝",
"state_before": "α : Typ... | [
684,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_sub | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.mapsTo_emetric_ball | [] | [
152,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_zero | [] | [
452,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/CategoryTheory/Abelian/Opposite.lean | CategoryTheory.factorThruImage_comp_imageUnopOp_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y : C\nf : X ⟶ Y\nA B : Cᵒᵖ\ng : A ⟶ B\n⊢ factorThruImage g ≫ (imageUnopOp g).inv = (image.ι g.unop).op",
"tactic": "rw [Iso.comp_inv_eq, image_ι_op_comp_imageUnopOp_hom]"
}
] | [
190,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_self | [] | [
362,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_inv | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Init/Data/Subtype/Basic.lean | Subtype.exists_of_subtype | [] | [
25,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/Order/Max.lean | IsBot.fst | [] | [
419,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.ext | [] | [
111,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/Maps.lean | Inducing.closure_eq_preimage_closure_image | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.5388\nδ : Type ?u.5391\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : Inducing f\ns : Set α\nx : α\n⊢ x ∈ closure s ↔ x ∈ f ⁻¹' closure (f '' s)",
"state_bef... | [
158,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.liftIoc_coe_apply | [
{
"state_after": "𝕜 : Type u_1\nB : Type u_2\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : TopologicalSpace 𝕜\ninst✝¹ : OrderTopology 𝕜\np : 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝ : Archimedean 𝕜\nf : 𝕜 → B\nx : 𝕜\nhx : x ∈ Ioc a (a + p)\nthis : ↑(equivIoc p a) ↑x = { val := x, property := hx }\n⊢ liftIo... | [
262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/CompleteLattice.lean | disjoint_sSup_right | [] | [
1955,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1953,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_zero | [
{
"state_after": "case H.h\nn : ℕ\nj : Fin (Nat.succ n)\n⊢ ↑(↑(cycleRange 0) j) = ↑(↑1 j)",
"state_before": "n : ℕ\n⊢ cycleRange 0 = 1",
"tactic": "ext j"
},
{
"state_after": "case H.h.refine'_1\nn : ℕ\nj : Fin (Nat.succ n)\n⊢ ↑(↑(cycleRange 0) 0) = ↑(↑1 0)\n\ncase H.h.refine'_2\nn : ℕ\nj✝ : Fin... | [
232,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.mem_coe | [] | [
164,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/Max.lean | IsMin.eq_of_ge | [] | [
390,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
11
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.toSubsemiring_injective | [] | [
256,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_le_ceil | [] | [
1224,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/LinearAlgebra/Multilinear/TensorProduct.lean | MultilinearMap.domCoprod_domDomCongr_sumCongr | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_csSup | [] | [
1326,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_insert_update | [] | [
2069,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2067,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_sq | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sin x ^ 2 = 1 - cos x ^ 2",
"tactic": "rw [← sin_sq_add_cos_sq x, add_sub_cancel]"
}
] | [
1048,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isBigO_exp_comp_one | [
{
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"tactic": "simp only [isBigO_one_iff, norm_eq_abs, abs_exp, isBoundedUnder_le_exp_comp]"
}
] | [
409,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/CategoryTheory/Groupoid/VertexGroup.lean | CategoryTheory.Groupoid.vertexGroup.inv_eq_inv | [] | [
59,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.subtypeRestr_symm_trans_subtypeRestr | [
{
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1399,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_finset_sup | [] | [
190,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/Order/Filter/Lift.lean | Filter.tendsto_lift' | [
{
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"tactic": "simp only [Filter.lift', tend... | [
255,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.le_congr | [] | [
802,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.rootSet_C_mul_X_pow | [
{
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"tactic": "rw [C_mul_X_pow... | [
376,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.comap_pure | [
{
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"tactic": "rw [coe_pure, ← principal_singleton, ← image_singleton... | [
306,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.ae_eq | [] | [
532,
31
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1
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Mathlib/Computability/Ackermann.lean | max_ack_right | [] | [
174,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.pow_multiset_sum_mem_span_pow | [
{
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611,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
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Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.tendsto_lintegral_thickenedIndicator_of_isClosed | [
{
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333,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_toAffineMap | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.mem_smul_pointwise_iff_exists | [] | [
77,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
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Mathlib/Data/Set/Basic.lean | Set.ite_inter_compl_self | [
{
"state_after": "no goals",
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"tactic": "rw [← ite_compl, ite_inter_self]"
}
] | [
2257,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2256,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_inv_desc | [
{
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"tactic":... | [
683,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Path.cast_heq | [
{
