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/ZMod/Basic.lean | ZMod.cast_one' | [] | [
374,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.res_apply | [] | [
285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.odd_card_of_char_ne_two | [] | [
521,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/RingTheory/Algebraic.lean | Algebra.isIntegral_of_finite | [] | [
255,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.measure_smul_set_average | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.210759\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : Measure α\ns✝ : Set E\nf : α → E\ns : Set α\nh : ↑↑μ ... | [
148,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_lcm_helper | [
{
"state_after": "x y d m : ℕ\nhd : Nat.gcd x y = d\nd0 : Nat.beq d 0 = false\ndm : x * y = d * m\n⊢ d * Nat.lcm x y = d * m",
"state_before": "x y d m : ℕ\nhd : Nat.gcd x y = d\nd0 : Nat.beq d 0 = false\ndm : x * y = d * m\n⊢ (fun x x_1 => x * x_1) d (Nat.lcm x y) = (fun x x_1 => x * x_1) d m",
"tactic... | [
62,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.mem_resolventSet_of_left_right_inverse | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nr : R\na b c : A\nh₁ : (↑↑ₐ r - a) * b = 1\nh₂ : c * (↑↑ₐ r - a) = 1\n⊢ b * (↑↑ₐ r - a) = 1",
"tactic": "rwa [← left_inv_eq_right_inv h₂ h₁]"
}
] | [
131,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.hasFDerivWithinAt | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\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 : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
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Mathlib/RepresentationTheory/Basic.lean | Representation.smul_one_tprod_asModule | [
{
"state_after": "k : Type u_1\nG : Type u_2\nV : Type u_4\nW : Type u_3\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\ninst✝¹ : AddCommMonoid W\ninst✝ : Module k W\nρV : Representation k G V\nρW : Representation k G W\nr : MonoidAlgebra k G\nx : V\ny : W\n⊢ ↑(↑(asAl... | [
395,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
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Mathlib/Tactic/Positivity/Basic.lean | Mathlib.Meta.Positivity.mul_ne_zero_of_ne_zero_of_pos | [] | [
122,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
9
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_zsmul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIcoMod hp (a + m • p) b = toIcoMod hp a b + m • p",
"tactic": "simp only [toIcoMod, toIcoDiv_add_zsmul', sub_smul, sub_add]"
}... | [
413,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.support_toPartitionOfUnity_subset | [] | [
479,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Std/Logic.lean | imp_congr_ctx | [] | [
137,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
136,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.Ico_eq_finset_subtype | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_nhds_left | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhdf : ∀ᶠ (x : ℝ) in 𝓝[Iio a] a, DifferentiableAt ℝ f x\nhg' : ∀ᶠ (x : ℝ) in 𝓝[Iio a] a, deriv g x ≠ 0\nhfa : Tendsto f (𝓝[Iio a] a) (𝓝 0)\nhga : Tendsto g (𝓝[Iio a] a) (𝓝 0)\nhdiv : Tendsto (fun x => deriv f x / deriv g x) (𝓝[Iio a]... | [
411,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
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Std/Data/Int/DivMod.lean | Int.mul_sign | [] | [
842,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
839,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.self_distrib_inv | [
{
"state_after": "R : Type u_1\ninst✝ : Rack R\nx y z : R\n⊢ (x ◃ x ◃⁻¹ y) ◃ x ◃ x ◃⁻¹ y ◃⁻¹ z = z",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y z : R\n⊢ x ◃⁻¹ y ◃⁻¹ z = (x ◃⁻¹ y) ◃⁻¹ x ◃⁻¹ z",
"tactic": "rw [← left_cancel (x ◃⁻¹ y), right_inv, ← left_cancel x, right_inv, self_distrib]"
},
{
... | [
244,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_neg | [] | [
1167,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.X_comp | [] | [
542,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_subtype_iff_indicator | [] | [
