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/TypeVec.lean | TypeVec.drop_append1 | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousOn.integrableAt_nhdsWithin_of_isSeparable | [] | [
561,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.center_eq_top | [] | [
741,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.comp_def | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_nsmul | [] | [
198,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_iUnion_apply_eq_iSup | [
{
"state_after": "α : Type u_2\nβ : Type ?u.304451\nγ : Type ?u.304454\nδ : Type ?u.304457\nι : Type u_1\nR : Type ?u.304463\nR' : Type ?u.304466\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\ninst✝ : Countable ι\ns : ι → Set... | [
1774,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1770,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.eq_empty_or_nonempty | [] | [
617,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_zero | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Order/Monotone/Basic.lean | Nat.exists_strictAnti | [] | [
1034,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.prod_mem | [] | [
311,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
11
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_C_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\na0 : a ≠ 0\n⊢ natDegree (↑C a * p) = natDegree p",
"tactic": "simp only [natDegree, degree_C_mul a0]"
}
] | [
341,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_le_one_iff | [] | [
667,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.cos_eq_tsum | [] | [
96,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toLp_add | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.pure_bind | [] | [
608,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.zero | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : Algebra A B\nx : B\ninst✝ : Nontrivial B\n⊢ minpoly A 0 = X",
"tactic": "simpa only [add_zero, C_0, sub_eq_add_neg, neg_zero, RingHom.map_zero] using eq_X_sub_C B (0 : A)"
}
] | [
226,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_eq_sSup | [] | [
876,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_eq_of_subset | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.852623\nγ : Type ?u.852626\nδ : Type ?u.852629\nm : MeasurableSpace α\nμ ν : Measure α\nf : α →ₛ ℝ≥0∞\ns : Finset ℝ≥0∞\nhs : ∀ (x : α), ↑f x ≠ 0 → ↑↑μ (↑f ⁻¹' {↑f x}) ≠ 0 → ↑f x ∈ s\n⊢ ∀ (a : ℝ≥0∞) (h₁ : a ∈ SimpleFunc.range f) (h₂ : a * ↑↑μ (↑f ⁻¹' {a... | [
983,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.left_le_pair | [
{
"state_after": "no goals",
"state_before": "a b : ℕ\n⊢ a ≤ pair a b",
"tactic": "simpa using unpair_left_le (pair a b)"
}
] | [
118,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.inv_eq_inv_aux | [] | [
2117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2116,
1
] |
Mathlib/Order/Compare.lean | Eq.cmp_eq_eq | [] | [
277,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_self' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.74425\nα : Type u_1\nβ : Type ?u.74431\nπ : ι → Type ?u.74436\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b ∆ a = b",
"tactic": "rw [symmDiff_comm, symmDiff_symmDiff_cancel_left]"
}
] | [
506,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | derivWithin.log | [] | [
123,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.apply | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bodd_add | [
{
"state_after": "case zero\nm : ℕ\n⊢ bodd (m + zero) = bxor (bodd m) (bodd zero)\n\ncase succ\nm n : ℕ\nIH : bodd (m + n) = bxor (bodd m) (bodd n)\n⊢ bodd (m + succ n) = bxor (bodd m) (bodd (succ n))",
"state_before": "m n : ℕ\n⊢ bodd (m + n) = bxor (bodd m) (bodd n)",
"tactic": "induction' n with n IH... | [
80,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.hasDerivAt_sinh | [] | [
636,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.add_rpow_le_rpow_add | [
{
"state_after": "ι : Type u\ns : Finset ι\np : ℝ\na b : ℝ≥0\nhp1 : 1 ≤ p\nhp_pos : 0 < p\n⊢ a ^ p + b ^ p ≤ (a + b) ^ p",
"state_before": "ι : Type u\ns : Finset ι\np : ℝ\na b : ℝ≥0\nhp1 : 1 ≤ p\n⊢ a ^ p + b ^ p ≤ (a + b) ^ p",
"tactic": "have hp_pos : 0 < p := by positivity"
},
{
"state_after"... | [
197,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/ShrinkingLemma.lean | ShrinkingLemma.PartialRefinement.apply_eq_of_chain | [] | [
106,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.hom_ext | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Mul β\nf g : FreeMagma α →ₙ* β\nh : ↑f ∘ of = ↑g ∘ of\nx x✝ y✝ : FreeMagma α\na✝¹ : ↑f x✝ = ↑g x✝\na✝ : ↑f y✝ = ↑g y✝\n⊢ ↑f (x✝ * y✝) = ↑g (x✝ * y✝)",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Mul β\nf g : FreeMagma α →ₙ* β\nh : ↑f ∘ of = ↑g ∘ of\nx :... | [
