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/Equalizers.lean | CategoryTheory.Limits.Cofork.π_precompose | [] | [
671,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | aestronglyMeasurable_deriv | [] | [
450,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.toFun_eq_coe | [] | [
609,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Finset.card_dfinsupp | [] | [
46,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.spanningSetsIndex_eq_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.728649\nγ : Type ?u.728652\nδ : Type ?u.728655\nι : Type ?u.728658\nR : Type ?u.728661\nR' : Type ?u.728664\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Se... | [
3507,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3505,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.sdiff_fundamentalInterior | [] | [
605,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
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src/lean/Init/Core.lean | Decidable.byContradiction | [] | [
739,
43
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
738,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_pi | [
{
"state_after": "α : Type u_3\nβ : Type ?u.690828\nE : Type ?u.690831\nF : Type ?u.690834\nG : Type ?u.690837\nE'✝ : Type ?u.690840\nF' : Type u_4\nG' : Type ?u.690846\nE'' : Type ?u.690849\nF'' : Type ?u.690852\nG'' : Type ?u.690855\nR : Type ?u.690858\nR' : Type ?u.690861\n𝕜 : Type ?u.690864\n𝕜' : Type ?u.... | [
2138,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2134,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.Valid.setCurr | [
{
"state_after": "c : Char\nit : Iterator\nh✝ : Valid it\nl r : List Char\nh : ValidFor l r it\n⊢ Valid (Iterator.setCurr it c)",
"state_before": "c : Char\nit : Iterator\nh : Valid it\n⊢ Valid (Iterator.setCurr it c)",
"tactic": "let ⟨l, r, h⟩ := h.validFor"
},
{
"state_after": "no goals",
... | [
649,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
646,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.mul_pure | [] | [
360,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.mul_iSup | [
{
"state_after": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (↑a * ⨆ (i : ι), ↑(f i)) = ⨆ (i : ι), ↑(a * f i)",
"state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (a * ⨆ (i : ι), f i) = ⨆ (i : ι), a * f i",
"tactic": "rw [← NNReal.coe_eq, NNReal.coe_mul, NNReal.coe_iSup, NNReal.coe_iSup]"
},
{
... | [
964,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_zero_iff | [] | [
210,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sum_eq_top_iff | [] | [
1232,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.coe_top | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_cons | [] | [
3883,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3882,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nhds_top_iff_nat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.40146\nγ : Type ?u.40149\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nm : α → ℝ≥0∞\nf : Filter α\nh : ∀ (x : ℝ≥0), ∀ᶠ (a : α) in f, ↑x < m a\nn : ℕ\n⊢ ∀ᶠ (a : α) in f, ↑n < m a",
"tactic": "simpa only [ENNReal.c... | [
173,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_iInf₂_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.60515\nγ : Type ?u.60518\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\nf : (i : ι) → κ i → UpperSet α\n⊢ (a ∈ ⨅ (i : ι) (j : κ i), f i j) ↔ ∃ i j, a ∈ f i j",
"tactic": "simp_rw [mem_i... | [
619,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | Subring.le_topologicalClosure | [] | [
255,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | Ideal.Quotient.norm_mk_le | [] | [
497,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Order/Disjointed.lean | disjointed_le | [] | [
74,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.toSpanSingleton_zero | [
{
"state_after": "case h\nR : Type u_1\nR₂ : Type ?u.332387\nK : Type ?u.332390\nM : Type u_2\nM₂ : Type ?u.332396\nV : Type ?u.332399\nS : Type ?u.332402\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ ↑(toSpanSingleton R M 0) 1 = ↑0 1",
"state_before": "R : Type u_1\nR₂ : Type ?u.332... | [
933,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_empty | [] | [
1478,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDerivWithin_const_smul_apply | [] | [
