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/Algebra/GroupWithZero/Units/Lemmas.lean | mul_div_cancel_of_imp | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9473\nM₀ : Type ?u.9476\nG₀ : Type u_1\nM₀' : Type ?u.9482\nG₀' : Type ?u.9485\nF : Type ?u.9488\nF' : Type ?u.9491\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na✝ b✝ c a b : G₀\nh : b = 0 → a = 0\nhb : b = 0\n⊢ a * b / b = a",
"tactic"... | [
144,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.inv_zetaUnit | [] | [
1080,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
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Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbent.zero_mem | [] | [
402,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr' | [] | [
124,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.pow_mul_meas_ge_le_norm | [] | [
1788,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittPow_vars | [] | [
426,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_toEquiv | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.quotientToQuotientRangePowQuotSuccAux_mk | [
{
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"state_before": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhfp : NeZero e\ni : ℕ\na : S\na_mem : a ∈ P ^ i\nx : S\n⊢ quotientToQuotientRangePowQuotSuccAux f p P a_mem (Submodule.Quotient.mk x) =\n Submodule.Quotien... | [
525,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.div_mem_nhds_one_of_haar_pos | [
{
"state_after": "G : Type u_1\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : T2Space G\ninst✝⁵ : TopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : SecondCountableTopology G\nμ : Measure G\ninst✝¹ : IsHaarMeasure μ\ninst✝ : LocallyCompactSpace G\nE : Set G\nhE : Measurabl... | [
798,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
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Mathlib/Logic/Function/Basic.lean | Function.const_inj | [] | [
60,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_pow_of_pell_lem | [
{
"state_after": "a y k : ℕ\nhy0 : y ≠ 0\nhk0 : k ≠ 0\nhyk : y ^ k < a\nhya : y < a\n⊢ 1 < ↑a",
"state_before": "a y k : ℕ\nhy0 : y ≠ 0\nhk0 : k ≠ 0\nhyk : y ^ k < a\nhya : y < a\n⊢ ↑a ≤ ↑a ^ 2 - (↑a - 1) ^ 2 - 1",
"tactic": "rw [sub_sq, mul_one, one_pow, sub_add, sub_sub_cancel, two_mul, sub_sub, ← add... | [
942,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\np : α\nhp : Irreducible p\nk : ℕ\n⊢ normalizedFactors (p ^ k) = Multiset.replicate k (↑normalize p)",
"tactic": "r... | [
742,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.norm_setToL1_le_mul_norm | [] | [
1230,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_sdiff | [] | [
337,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_pow | [] | [
527,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/Data/Nat/Parity.lean | Nat.two_not_dvd_two_mul_add_one | [
{
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"tactic": "simp [add_mod]"
}
] | [
133,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nA : Type u₂\ninst✝¹ : Category A\nJ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ A\nX : C\nS : Sieve X\nR : Presieve X\nE : Aᵒᵖ\nx : FamilyOfElements (P ⋙ coyoneda.obj E) S.arrows\nhx : SieveCompatible x\ninst✝ : HasPullbacks C\nK : Pretopology C\n⊢ (∀ (E : A), Presiev... | [
210,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Logic/Lemmas.lean | ite_dite_distrib_left | [] | [
48,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.neg_eq_self_iff | [
{
"state_after": "n : ℕ\na : ZMod n\n⊢ 2 * a = 0 ↔ a = 0 ∨ 2 * val a = n",
"state_before": "n : ℕ\na : ZMod n\n⊢ -a = a ↔ a = 0 ∨ 2 * val a = n",
"tactic": "rw [neg_eq_iff_add_eq_zero, ← two_mul]"
},
{
"state_after": "case zero\na : ZMod Nat.zero\n⊢ 2 * a = 0 ↔ a = 0 ∨ 2 * val a = Nat.zero\n\nca... | [
871,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
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Mathlib/RingTheory/PolynomialAlgebra.lean | matPolyEquiv_coeff_apply_aux_1 | [
{