87,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_insert | [] | [
1164,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_zero | [] | [
329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_log | [] | [
130,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.arith_mean_le_rpow_mean | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ≥0\nhw' : ∑ i in s, w i = 1\np : ℝ\nhp : 1 ≤ p\n⊢ ∑ i in s, w i * z i ≤ (∑ i in s, w i * z i ^ p) ^ (1 / p)",
"tactic": "exact_mod_cast\n Real.arith_mean_le_rpow_mean s _ _ (fun i _ => (w i).coe_nonneg) (by exact_mod_cas... | [
173,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebra_le | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁷ : Fintype ι\ninst✝¹⁶ : Fintype ι'\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
810,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Std/Data/Int/DivMod.lean | Int.div_add_mod' | [
{
"state_after": "m k : Int\n⊢ k * div m k + mod m k = m",
"state_before": "m k : Int\n⊢ div m k * k + mod m k = m",
"tactic": "rw [Int.mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m k : Int\n⊢ k * div m k + mod m k = m",
"tactic": "apply div_add_mod"
}
] | [
396,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
395,
1
] |
Mathlib/Algebra/Category/ModuleCat/EpiMono.lean | ModuleCat.mono_iff_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : Ring R\nX Y : ModuleCat R\nf : X ⟶ Y\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\n⊢ Mono f ↔ Function.Injective ↑f",
"tactic": "rw [mono_iff_ker_eq_bot, LinearMap.ker_eq_bot]"
}
] | [
49,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Topology/Separation.lean | t1Space_iff_continuous_cofinite_of | [] | [
499,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_or_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.144374\nι : Sort x\nf : Filter α\np : α → Prop\nq : Prop\n⊢ (∀ᶠ (x : α) in f, p x ∨ q) ↔ (∀ᶠ (x : α) in f, p x) ∨ q",
"tactic": "simp only [@or_comm _ q, eventually_or_distrib_left]"
}
] | [
1193,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.range_restrict | [] | [
376,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mapsTo_sUnion | [] | [
1423,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.inductionOn₃ | [] | [
155,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.asModuleEquiv_symm_map_rho | [
{
"state_after": "k : Type u_2\nG : Type u_3\nV : Type u_1\ninst✝³ : CommSemiring k\ninst✝² : Monoid G\ninst✝¹ : AddCommMonoid V\ninst✝ : Module k V\nρ : Representation k G V\ng : G\nx : V\n⊢ ↑(asModuleEquiv ρ) (↑(AddEquiv.symm (asModuleEquiv ρ)) (↑(↑ρ g) x)) =\n ↑(asModuleEquiv ρ) (↑(of k G) g • ↑(AddEquiv.... | [
156,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.center_le_normalizer | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.384795\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.384804\ninst✝ : AddGroup A\nH K : Subgroup G\nx : G\nhx : x ∈ center G\ny : G\n⊢ y ∈ H ↔ x * y * x⁻¹ ∈ H",
"tactic": "simp [← mem_center_iff.mp hx y, mul_assoc]"
}
] | [
2193,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2192,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_ofLE | [
{
"state_after": "case mk\nα : Type ?u.13886\nX : Type u_1\nY : Type ?u.13892\nZ : Type ?u.13895\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS A B C : DiscreteQuotient X\nh₁ : A ≤ B\nh₂ : B ≤ C\nx : Quotient A.toSetoid\na✝ : X\n⊢ ofLE h₂ (ofLE h₁ (Quot.mk Setoid.r a✝))... | [
228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mrange_snd | [] | [
1317,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_cast | [
{
"state_after": "α β : Type u\nn : ℕ\n⊢ ↑(choose (_ : ∃ n_1, ↑n = ↑n_1)) = ↑n",
"state_before": "α β : Type u\nn : ℕ\n⊢ ↑toNat ↑n = n",
"tactic": "rw [toNat_apply_of_lt_aleph0 (nat_lt_aleph0 n), ← natCast_inj]"
},
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\n⊢ ↑(choose... | [
1716,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.ne_zero_of_finite_field_extension | [] | [
49,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_support | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.right_continuous | [] | [
230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_sub_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonAssocRing α\na b : α\n⊢ a * (b - 1) = a * b - a",
"tactic": "rw [mul_sub, mul_one]"
}
] | [
413,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion₂_smul | [] | [
257,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.prev_nat_succ | [] | [
167,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.σ_naturality | [] | [
219,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/List/Perm.lean | List.Nodup.sublist_ext | [