1572,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.one_add | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.30381\nn : PosNum\n⊢ 1 + n = succ n",
"tactic": "cases n <;> rfl"
}
] | [
83,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.card_Iic_finset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ card (Iic s) = 2 ^ card s",
"tactic": "rw [Iic_eq_powerset, card_powerset]"
}
] | [
123,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.range_re | [] | [
76,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.sub | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.401752\nδ : Type ?u.401755\ninst✝² : AddCommGroup α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalAddGroup α\nf g : β → α\na a₁ a₂ : α\nhf : HasSum f a₁\nhg : HasSum g a₂\n⊢ HasSum (fun b => f b + -g b) (a₁ + -a₂)",
"state_before": "α : Type u_1\n... | [
822,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/List/Sections.lean | List.mem_sections_length | [] | [
41,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.comap_coe_eq_uniformity | [
{
"state_after": "α : Type u_1\ninst✝² : UniformSpace α\nβ : Type ?u.37466\ninst✝¹ : UniformSpace β\nγ : Type ?u.37472\ninst✝ : UniformSpace γ\nthis :\n (fun x => (↑α x.fst, ↑α x.snd)) =\n (fun x =>\n (Quotient.mk (separationSetoid (CauchyFilter α)) x.fst,\n Quotient.mk (separationSetoid (Ca... | [
408,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_le_zpow_iff' | [] | [
409,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.smul_of | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.464052\ninst✝¹ : Semiring k\ninst✝ : MulOneClass G\ng : G\nr : k\n⊢ r • ↑(of k G) g = single g r",
"tactic": "rw [of_apply, smul_single', mul_one]"
}
] | [
520,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_empty | [
{
"state_after": "case inl\nι : Sort ?u.74934\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : s = ∅\n⊢ hausdorffDist s ∅ = 0\n\ncase inr\nι : Sort ?u.74934\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace ... | [
734,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/GroupTheory/Exponent.lean | Nat.Prime.exists_orderOf_eq_pow_factorization_exponent | [
{
"state_after": "G : Type u\ninst✝ : Monoid G\np : ℕ\nhp : Nat.Prime p\nthis : Fact (Nat.Prime p)\n⊢ ∃ g, orderOf g = p ^ ↑(Nat.factorization (exponent G)) p",
"state_before": "G : Type u\ninst✝ : Monoid G\np : ℕ\nhp : Nat.Prime p\n⊢ ∃ g, orderOf g = p ^ ↑(Nat.factorization (exponent G)) p",
"tactic": ... | [
217,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Init/Logic.lean | false_or_iff | [] | [
183,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_coe_symm | [] | [
579,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_map | [] | [
466,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.inter | [] | [
115,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.446340\n𝕝 : Type ?u.446343\n𝕝₂ : Type ?u.446346\nE : Type u_2\nF : Type ?u.446352\nG : Type ?u.446355\nι : Type u_3\nι' : Type ?u.446361\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\nt : TopologicalSpace E\ninst✝ : ... | [
463,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_iff_linearIndependent_vsub | [
{
"state_after": "case mp\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni1 : ι\n⊢ AffineIndependent k p → LinearIndependent k fun i => p ↑i -ᵥ p i1\n\ncase mpr\nk : Type u_1\nV : Type u_2\nP : Type u_3\... | [
139,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.ne_of_disjoint_coe | [] | [
195,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.SurjectiveOnWith.surjOn | [] | [
205,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | iter_deriv_pow' | [] | [
141,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.abs_sin_eq_of_two_nsmul_eq | [
{
"state_after": "θ ψ : Angle\nh : θ = ψ ∨ θ = ψ + ↑π\n⊢ abs (sin θ) = abs (sin ψ)",
"state_before": "θ ψ : Angle\nh : 2 • θ = 2 • ψ\n⊢ abs (sin θ) = abs (sin ψ)",
"tactic": "rw [two_nsmul_eq_iff] at h"
},
{
"state_after": "case inl\nθ : Angle\n⊢ abs (sin θ) = abs (sin θ)\n\ncase inr\nψ : Angle\... | [
484,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Topology/Connected.lean | IsPreirreducible.isPreconnected | [] | [