165,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.eval_single | [] | [
283,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.ext_iff | [] | [
145,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.sup'_lt_iff | [
{
"state_after": "F : Type ?u.304015\nα : Type u_1\nβ : Type ?u.304021\nγ : Type ?u.304024\nι : Type u_2\nκ : Type ?u.304030\ninst✝ : LinearOrder α\ns : Finset ι\nH : Finset.Nonempty s\nf : ι → α\na : α\n⊢ (∀ (b : ι), b ∈ s → (WithBot.some ∘ f) b < ↑a) ↔ ∀ (i : ι), i ∈ s → f i < a",
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1098,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_map_mul_left | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.111733\nγ : Type ?u.111736\ninst✝ : NonUnitalNonAssocSemiring α\na : α\ns : Multiset ι\nf : ι → α\n⊢ sum (map (fun i => a * f i) 0) = a * sum (map f 0)",
"tactic": "simp"
},
{
"state_after": "no goals",
"st... | [
339,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Logic/Small/Basic.lean | small_of_surjective | [] | [
99,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_le | [
{
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1370,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
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Mathlib/Algebra/IsPrimePow.lean | not_isPrimePow_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommMonoidWithZero R\nn p : R\nk : ℕ\ninst✝ : NoZeroDivisors R\n⊢ ∀ (x : R) (x_1 : ℕ), 0 < x_1 → x ^ x_1 = 0 → ¬Prime x",
"state_before": "R : Type u_1\ninst✝¹ : CommMonoidWithZero R\nn p : R\nk : ℕ\ninst✝ : NoZeroDivisors R\n⊢ ¬IsPrimePow 0",
"tactic": "simp onl... | [
45,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.apply_eq_zero_of_comp_eq_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q R : C\nf : Q ⟶ R\na : P ⟶ Q\nh : a ≫ f = 0\n⊢ pseudoApply f (Quot.mk (PseudoEqual Q) (Over.mk a)) = 0",
"tactic": "simp [over_coe_def, pseudoApply_mk', Over.coe_hom, h]"
}
] | [
395,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_cancel_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.74084\nα : Type u_1\nβ : Type ?u.74090\nπ : ι → Type ?u.74095\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ b ∆ a ∆ a = b",
"tactic": "simp [symmDiff_assoc]"
}
] | [
501,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_eq_iInf_iSup_of_nat' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.108288\nγ : Type ?u.108291\nι : Type ?u.108294\ninst✝ : CompleteLattice α\nu : ℕ → α\n⊢ limsup u atTop = ⨅ (n : ℕ), ⨆ (i : ℕ), u (i + n)",
"tactic": "simp only [limsup_eq_iInf_iSup_of_nat, iSup_ge_eq_iSup_nat_add]"
}
] | [
704,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Algebra/Opposites.lean | AddOpposite.unop_mul | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mapEquiv_apply | [] | [
828,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Order/PartialSups.lean | partialSups_eq_ciSup_Iic | [
{
"state_after": "α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nf : ℕ → α\nn : ℕ\nthis : Set.Iio (n + 1) = Set.Iic n\n⊢ ↑(partialSups f) n = ⨆ (i : ↑(Set.Iic n)), f ↑i",
"state_before": "α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nf : ℕ → α\nn : ℕ\n⊢ ↑(partialSups f) n = ⨆ (i : ↑(Set.Iic n... | [
158,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.copy_eq | [] | [
147,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_one_embedding | [] | [
2490,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2488,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass | [
{
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467,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Algebra/Squarefree.lean | UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors | [
{
"state_after": "R : Type u_1\ninst✝³ : CancelCommMonoidWithZero R\ninst✝² : UniqueFactorizationMonoid R\ninst✝¹ : NormalizationMonoid R\ninst✝ : DecidableEq R\nx : R\nx0 : x ≠ 0\ndrel : DecidableRel Dvd.dvd\n⊢ Squarefree x ↔ Multiset.Nodup (normalizedFactors x)",
"state_before": "R : Type u_1\ninst✝³ : Ca... | [
257,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.map_exp_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.84797\nx y z : ℝ\nl : Filter α\n⊢ Filter.map exp atTop = atTop",