{
"state_after": "case slnil\nα : Type uu\nβ : Type vv\nl₁✝¹ l₂✝ l₁✝ l₂ l : List α\nd✝ : Nodup l\ns₁✝ : l₁✝ <+ l\nh✝ : l₁✝ ~ l₂\nl₁ : List α\nd : Nodup []\ns₁ : l₁ <+ []\nh : l₁ ~ []\n⊢ l₁ = []\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁✝¹ l₂✝¹ l₁✝ l₂✝ l✝ : List α\nd✝ : Nodup l✝\ns₁✝ : l₁✝ <+ l✝\nh✝ : l₁✝ ~ l₂✝\... | [
763,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Algebra/CharP/Basic.lean | Ring.eq_self_iff_eq_zero_of_char_ne_two | [] | [
639,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Order/Antichain.lean | IsStrongAntichain.isAntichain | [] | [
299,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.prod_atTop | [
{
"state_after": "ι : Type ?u.288498\nι' : Type ?u.288501\nα : Type u_1\nβ : Type ?u.288507\nγ : Type u_2\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup γ\nf g : α → γ\nhf : Tendsto f atTop atTop\nhg : Tendsto g atTop atTop\n⊢ Tendsto (Prod.map f g) (atTop ×ˢ atTop) atTop",
"state_before": "ι : Type ?u.... | [
1465,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.bicone_ι_π_self | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasZeroMorphisms C\nF : J → C\nB : Bicone F\nj : J\n⊢ Bicone.ι B j ≫ Bicone.π B j = 𝟙 (F j)",
"tactic": "simpa using B.ι_π j j"
}
] | [
88,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Std/Data/List/Lemmas.lean | List.dropLast_concat | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ : List α✝\nb : α✝\n⊢ dropLast (l₁ ++ [b]) = l₁",
"tactic": "simp"
}
] | [
492,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
492,
14
] |
Mathlib/Data/Polynomial/Monic.lean | Function.Injective.monic_map_iff | [] | [
363,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.mem_def | [] | [
143,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_insert_of_not_mem' | [
{
"state_after": "case h.e'_2.h.e'_2.h.a\nF : Type ?u.151034\nι : Type ?u.151037\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.151046\nf✝ : α → β → β\nop : α → α → α\ninst✝² : Monoid β\ninst✝¹ : Monoid γ\ninst✝ : DecidableEq α\ns : Finset α\na : α\nf : α → β\ncomm : Set.Pairwise ↑(insert a s) fun a b => Commute (f a... | [
306,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Topology/Constructions.lean | Filter.Eventually.prod_inr_nhds | [] | [
480,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuous_sum | [] | [
541,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | MulMemClass.mul_left_mem_add_closure | [] | [
674,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.length | [
{
"state_after": "case refl\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\n⊢ ∃ n, List.length L₁ = List.length L₁ + 2 * n\n\ncase tail\nα : Type u\nL L₁ L₂✝ L₃✝ L₄ L₂ L₃ : List (α × Bool)\n_h₁₂ : ReflTransGen Step L₁ L₂\nh₂₃ : Step L₂ L₃\nih : ∃ n, List.length L₁ = List.length L₂ + 2 * n\n⊢ ∃ n, List.length L₁ =... | [
436,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.tendsto_nhds_iff | [] | [
130,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_lt_antisymm | [] | [
345,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
344,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.tan_arg | [
{
"state_after": "case pos\nx : ℂ\nh : x = 0\n⊢ Real.tan (arg x) = x.im / x.re\n\ncase neg\nx : ℂ\nh : ¬x = 0\n⊢ Real.tan (arg x) = x.im / x.re",
"state_before": "x : ℂ\n⊢ Real.tan (arg x) = x.im / x.re",
"tactic": "by_cases h : x = 0"
},
{
"state_after": "no goals",
"state_before": "case ne... | [
218,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_arrow | [] | [
126,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Filter.Tendsto.const_mul | [] | [
132,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.dist_le_op_norm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type ?u.308122\nE : Type u_2\nEₗ : Type ?u.308128\nF : Type u_1\nFₗ : Type ?u.308134\nG : Type ?u.308137\nGₗ : Type ?u.308140\n𝓕 : Type ?u.308143\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst... | [
211,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finsupp_of_infinite | [
{
"state_after": "no goals",
"state_before": "α β : Type u\ninst✝² : Infinite α\ninst✝¹ : Zero β\ninst✝ : Nontrivial β\n⊢ (#α →₀ β) = max (#α) (#β)",
"tactic": "simp"
}
] | [
1050,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coeff_coe | [] | [
2545,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2544,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_pi_div_two_sub | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ cos (↑(π / 2) - ↑x✝) = sin ↑x✝",
"state_before": "θ : Angle\n⊢ cos (↑(π / 2) - θ) = sin θ",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ cos (↑(π / 2) - ↑x✝) = sin ↑x✝",
"tacti... | [
476,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_left_cancel | [
