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/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_right | [] | [
537,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Data/Bundle.lean | Bundle.coe_snd | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.ae_tendsto_rnDeriv | [
{
"state_after": "case h\nα : Type ?u.1047956\ninst✝¹¹ : MetricSpace α\nβ : Type u\ninst✝¹⁰ : SecondCountableTopology α\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : OpensMeasurableSpace α\ninst✝⁷ : HasBesicovitchCovering α\ninst✝⁶ : MetricSpace β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : BorelSpace β\ninst✝³ : SecondCount... | [
1165,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.units_pow_card_sub_one_eq_one | [
{
"state_after": "no goals",
"state_before": "K : Type ?u.1007117\nR : Type ?u.1007120\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : (ZMod p)ˣ\n⊢ a ^ (p - 1) = 1",
"tactic": "rw [← card_units p, pow_card_eq_one]"
}
] | [
429,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_bounded_of_finset_linearIndependent_bounded | [
{
"state_after": "ι : Type u'\nι' : Type ?u.142157\nR : Type u_2\nK : Type ?u.142163\nM : Type u_1\nM' : Type ?u.142169\nM'' : Type ?u.142172\nV : Type u\nV' : Type ?u.142177\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\nin... | [
342,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_natCast_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.992438\nm : Type u_2\nn : Type u_3\no : Type ?u.992447\nm' : o → Type ?u.992452\nn' : o → Type ?u.992457\nR : Type u_1\nS : Type ?u.992463\nα : Type v\nβ : Type w\nγ : Type ?u.992470\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid α\ninst✝¹ : StarAddMon... | [
2206,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2204,
1
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Mathlib/Data/Set/Function.lean | Set.surjOn_empty | [] | [
770,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
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Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.pure_seq | [] | [
267,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.hypograph | [] | [
245,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.union_ae_eq_right_of_ae_eq_empty | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type ?u.117614\nγ : Type ?u.117617\nδ : Type ?u.117620\nι : Type ?u.117623\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : s =ᵐ[μ] ∅\n⊢ t = ∅ ∪ t",
"state_before": "α : Type u_1\nβ : Type ?u.117614\nγ : Type ?u.117617\nδ : Type ?u.1176... | [
523,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | map_wittPolynomial | [
{
"state_after": "p : ℕ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : DecidableEq R\nS : Type u_2\ninst✝ : CommRing S\nf : R →+* S\nn : ℕ\n⊢ ∑ x in range (n + 1), ↑(map f) (↑(monomial (single x (p ^ (n - x)))) (↑p ^ x)) =\n ∑ i in range (n + 1), ↑(monomial (single i (p ^ (n - i)))) (↑p ^ i)",
"state_befor... | [
125,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective | [] | [
490,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero | [] | [
274,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.fromSubtype_π | [
{
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592,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/Data/Finset/Pi.lean | Finset.Pi.cons_ne | [] | [
74,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_of_mod_eq_zero | [
{
"state_after": "m n : Nat\nH : n % m = 0\n⊢ n = m * (n / m)",
"state_before": "m n : Nat\nH : n % m = 0\n⊢ m ∣ n",
"tactic": "exists n / m"
},
{
"state_after": "m n : Nat\nH : n % m = 0\nthis : n = n % m + m * (n / m)\n⊢ n = m * (n / m)",
"state_before": "m n : Nat\nH : n % m = 0\n⊢ n = m ... | [
721,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
718,
1
] |
Mathlib/Algebra/Squarefree.lean | Squarefree.gcd_left | [] | [
100,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/Max.lean | not_isMin_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9140\ninst✝ : Preorder α\na b : α\n⊢ ¬IsMin a ↔ ∃ b, b < a",
"tactic": "simp [lt_iff_le_not_le, IsMin, not_forall, exists_prop]"
}
] | [
341,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.shiftl_eq_mul_pow | [
{
"state_after": "m k : ℕ\n⊢ bit0 (shiftl m k) = m * (2 ^ k * 2)",
"state_before": "m k : ℕ\n⊢ shiftl m (k + 1) = m * 2 ^ (k + 1)",
"tactic": "show bit0 (shiftl m k) = m * (2 ^ k * 2)"
},
{
"state_after": "no goals",