"tactic": "rw [← coe_comp_expOrderIso, ← Filter.map_map, OrderIso.map_atTop, map_val_Ioi_atTop]"
}
] | [
302,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.of_leftInverse | [
{
"state_after": "no goals",
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"tactic": "simp only [lift_of, Pi.mulSingle_eq_same,... | [
188,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Prod.lean | Set.empty_pi | [
{
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654,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.ccos | [] | [
361,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
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Mathlib/ModelTheory/Definability.lean | Set.Definable.union | [
{
"state_after": "case intro\nM : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.12600\nB : Set M\ns f g : Set (α → M)\nhg : Definable A L g\nφ : Formula (L[[↑A]]) α\nhφ : f = setOf (Formula.Realize φ)\n⊢ Definable A L (f ∪ g)",
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88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Complex.differentiableAt_exp | [] | [
49,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | Int.norm_coe_nat | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1796,
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Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_div_mul_left | [] | [
180,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Data/Finset/Prod.lean | Finset.product_subset_product | [] | [
94,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_one | [] | [
248,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.iff_preimage_eq | [] | [
511,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Order/OrderIsoNat.lean | RelEmbedding.wellFounded_iff_no_descending_seq | [
{
"state_after": "case mp\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\n⊢ WellFounded r → IsEmpty ((fun x x_1 => x > x_1) ↪r r)\n\ncase mpr\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\n⊢ IsEmpty ((fun x x_1 => x > x_1) ↪r r) → WellFounded r",
"state_before": "α : Type u_1\nr : α... | [
98,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Vector3.lean | Vector3.insert_fs | [
{
"state_after": "case refine'_2\nα : Type u_1\nm n : ℕ\na b : α\nv : Vector3 α n\ni : Fin2 (succ n)\nj✝ : Fin2 (succ (succ n))\nj : Fin2 (n + 1)\n⊢ (a :: b :: v)\n (match insertPerm i j with\n | fz => fz\n | fs k => fs (fs k)) =\n (a :: v) (insertPerm i j)",
"state_before": "α : Type u_1\... | [
201,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.congr_apply | [] | [
905,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.setOf_mem | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.inclusion_right | [
{
"state_after": "case mk\nG : Type u_2\nG' : Type ?u.62545\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.62554\ninst✝⁴ : AddGroup A\nM : Type ?u.62560\nS : Type u_1\ninst✝³ : DivInvMonoid M\ninst✝² : SetLike S M\nhSM : SubgroupClass S M\nH K : S\ninst✝¹ : SetLike S G\ninst✝ : SubgroupClass S G\nh : H ≤ K\n... | [
333,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffAt.ccos | [] | [
356,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.constant_of_preserves_morphisms | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : IsPreconnected J\nα : Type u₁\nF : J → α\nh : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → F j₁ = F j₂\nj j' : J\n⊢ F j = F j'",
"tactic": "simpa using\n any_functor_const_on_obj\n { obj := Discre... | [
130,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Rel.lean | Rel.preimage_def | [] | [
184,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_natAbs | [
{
"state_after": "a : Int\nh : 0 ≤ a\n⊢ ↑(natAbs a) ≤ ↑(natAbs ↑(natAbs a))",
"state_before": "a : Int\nh : 0 ≤ a\n⊢ a ≤ ↑(natAbs a)",
"tactic": "rw [eq_natAbs_of_zero_le h]"
},
{
"state_after": "no goals",
"state_before": "a : Int\nh : 0 ≤ a\n⊢ ↑(natAbs a) ≤ ↑(natAbs ↑(natAbs a))",
"tac... | [
735,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