77,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Deprecated/Group.lean | IsMonoidHom.id | [] | [
209,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Nat/Factorial/DoubleFactorial.lean | Nat.factorial_eq_mul_doubleFactorial | [
{
"state_after": "no goals",
"state_before": "k : ℕ\n⊢ (k + 1 + 1)! = (k + 1 + 1)‼ * (k + 1)‼",
"tactic": "rw [doubleFactorial_add_two, factorial, factorial_eq_mul_doubleFactorial _, mul_comm _ k‼,\n mul_assoc]"
}
] | [
53,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/Convex/Slope.lean | ConvexOn.secant_mono | [
{
"state_after": "case inl\n𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : ConvexOn 𝕜 s f\na x : 𝕜\nha : a ∈ s\nhx : x ∈ s\nhxa : x ≠ a\nhy : x ∈ s\nhya : x ≠ a\nhxy : x ≤ x\n⊢ (f x - f a) / (x - a) ≤ (f x - f a) / (x - a)\n\ncase inr\n𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\... | [
287,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_eq_iSup | [
{
"state_after": "case inl\nF : Type ?u.306605\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nf g : α →ᵇ β\nx : α\nC : ℝ\nh✝ : IsEmpty α\n⊢ dist f g = ⨆ (x : α), dist (↑f x) (↑g x)\n\ncase inr\nF : Type ?u.306605\nα : Type u\nβ : Type... | [
256,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.refl_symm | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.eq_one_of_prod_eq_one | [
{
"state_after": "ι : Type ?u.804263\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\na : α\nhp : ∏ x in s, f x = 1\nh1 : ∀ (x : α), x ∈ s → x ≠ a → f x = 1\nx : α\nhx : x ∈ s\n⊢ f x = 1",
"state_before": "ι : Type ?u.804263\nβ : ... | [
1719,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_le_sub_of_hasDeriv_right_of_le | [
{
"state_after": "ι : Type ?u.1832713\n𝕜 : Type ?u.1832716\nE : Type ?u.1832719\nF : Type ?u.1832722\nA : Type ?u.1832725\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\ng' g φ : ℝ → ℝ\na b : ℝ\nhab : a ≤ b\nhcont : ContinuousOn g (Icc a b)\nhderiv : ∀ (x : ℝ), x ∈... | [
1156,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ioc_update_right | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_1\ninst✝¹ : (i : ι) → Preorder (α i)\nx✝ y✝ : (i : ι) → α i\ninst✝ : DecidableEq ι\nx y : (i : ι) → α i\ni₀ : ι\nm : α i₀\nhm : m ≤ y i₀\nthis : Ioc (x i₀) m = Iic m ∩ Ioc (x i₀) (y i₀)\n⊢ (pi univ fun i => Ioc (x i) (update y i₀ m i)) = {z | z i₀ ≤ m} ∩ pi univ fu... | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.trans | [
{
"state_after": "no goals",
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"tactic": "simp [add_smul, ← hm, ← hn]"
}
] | [
75,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_ssubset_toFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.85081\nγ : Type ?u.85084\ns t : Set α\ninst✝¹ : Fintype ↑s\ninst✝ : Fintype ↑t\n⊢ toFinset s ⊂ toFinset t ↔ s ⊂ t",
"tactic": "simp only [Finset.ssubset_def, toFinset_subset_toFinset, ssubset_def]"
}
] | [
673,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Pi.segment_subset | [
{
"state_after": "case intro.intro.intro.intro.intro\n𝕜 : Type u_3\nE : Type ?u.376048\nF : Type ?u.376051\nG : Type ?u.376054\nι : Type u_1\nπ : ι → Type u_2\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : (i : ι) → AddCommMonoid (π i)\ninst✝ : (i : ι) → Module 𝕜 (π i)\ns : Set ι\nx y z : (i : ι) → π i\na b : 𝕜\nha ... | [
648,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_eq | [
{
"state_after": "⊢ ∀ (x : ℝ), ‖↑x‖ = abs (x - ↑(round x))",
"state_before": "p x : ℝ\n⊢ ∀ (x : ℝ), ‖↑x‖ = abs (x - ↑(round x))",
"tactic": "clear! x p"
},
{
"state_after": "x : ℝ\n⊢ ‖↑x‖ = abs (x - ↑(round x))",
"state_before": "⊢ ∀ (x : ℝ), ‖↑x‖ = abs (x - ↑(round x))",
"tactic": "intr... | [
121,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_lt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\n⊢ Unbounded (fun x x_1 => x < x_1) s ↔ ∀ (a : α), ∃ b, b ∈ s ∧ a ≤ b",
"tactic": "simp only [Unbounded, not_lt]"
}
] | [
57,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_bot_sup_bot_prod | [] | [
1261,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.mk'_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_3\nB : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : Algebra R B\ninst✝¹ : Algebra A B\ninst✝ : IsIntegralClosure A R B\nh : optParam (IsIntegral R 0) (_ : IsIntegral R 0)\n⊢ ↑(algebraMap A B) (mk' A 0... | [