"state_before": "m k : ℕ\n⊢ bit0 (shiftl m k) = m * (2 ^ k * 2)",
"tact... | [
27,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/CategoryTheory/Sites/Whiskering.lean | CategoryTheory.GrothendieckTopology.Cover.multicospanComp_hom_inv_left | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.All.trivial | [] | [
25,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
23,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_neBot_of_directed' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.110309\nι : Sort x\nf✝ g : Filter α\ns t : Set α\nf : ι → Filter α\ninst✝ : Nonempty ι\nhd : Directed (fun x x_1 => x ≥ x_1) f\n⊢ ¬NeBot (iInf f) → ¬∀ (i : ι), NeBot (f i)",
"tactic": "simpa only [not_forall, n... | [
911,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_sub_two_pi | [] | [
1157,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_eq_iInf_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.105898\nι : Type ?u.105901\ninst✝ : CompleteLattice α\nf : Filter β\nu : β → α\n⊢ (⨅ (i : Set β) (_ : i ∈ f), sSup (u '' id i)) = ⨅ (s : Set β) (_ : s ∈ f), ⨆ (a : β) (_ : a ∈ s), u a",
"tactic": "simp only [sSup_image... | [
696,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_zero | [] | [
40,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_eq_right_of_subset_of_measure_add_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.139389\nγ : Type ?u.139392\nδ : Type ?u.139395\nι : Type ?u.139398\nR : Type ?u.139401\nR' : Type ?u.139404\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t : Set α\nh : ↑↑(ν + μ) t ≠ ⊤\nh'... | [
931,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.continuousWithinAt_Ioi_iff_rightLim_eq | [] | [
203,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_ball | [] | [
418,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_zero | [
{
"state_after": "no goals",
"state_before": "⊢ tan 0 = 0",
"tactic": "rw [← coe_zero, tan_coe, Real.tan_zero]"
}
] | [
789,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Std/Data/List/Lemmas.lean | List.range'_eq_map_range | [
{
"state_after": "s n : Nat\n⊢ range' s n = range' (s + 0) n",
"state_before": "s n : Nat\n⊢ range' s n = map (fun x => s + x) (range n)",
"tactic": "rw [range_eq_range', map_add_range']"
},
{
"state_after": "no goals",
"state_before": "s n : Nat\n⊢ range' s n = range' (s + 0) n",
"tacti... | [
1898,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1897,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_dist_tendsto' | [] | [
410,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
9
] |
Mathlib/Logic/Relation.lean | Relation.transGen_idem | [] | [
471,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Order/Atoms.lean | OrderIso.isCoatomic_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : OrderTop α\ninst✝ : OrderTop β\nf : α ≃o β\n⊢ IsCoatomic α ↔ IsCoatomic β",
"tactic": "simp only [← isAtomic_dual_iff_isCoatomic, f.dual.isAtomic_iff]"
}
] | [
834,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
11
] |
Mathlib/Topology/Algebra/Valuation.lean | Valued.hasBasis_uniformity | [
{
"state_after": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\n⊢ Filter.HasBasis (Filter.comap (fun x => x.snd - x.fst) (𝓝 0)) (fun x => True) fun γ => {p | ↑v (p.snd - p.fst) < ↑γ}",
"state_before": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ ... | [
129,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Logic/Basic.lean | exists_exists_and_eq_and | [] | [
782,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
9
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_mono | [] | [
143,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_congr | [] | [
107,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_neg | [] | [
128,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_add_sub | [
{
"state_after": "R : Type u_2\nV : Type u_1\nV' : Type ?u.143234\nP : Type ?u.143237\nP' : Type ?u.143240\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx✝ y✝ z : P\nx y : V\... | [
235,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vadd_left_mem_affineSpan_pair | [
{
"state_after": "no goals",
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"tactic": "rw [vadd_mem_iff_... | [
1341,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1338,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.uncurry_natural_left | [] | [