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"state_before": "U : Type u_1\ninst✝ : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\np : Path u v\n⊢ HEq (cast hu hv p) p",
"tactic": "rw [P... | [
118,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Analysis/NormedSpace/LpEquiv.lean | Memℓp.all | [
{
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57,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
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Mathlib/Data/Rat/Floor.lean | Rat.ceil_cast | [
{
"state_after": "no goals",
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"tactic": "rw [← neg_inj, ← floor_neg, ← floor_neg, ← Rat.cast_neg, Rat.floor_cast]"
}
] | [
79,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
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Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_lt_lift | [
{
"state_after": "no goals",
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"tactic": "rw [← lift_continuum.{u,v}, lift_lt]"
}
] | [
64,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
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Mathlib/Algebra/Field/Basic.lean | same_add_div | [
{
"state_after": "no goals",
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"tactic": "rw [← div_self h, add_div]"
}
] | [
40,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_liminf | [] | [
526,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.fderivWithin | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
1018,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
11
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_sup_left | [] | [
408,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_cond_eq_cond_inter | [] | [
141,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_iInter₂ | [] | [
205,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augment_d_one_zero | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_finset_prod_of_mulSupport_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.180289\nι : Type ?u.180292\nG : Type ?u.180295\nM : Type u_2\nN : Type ?u.180301\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\ns : Finset α\nh : mulSupport f ⊆ ↑s\n⊢ Finite.toFinset (_ : Set.Finite (mulSupport f)) ⊆ s",
"... | [
408,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_sups_sups_comm | [] | [
211,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone | [] | [
527,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_pos | [
{
"state_after": "K : Type u_1\nE : Type ?u.4450828\ninst✝ : IsROrC K\nz : K\n⊢ 0 ≤ ↑normSq z ∧ ¬↑normSq z = 0 ↔ z ≠ 0",
"state_before": "K : Type u_1\nE : Type ?u.4450828\ninst✝ : IsROrC K\nz : K\n⊢ 0 < ↑normSq z ↔ z ≠ 0",
"tactic": "rw [lt_iff_le_and_ne, Ne, eq_comm]"
},
{
"state_after": "no g... | [
494,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformEmbedding_iff' | [
{
"state_after": "no goals",
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2927,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2923,
1
] |
Mathlib/CategoryTheory/FintypeCat.lean | FintypeCat.Skeleton.incl_mk_nat_card | [
{
"state_after": "case h.e'_2\nn : ℕ\n⊢ Fintype.card ↑(incl.obj (mk n)) = Finset.card Finset.univ",
"state_before": "n : ℕ\n⊢ Fintype.card ↑(incl.obj (mk n)) = n",
"tactic": "convert Finset.card_fin n"
},
{
"state_after": "no goals",
"state_before": "case h.e'_2\nn : ℕ\n⊢ Fintype.card ↑(incl... | [
207,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
src/lean/Init/Classical.lean | Classical.axiomOfChoice | [] | [
108,
34
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
107,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.cast_pos | [
{
"state_after": "no goals",
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"tactic": "simp [e]"
}
] | [
832,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Order/WithBot.lean | WithTop.untop_coe | [] | [
782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_direction_iff_eq_vsub_left | [
{
"state_after": "k : 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\ns : AffineSubspace k P\np : P\nhp : p ∈ s\nv : V\n⊢ v ∈ (fun x x_1 => x -ᵥ x_1) p '' ↑s ↔ ∃ p2, p2 ∈ s ∧ v = p -ᵥ p2",
"state_before": "k : Type u_1\nV : Type u... | [
331,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_omega | [] | [
807,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.mono_of_mono | [
{
"state_after": "case right_cancellation\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Mono (f ≫ g)\n⊢ ∀ {Z : C} (g h : Z ⟶ X), g ≫ f = h ≫ f → g = h",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Mono (f ≫ g)\n⊢ M... | [
327,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_bijective | [] | [
95,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_of_gt | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : ↑Fin.castSucc j < i\n⊢ X.map (SimplexCategory.σ (↑Fin.castSucc j)).op ≫ X.map (SimplexCategory.δ (Fin.succ i)).op =\n X.map (SimplexCategory.δ i).op ≫ X.map (SimplexCategory.σ j).op",
"s... | [
188,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_le_of_le_mul' | [] | [
1594,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1593,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.Chain.nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\n⊢ Chain r Cycle.nil",
"tactic": "trivial"
}
] | [
935,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Std/Data/List/Init/Lemmas.lean | List.foldrM_reverse | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝ : Monad m\nl : List α\nf : α → β → m β\nb : β\n⊢ List.foldlM (fun y x => f x y) b (reverse (reverse l)) = List.foldlM (fun x y => f y x) b l",
"tactic": "simp"
}
] | [
175,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
173,
9
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropAt_symm_of_mem_maximalAtlas | [
{
"state_after": "H : Type u_1\nM : Type u_2\nH' : Type ?u.56211\nM' : Type ?u.56214\nX : Type ?u.56217\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\ninst✝⁴ : TopologicalSpace H'\ninst✝³ : TopologicalSpace M'\ninst✝² : ChartedSpace H' M'\ninst✝¹ : TopologicalSpace X\nG : ... | [
501,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
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