878,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.HasAntitoneBasis.eventually_subset | [] | [
1766,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.diam_range | [] | [
337,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | IsOpen.exists_between_affineIndependent_span_eq_top | [
{
"state_after": "case intro\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns u : Set P\nhu : IsOpen u\nhsu : s ⊆ u\nh : AffineIndependent ℝ Subtype.val\nq : P\nhq : q ∈ s\n⊢ ∃ t, s ⊆ t ∧ t ⊆ u ∧ AffineIndependent ℝ Subt... | [
118,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.comp_right_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nδ : Type ?u.163029\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nμa : Measure α\nμb : Measure β\nμc : Measure γ\nμd : Measure δ\ng : α → β\ne : γ ≃ᵐ α\nh : MeasurePreserving ↑e\nhg : Mea... | [
116,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
] |
Mathlib/Topology/Separation.lean | t1Space_iff_exists_open | [] | [
508,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.biUnion_image_sup_left | [] | [
187,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.Valid.remainingToString | [
{
"state_after": "case refl\nl r : List Char\nh : ValidFor l r { s := { data := List.reverseAux l r }, i := { byteIdx := utf8Len l } }\n⊢ Iterator.remainingToString { s := { data := List.reverseAux l r }, i := { byteIdx := utf8Len l } } = { data := r }",
"state_before": "l r : List Char\nit : Iterator\nh : ... | [
655,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
653,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.mul_bot | [] | [
240,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_add_nat_mul_two_pi | [] | [
356,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_ℝ_ℂ_eq_exp_ℂ_ℂ | [] | [
668,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | RingHom.map_pthRoot | [] | [
115,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.coe_sup | [] | [
128,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_thickening_iff_infDist_lt | [] | [
973,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_diff_cancel_left | [] | [
1834,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1833,
1
] |
src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.run_bind_lift | [] | [
58,
162
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
58,
9
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_bot_right | [] | [
194,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.apply_mem_iff | [] | [
478,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.image | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ_[p]\nf : CauSeq ℚ (padicNorm p)\nhf : Quotient.mk equiv f ≠ 0\nthis : ¬f ≈ 0\nn : ℤ\nhn : PadicSeq.norm f = ↑p ^ (-n)\n⊢ ‖Quotient.mk equiv f‖ = ↑(PadicSeq.norm f)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ_[p]\nf : CauSeq ℚ (padicNorm p)... | [
876,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
11
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.algebraMap₀_one | [] | [
241,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_sum | [
{
"state_after": "α : Type u_1\nβ : Type ?u.884606\nγ : Type ?u.884609\nδ : Type ?u.884612\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nm : MeasurableSpace α\nι : Type u_2\nf : α →ₛ ℝ≥0∞\nμ : ι → Measure α\n⊢ (∑' (x : { x // x ∈ SimpleFunc.range f }) (i : ι), ↑x * ↑↑(μ i) (↑f ⁻¹' {↑x})) =\n ∑' (i : ι) (x : { x... | [
1062,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.embedding_coe | [
{
"state_after": "α : Type ?u.1479\nβ : Type ?u.1482\nγ : Type ?u.1485\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\n⊢ OrdConnected (Iio ⊤)",
"state_before": "α : Type ?u.1479\nβ : Type ?u.1482\nγ : Type ?u.1485\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\n⊢ OrdConne... | [
54,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | eq_or_eq_neg_of_sq_eq_sq | [] | [
301,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Set/Prod.lean | Set.snd_image_prod | [] | [
373,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.strongInductionOn_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.74655\ns✝ t : Finset α\nf : α → β\nn : ℕ\np : Finset α → Sort u_2\ns : Finset α\nH : (s : Finset α) → ((t : Finset α) → t ⊂ s → p t) → p s\n⊢ strongInduction H s = H s fun t x => strongInduction H t",