198,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/CategoryTheory/Abelian/LeftDerived.lean | CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp | [
{
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151,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
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Mathlib/CategoryTheory/Noetherian.lean | CategoryTheory.exists_simple_subobject | [
{
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"state_before": "C : Type u_1\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nins... | [
90,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsLocalMaxOn.closure | [
{
"state_after": "case intro.intro.intro\nX : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : Preorder Y\ninst✝ : OrderClosedTopology Y\nf g : X → Y\ns : Set X\na : X\nh : IsLocalMaxOn f s a\nhc : ContinuousOn f (closure s)\nU : Set X\nUo : IsOpen U\naU : a ∈ U\nhU : U... | [
54,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
11
] |
Mathlib/Topology/Basic.lean | isClosed_iUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝¹ : TopologicalSpace α\ninst✝ : Finite ι\ns : ι → Set α\nh : ∀ (i : ι), IsOpen (s iᶜ)\n⊢ IsOpen (⋂ (i : ι), s iᶜ)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p... | [
262,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_lagrange | [
{
"state_after": "𝕜 : Type ?u.315018\nE : Type ?u.315021\nF : Type ?u.315024\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → ℝ\nx x₀ : ℝ\nn : ℕ\nhx : x₀ < x\nhf : ContDiffOn ℝ (↑n) f (Icc x₀ x)\nhf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc x₀ x)) (Ioo x₀ x)\ngcont : ContinuousOn (fun... | [
303,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_le_nnnorm_add_nnnorm_div | [] | [
953,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_posPart_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13833\ninst✝ : MeasurableSpace α\nj : JordanDecomposition α\nr : ℝ\nhr : r < 0\n⊢ (r • j).posPart = Real.toNNReal (-r) • j.negPart",
"tactic": "rw [real_smul_def, ← smul_negPart, if_neg (not_le.2 hr), neg_posPart]"
}
] | [
163,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | StrictAnti.inv | [] | [
1324,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_nontrivial_singleton | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nx : α\nH : ∃ y, y ∈ {x} ∧ y ≠ x\n⊢ False",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nx : α\nH : Set.Nontrivial {x}\n⊢ False",
"tactic": "rw [no... | [
2543,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2540,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_add_of_sub_left_le | [
{
"state_after": "a b c : Int\nh✝ : a - b ≤ c\nh : a - b + b ≤ c + b\n⊢ a ≤ b + c",
"state_before": "a b c : Int\nh : a - b ≤ c\n⊢ a ≤ b + c",
"tactic": "have h := Int.add_le_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a - b ≤ c\nh : a - b + b ≤ c + b\n⊢... | [
984,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
982,
11
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.sum_eapproxDiff | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.843173\nγ : Type ?u.843176\nδ : Type ?u.843179\ninst✝ : MeasurableSpace α\nK : Type ?u.843185\nf : α → ℝ≥0∞\na : α\n⊢ ∑ k in Finset.range (Nat.zero + 1), ↑(↑(eapproxDiff f k) a) = ↑(eapprox f Nat.zero) a\n\ncase succ\nα : Type u_1\nβ : Type ?u.843173\nγ : T... | [
949,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_floor_right_pure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5764\nγ : Type ?u.5767\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nn : ℤ\n⊢ Tendsto floor (𝓝[Ici ↑n] ↑n) (pure n)",
"tactic": "simpa only [floor_intCast] using te... | [
77,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.mul_def | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Faces.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY : C\nn q : ℕ\nφ : Y ⟶ X.obj [n + 1].op\nv : HigherFacesVanish q φ\nhqn : n < q\n⊢ φ ≫\n (HomologicalComplex.d (AlternatingFaceMapComplex.obj X) (n + 1) n ≫\n hσ' q n (n + 1) (_ : ComplexShape.Rel ... | [
169,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.Monic.geom_sum' | [] | [
249,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.coe_cliqueFinset | [] | [
293,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.hasSum_log_one_add_inv | [
{
"state_after": "case h.e'_6\na : ℝ\nh : 0 < a\nh₁ : abs (1 / (2 * a + 1)) < 1\n⊢ log (1 + a⁻¹) = log (1 + 1 / (2 * a + 1)) - log (1 - 1 / (2 * a + 1))",