732,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_iInf | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nf : ι → Subgraph G\nv : V\n⊢ neighborSet (⨅ (i : ι), f i) v = (⋂ (i : ι), neighborSet (f i) v) ∩ SimpleGraph.neighborSet G v",
"tactic": "simp [iInf]"
}
] | [
535,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.concyclic_singleton | [] | [
227,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/List/Lattice.lean | List.mem_union_left | [] | [
91,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | cauchy_series_of_le_geometric | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1068136\nι : Type ?u.1068139\ninst✝ : SeminormedAddCommGroup α\nr✝ C✝ : ℝ\nf : ℕ → α\nC : ℝ\nu : ℕ → α\nr : ℝ\nhr : r < 1\nh : ∀ (n : ℕ), ‖u n‖ ≤ C * r ^ n\n⊢ ∀ (n : ℕ), dist (∑ k in Finset.range n, u k) (∑ k in Finset.range (n + 1), u ... | [
422,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_C_mul_X_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\n⊢ degree (↑C a * X) ≤ 1",
"tactic": "simpa only [pow_one] using degree_C_mul_X_pow_le 1 a"
}
] | [
313,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.ext | [] | [
774,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.mul | [] | [
1519,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/Algebra/Category/GroupCat/Biproducts.lean | AddCommGroupCat.biprodIsoProd_inv_comp_snd | [] | [
91,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_zmod_val | [
{
"state_after": "case zero\nn : ℕ\nR : Type ?u.21503\ninst✝ : NeZero Nat.zero\na : ZMod Nat.zero\n⊢ ↑(val a) = a\n\ncase succ\nn : ℕ\nR : Type ?u.21503\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\na : ZMod (Nat.succ n✝)\n⊢ ↑(val a) = a",
"state_before": "n✝ : ℕ\nR : Type ?u.21503\nn : ℕ\ninst✝ : NeZero n\na : ZM... | [
197,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.span_pow | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n : A\ns : Set A\n⊢ span R s ^ 0 = span R (s ^ 0)",
"tactic": "rw [pow_zero, pow_zero, one_eq_span_one_set]"
},
... | [
404,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.map_zero | [
{
"state_after": "case pos\nα : Type u_3\nβ : Type u_1\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\nf : α → β\nhf : Measurable f\n⊢ map 0 f = 0\n\ncase neg\nα : Type u_3\nβ : Type u_1\nm inst✝³ : MeasurableS... | [
603,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.coprodᵢ_bot | [] | [
239,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.coe_sdiff | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/List/Basic.lean | List.getI_cons_zero | [] | [
4463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4462,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.smul_left | [] | [
101,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.subsingleton_iff | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.19160\nA : Type ?u.19163\ninst✝¹ : MulOneClass M\ns : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\nh : Subsingleton M\nx y : Submonoid M\ni : M\n⊢ 1 ∈ x ↔ 1 ∈ y",
"tactic": "simp [Submonoid.one_mem]"
}
] | [
367,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_comm | [] | [
107,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | T_pow_nonneg | [] | [
135,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
9
] |
Mathlib/Topology/ContinuousOn.lean | diff_mem_nhdsWithin_diff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.5955\nγ : Type ?u.5958\nδ : Type ?u.5961\ninst✝ : TopologicalSpace α\nx : α\ns t : Set α\nhs : s ∈ 𝓝[t] x\nt' : Set α\n⊢ s ∩ t'ᶜ ∈ 𝓝 x ⊓ 𝓟 t ⊓ 𝓟 (t'ᶜ)",
"state_before": "α : Type u_1\nβ : Type ?u.5955\nγ : Type ?u.5958\nδ : Type ?u.5961\ninst✝ : TopologicalSpa... | [
112,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.isAtom_iff | [
{
"state_after": "ι : Type ?u.25211\nα : Type u_1\nβ : Type ?u.25217\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T1Space α\ns : Closeds α\nthis : IsAtom ↑s ↔ IsAtom s\n⊢ IsAtom s ↔ ∃ x, s = singleton x",
"state_before": "ι : Type ?u.25211\nα : Type u_1\nβ : Type ?u.25217\ninst✝² : Top... | [
262,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.eq_iff_lt_minimalPeriod_of_iterate_eq | [] | [
365,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/List/OfFn.lean | List.pairwise_ofFn | [