{
"state_after": "no goals",
"state_before": "m n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : a + c ≡ b + d [ZMOD n]\n⊢ d - c = b + d - (a + c) - (b - a)",
"tactic": "ring"
},
{
"state_after": "m n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : a + c ≡ b + d [ZMOD n]\nthis : d - c = b + d - (a + c) - (b - a)... | [
163,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_inf_of_mem_inf | [] | [
920,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Data/Part.lean | Part.right_dom_of_sdiff_dom | [] | [
869,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.compare_coe | [] | [
258,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | range_nnnorm | [] | [
371,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.sign_cycleRange | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ni : Fin n\n⊢ ↑sign (cycleRange i) = (-1) ^ ↑i",
"tactic": "simp [cycleRange]"
}
] | [
250,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_mkRat | [
{
"state_after": "n✝¹ num✝ : ℤ\nn✝ denom✝ : ℕ\ninv✝ : Invertible ↑denom✝\nh : ↑n✝¹ / ↑n✝ = ↑num✝ * ⅟↑denom✝\n⊢ IsRat (↑↑n✝¹ / ↑↑n✝) num✝ denom✝",
"state_before": "n✝¹ num✝ : ℤ\nn✝ denom✝ : ℕ\ninv✝ : Invertible ↑denom✝\nh : ↑n✝¹ / ↑n✝ = ↑num✝ * ⅟↑denom✝\n⊢ IsRat (mkRat ↑n✝¹ ↑n✝) num✝ denom✝",
"tactic": "... | [
574,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | cross_cross | [] | [
160,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_edist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.24798\nι : Type ?u.24801\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ dist x y = ENNReal.toReal (edist x y)",
"tactic": "rw [edist_dist, ENNReal.toReal_ofReal dist_nonneg]"
}
] | [
403,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Topology/Separation.lean | specializes_eq_eq | [] | [
540,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
9
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.refl_symm | [] | [
747,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Order/ModularLattice.lean | covby_sup_of_inf_covby_of_inf_covby_left | [] | [
102,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.disjoint | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : EMetricSpace X\ns t : Set X\nx✝ y : X\nh : IsMetricSeparated s t\nr : ENNReal\nr0 : r ≠ 0\nhr : ∀ (x : X), x ∈ s → ∀ (y : X), y ∈ t → r ≤ edist x y\nx : X\nhx1 : x ∈ s\nhx2 : x ∈ t\n⊢ r = 0",
"tactic": "simpa using hr x hx1 x hx2"
}
] | [
60,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
11
] |
Mathlib/Data/Seq/Computation.lean | Computation.of_think_mem | [
{
"state_after": "case zero\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\na : α\nh : some a = Stream'.nth (↑(think s)) Nat.zero\n⊢ a ∈ s\n\ncase succ\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\na : α\nn' : ℕ\nh : some a = Stream'.nth (↑(think s)) (Nat.succ n')\n⊢ a ∈ s",
"state_before"... | [
395,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_int_gt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : StrictOrderedRing α\ninst✝ : Archimedean α\nx : α\nn : ℕ\nh : x < ↑n\n⊢ x < ↑↑n",
"tactic": "rwa [Int.cast_ofNat]"
}
] | [
151,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_replicate | [] | [
1344,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_smul | [] | [
303,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.lift_eval_of | [] | [
262,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_mem_aux | [
{
"state_after": "S : Set Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\no : Ordinal\n⊢ sInf (S ∩ Ici (blsub o fun a x => enumOrd S a)) ∈ S ∩ Ici (blsub o fun c x => enumOrd S c)",
"state_before": "S : Set Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\no : Ordinal\n⊢ enumOrd S o ∈ S ∩ Ici (blsub o fun... | [
2175,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
9
] |
Mathlib/Topology/Algebra/Monoid.lean | Submonoid.topologicalClosure_minimal | [] | [
457,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_singleton | [] | [
1090,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.swap_rightInverse | [] | [
193,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.map_dvd_map | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : CommRing S\nf : R →+* S\nhf : Function.Injective ↑f\nx y : R[X]\nhx : Monic x\n⊢ map f (y %ₘ x) = 0 ↔ y %ₘ x = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b :... | [
410,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Control/Functor/Multivariate.lean | MvFunctor.map_map | [] | [
119,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/Order.lean | generateFrom_iInter | [] | [
985,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
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