"state_before": "α : Type u_1\nβ : Type ?u.74655\ns✝ t : Finset... | [
660,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.node4L_size | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\nhm : Sized m\n⊢ size (node4L l x m y r) = size l + size m + size r + 2",
"tactic": "cases m <;> simp [node4L, node3L, node'] <;> [skip; simp [size, hm.1]] <;> abel"
}
] | [
399,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.congr_arg | [] | [
278,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.zsmul_apply | [] | [
581,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.coeFn_univ | [] | [
144,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_dvd_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.103818\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Monoid R\na : R\nm n : ℕ\nh : m ≤ n\n⊢ a ^ n = a ^ m * a ^ (n - m)",
"tactic": "rw [← pow_add, Nat.add_comm, Nat.sub_add_cancel h]"
... | [
444,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.comp_map | [
{
"state_after": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nα β γ : TypeVec n\nf : α ⟹ β\ng : β ⟹ γ\nx : F α\n⊢ (g ⊚ f) <$$> abs (repr x) = g <$$> f <$$> abs (repr x)",
"state_before": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nα β γ : TypeVec n\nf : α ⟹ β\n... | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.continuousOn_exp | [] | [
128,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.hasSum_of_hasSum_Lp | [
{
"state_after": "case h.e'_6\nα : Type u_2\nE : Type u_4\nF : Type ?u.15733246\nG : Type ?u.15733249\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedAddCommGroup G\ninst✝⁸ : TopologicalSpace α\ninst✝⁷ : Bo... | [
1759,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1755,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_inv | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\nh : c ⟶ d\ni : d ⟶ e\n⊢ inv ((α_ (f ≫ g) h i).inv ≫ (α_ f g h).hom ▷ i ≫ (α_ f (g ≫ h) i).hom) =\n inv ((α_ f g (h ≫ i)).hom ≫ f ◁ (α_ g h i).inv)",
"tactic": "simp"
}
] | [
275,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_comm | [] | [
448,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearMap.linearIndependent_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.109994\nR : Type u_1\nK : Type ?u.110000\nM : Type u_2\nM' : Type u_3\nM'' : Type ?u.110009\nV : Type u\nV' : Type ?u.110014\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M'... | [
246,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
11
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.eq_aleph_of_eq_card_ord | [
{
"state_after": "case intro\no : Ordinal\nho : ord (card o) = o\nho' : ω ≤ o\na : Ordinal\nha : ord (aleph' a) = o\n⊢ ∃ a, ord (aleph a) = o",
"state_before": "o : Ordinal\nho : ord (card o) = o\nho' : ω ≤ o\n⊢ ∃ a, ord (aleph a) = o",
"tactic": "cases' eq_aleph'_of_eq_card_ord ho with a ha"
},
{
... | [
389,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_lt_iff_nontrivial | [
{
"state_after": "no goals",
"state_before": "α✝ β α : Type u\n⊢ 1 < (#α) ↔ Nontrivial α",
"tactic": "rw [← not_le, le_one_iff_subsingleton, ← not_nontrivial_iff_subsingleton, Classical.not_not]"
}
] | [
746,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.of_disjoint_inf_of_le' | [] | [
177,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\n𝓟 : Ideal R\nf : R[X]\nhf✝ : IsWeaklyEisensteinAt f 𝓟\nS : Type v\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\np : R\nx : S\nhx : ↑(aeval x) f = 0\nhmo : Monic f\nhf : IsWeaklyEisensteinAt f (Submodule.span R {p})\ni : ℕ\nhi : natDegree (Polynomial.map (algebra... | [
125,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Order/SMul.lean | Tactic.smul_ne_zero_of_pos_of_ne_zero | [] | [
321,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
9
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_div_den | [
{
"state_after": "a b c r : ℚ\n⊢ ↑r.num / ↑↑r.den = r",
"state_before": "a b c r : ℚ\n⊢ ↑r.num / ↑r.den = r",
"tactic": "rw [← Int.cast_ofNat]"
},
{
"state_after": "no goals",
"state_before": "a b c r : ℚ\n⊢ ↑r.num / ↑↑r.den = r",
"tactic": "erw [← divInt_eq_div, num_den]"
}
] | [
511,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
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