{
"state_after": "no goals",
"state_before": "α : Type u\nR : α → α → Prop\nn : ℕ\nf : Fin n → α\n⊢ Pairwise R (ofFn f) ↔ ∀ ⦃i j : Fin n⦄, i < j → R (f i) (f j)",
"tactic": "simp only [pairwise_iff_get, (Fin.cast (length_ofFn f)).surjective.forall, get_ofFn,\n OrderIso.lt_iff_lt]"
}
] | [
230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_lt_sdiff_right | [] | [
334,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Ideal.torsionOf_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ torsionOf R M 0 = ⊤",
"tactic": "simp [torsionOf]"
}
] | [
82,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.le_mulIndicator | [] | [
782,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Order/SemiconjSup.lean | IsOrderRightAdjoint.orderIso_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → α\nh : IsOrderRightAdjoint f g\ne : β ≃o γ\ny : γ\n⊢ IsLUB {x | (↑e ∘ f) x ≤ y} ((g ∘ ↑(OrderIso.symm e)) y)",
"tactic": "simpa [e.le_s... | [
73,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_bijective | [] | [
105,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.coe_mk | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\nE' : Type ?u.56213\nF : Type ?u.56216\nG : Type ?u.56219\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : NormedAddCommGroup G\ninst✝² : InnerPr... | [
127,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.multichoose_two | [
{
"state_after": "case zero\n\n⊢ multichoose 2 zero = zero + 1\n\ncase succ\nk : ℕ\nIH : multichoose 2 k = k + 1\n⊢ multichoose 2 (succ k) = succ k + 1",
"state_before": "k : ℕ\n⊢ multichoose 2 k = k + 1",
"tactic": "induction' k with k IH"
},
{
"state_after": "case succ\nk : ℕ\nIH : multichoose... | [
386,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_average | [
{
"state_after": "case h\nα : Type u_2\ninst✝⁷ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : BorelSpace α\ninst✝³ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝² ... | [
930,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | eq_of_sub_eq_zero' | [
{
"state_after": "no goals",
"state_before": "G₀ : Type u\nM₀ : Type ?u.15\nM₀' : Type ?u.18\nG₀' : Type ?u.21\nR : Type u_1\ninst✝ : AddGroup R\na b : R\nh : a - b = 0\n⊢ a + -b = b + -b",
"tactic": "rw [← sub_eq_add_neg, h, add_neg_self]"
}
] | [
38,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | open_map_of_strict_fderiv_equiv | [] | [
685,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Filter.Tendsto.edist | [] | [
1464,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.mul_eq_bot_iff | [] | [
254,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/List/Basic.lean | List.insert_pos | [] | [
259,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/ModelTheory/Ultraproducts.lean | FirstOrder.Language.Ultraproduct.boundedFormula_realize_cast | [
{
"state_after": "α : Type u_2\nM : α → Type u_3\nu : Ultrafilter α\nL : Language\ninst✝¹ : (a : α) → Structure L (M a)\ninst✝ : ∀ (a : α), Nonempty (M a)\nβ : Type u_1\nn : ℕ\nφ : BoundedFormula L β n\nx : β → (a : α) → M a\nv : Fin n → (a : α) → M a\nthis : Setoid ((a : α) → M a) := productSetoid (↑u) M\n⊢ (B... | [
150,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | exists_eq_mul_right_of_dvd | [] | [
59,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.congr_arg | [] | [
718,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.comp_linearIsometry | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2902038\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_3\nι' : Type ?u.2902090\nι'' : ... | [
1327,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.subset_pointwise_smul_iff | [] | [
302,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.22430\nβ : Type ?u.22433\na b c d : ℝ≥0∞\nr p✝ q : ℝ≥0\np : ℝ≥0∞ → Prop\n⊢ (∃ a, a ≠ ⊤ ∧ p a) ↔ ∃ r, p ↑r",
"tactic": "simp only [exists_ne_top', ← exists_prop]"
}
] | [
265,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Directed.sequence_mono | [] | [
664,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
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