"state_before": "a : ℝ\nh : 0 < a\nh₁ : abs (1 / (2 * a + 1)) < 1\n⊢ HasSum (fun k => 2 * (1 / (2 * ↑k + 1)) * (1 / (2 * a + 1)) ^ (2 * k + 1)) (log (1 +... | [
337,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | AffineEquiv.coe_toHomeomorphOfFiniteDimensional | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.fst_sup_snd | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.365753\nM₆ : Type ?u.365756\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np : Sub... | [
682,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_apply_right | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\ninst✝ : DecidableEq α\na b : α\n⊢ ↑(swap a b) b = a",
"tactic": "by_cases h:b = a <;> simp [swap_apply_def, h]"
}
] | [
1569,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1568,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsLocalization.integerNormalization_eval₂_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁵ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nP : Type ?u.47235\ninst✝² : CommRing P\ninst✝¹ : IsLocalization M S\nR' : Type u_2\ninst✝ : CommRing R'\ng : S →+* R'\np : S[X]\nx : R'\nhx : eval₂ g x p... | [
115,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_map | [] | [
1041,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.dvd_lcm | [] | [
76,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.image_lowerBounds_subset_upperBounds_image | [] | [
1230,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Std/Data/List/Lemmas.lean | List.modifyNthTail_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : List α → List α\nn : Nat\nl₁ l₂ : List α\n⊢ modifyNthTail f (length l₁ + n) (l₁ ++ l₂) = l₁ ++ modifyNthTail f n l₂",
"tactic": "induction l₁ <;> simp [*, Nat.succ_add]"
}
] | [
745,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
743,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.sections_zero | [] | [
35,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.move_left_right | [
{
"state_after": "case mk\nΓ : Type u_1\ninst✝ : Inhabited Γ\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ move Dir.right (move Dir.left { head := head✝, left := left✝, right := right✝ }) =\n { head := head✝, left := left✝, right := right✝ }",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\n⊢... | [
538,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.const_add | [] | [
132,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
8
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.measurable_measure | [] | [
76,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.toCone_π_app_mk | [] | [
120,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.zero_snd | [] | [
208,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
9
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.zero_comp | [] | [
339,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.sep | [
{
"state_after": "case intro.intro\nC : Type u\ninst✝⁶ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝⁵ : Category D\ninst✝⁴ : ConcreteCategory D\ninst✝³ : PreservesLimits (forget D)\ninst✝² : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultieq... | [
321,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.isAlgebraic_iSup | [
{
"state_after": "case mk\nK : Type u_2\nL : Type u_3\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nE1 E2 : IntermediateField K L\nι : Type u_1\nf : ι → IntermediateField K L\nh : ∀ (i : ι), Algebra.IsAlgebraic K { x // x ∈ f i }\nx : L\nhx : x ∈ ⨆ (i : ι), f i\n⊢ IsAlgebraic K { val := x, property ... | [
1262,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_X | [] | [
1454,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Std/Data/List/Lemmas.lean | List.suffix_nil | [] | [
1644,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1644,
9
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.posPart_sub_negPart | [
{
"state_after": "α : Type u_1\nE : Type ?u.94507\nF : Type ?u.94510\n𝕜 : Type ?u.94513\ninst✝² : LinearOrder E\ninst✝¹ : Zero E\ninst✝ : MeasurableSpace α\nf : α →ₛ ℝ\n⊢ map (fun b => max b 0) f - map (fun b => max b 0) (-f) = f",
"state_before": "α : Type u_1\nE : Type ?u.94507\nF : Type ?u.94510\n𝕜 : T... | [
289,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_surjective | [] | [
303,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.zero_mem | [] | [
133,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.openEmbedding_obj_top | [
{
"state_after": "case h\nX : TopCat\nU : Opens ↑X\n⊢ ↑((IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj ⊤) = ↑U",
"state_before": "X : TopCat\nU : Opens ↑X\n⊢ (IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj ⊤ = U",
"tactic": "ext1"
},
{
"st... | [
341,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_zero | [
{
"state_after": "ι : Type ?u.869344\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoidWithZero β\nha : a ∈ s\nh : f a = 0\nthis : DecidableEq α\n⊢ ∏ x in s, f x = 0",
"state_before": "ι : Type ?u.869344\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na ... | [
1907,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1905,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.toLinearPMap_range | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : Ring R\nE : Type u_3\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_2\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.674878\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\ng : Submodule R (E × F)\nhg : ∀ (x : E × F), x... | [
1005,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.tsnd_tfst | [
{
"state_after": "t : Type u → Type u → Type u\ninst✝⁵ : Bitraversable t\nβ : Type u\nF G : Type u → Type u\ninst✝⁴ : Applicative F\ninst✝³ : Applicative G\ninst✝² : IsLawfulBitraversable t\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα₀ α₁ β₀ β₁ : Type u\nf : α₀ → F α₁\nf' : β₀ → G β₁\nx : t α₀ ... | [
97,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.exists_affineBasis | [] | [
331,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.vadd_def | [] | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | CommGroupCat.range_eq_top_of_epi | [] | [
436,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_inter_union_subset | [
{
"state_after": "α : Type u_1\nα' : Type ?u.50587\nβ : Type u_2\nβ' : Type ?u.50593\nγ : Type ?u.50596\nγ' : Type ?u.50599\nδ : Type ?u.50602\nδ' : Type ?u.50605\nε : Type ?u.50608\nε' : Type ?u.50611\nζ : Type ?u.50614\nζ' : Type ?u.50617\nν : Type ?u.50620\nf✝ f' : α → β → γ\ng g' : α → β → γ → δ\ns✝ s' : Se... | [
465,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_one_one_charP | [
{
"state_after": "case h\nR : Type u_1\nS : Type ?u.318902\ninst✝³ : CommRing R\ninst✝² : CommRing S\nk : ℕ\na : R\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP R p\n⊢ 1 = ↑(ZMod.castHom (_ : p ∣ p) R) 1\n\nR : Type u_1\nS : Type ?u.318902\ninst✝³ : CommRing R\ninst✝² : CommRing S\nk : ℕ\na : R\np : ℕ\nins... | [
275,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Order/Monotone/Basic.lean | Antitone.imp | [] | [
368,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | GradedAlgebra.proj_recompose | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nR : Type u_3\nA : Type u_2\nσ : Type ?u.286140\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : AddMonoid ι\ninst✝³ : CommSemiring R\ninst✝² : Semiring A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\na : ⨁ (i : ι), { x // x ∈ 𝒜 i }\ni ... | [
235,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.symm_hom | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.map_one | [] | [
911,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
11
] |
Mathlib/GroupTheory/Congruence.lean | Con.coe_one | [] | [
755,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_op_norm_of_le | [] | [
215,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_count | [
{
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"state_before": "α : Type u_1\nβ :... | [
1405,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_eq_range_psigma | [
{
"state_after": "no goals",
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1273,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_comm | [
{
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185,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
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Mathlib/Analysis/SpecificLimits/Normed.lean | hasSum_geometric_of_norm_lt_1 | [
{
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"state_before": "α : Type ?u.133909\nβ : Type ?u.133912\nι : Type ?u.133915\nK : Type u_1\ninst✝ : NormedField K\nξ ... | [
294,
66
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286,
1
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Mathlib/Data/List/Duplicate.lean | List.Duplicate.duplicate_cons | [] | [
47,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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