"state_after": "R : Type u_1\nA : Type ?u.483263\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\ni j : n\nk : ℕ\nx : R\n⊢ ↑(AlgEquiv.symm (polyEquivTensor R (Matrix n n R)))\n (↑(Algebra.TensorProduct.comm R R[X] (Matrix n n R)) ... | [
244,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/Data/Complex/Basic.lean | Complex.re_eq_add_conj | [
{
"state_after": "z : ℂ\nthis : ↑2 = 2\n⊢ ↑z.re = (z + ↑(starRingEnd ℂ) z) / 2",
"state_before": "z : ℂ\n⊢ ↑z.re = (z + ↑(starRingEnd ℂ) z) / 2",
"tactic": "have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := by rfl"
},
{
"state_after": "no goals",
"state_before": "z : ℂ\nthis : ↑2 = 2\n⊢ ↑z.re = (z + ↑(st... | [
888,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.iSup_coe_nat | [] | [
2492,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2491,
1
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Mathlib/RingTheory/NonZeroDivisors.lean | mul_right_mem_nonZeroDivisors_eq_zero_iff | [
{
"state_after": "no goals",
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52,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_apply | [] | [
780,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_one_of_one_le_of_nonpos | [] | [
213,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Data/Set/NAry.lean | Set.image_image2_antidistrib | [
{
"state_after": "α : Type u_3\nα' : Type u_6\nβ : Type u_4\nβ' : Type u_5\nγ : Type u_2\nγ' : Type ?u.47516\nδ : Type u_1\nδ' : Type ?u.47522\nε : Type ?u.47525\nε' : Type ?u.47528\nζ : Type ?u.47531\nζ' : Type ?u.47534\nν : Type ?u.47537\nf f'✝ : α → β → γ\ng✝ g' : α → β → γ → δ\ns s' : Set α\nt t' : Set β\nu... | [
401,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_eq_of_le | [] | [
66,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.mem_span_pow' | [
{
"state_after": "R : Type u_2\nS : Type u_1\nT : Type ?u.12701\ninst✝⁷ : CommRing R\ninst✝⁶ : Ring S\ninst✝⁵ : Algebra R S\nA : Type ?u.13004\nB : Type ?u.13007\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : IsDomain B\ninst✝¹ : Algebra A B\nK : Type ?u.13429\ninst✝ : Field K\nx y : S\nd : ℕ\nthis : (Set.... | [
105,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_im_le | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | z.im ≤ a} = {z | z.im = a}",
"tactic": "simpa only [frontier_Iic] using frontier_preimage_im (Iic a)"
}
] | [
143,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearMap.injective_iff_surjective | [] | [
921,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.exists_closedBall_covering_tsum_measure_le | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝⁶ : MetricSpace α\nβ : Type u\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : MeasureTheory.Measure α\ninst✝¹ : SigmaFinite μ\ninst✝ : Measure.OuterRegular μ\nε :... | [
1085,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.iInf_const_zero | [
{
"state_after": "ι : Sort ?u.273037\nf : ι → ℝ≥0\nα : Sort u_1\n⊢ (⨅ (i : α), ↑0) = ↑0",
"state_before": "ι : Sort ?u.273037\nf : ι → ℝ≥0\nα : Sort u_1\n⊢ (⨅ (x : α), 0) = 0",
"tactic": "rw [← NNReal.coe_eq, coe_iInf]"
},
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.273037\nf :... | [
950,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
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Mathlib/Order/Lattice.lean | MonotoneOn.sup | [] | [
1137,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
11
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Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | hasFDerivAt_of_tendstoLocallyUniformlyOn | [
{
"state_after": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_3\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx : E\ninst✝ : ... | [
410,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_int | [
{
"state_after": "α : Type u\nβ : Type v\nf : α → β\nx y : FreeCommRing α\ns✝ t : Set α\ni✝ : ℤ\ns : Set α\ni : ℕ\nhi : IsSupported (↑↑i) s\n⊢ IsSupported (↑↑i + 1) s",
"state_before": "α : Type u\nβ : Type v\nf : α → β\nx y : FreeCommRing α\ns✝ t : Set α\ni✝ : ℤ\ns : Set α\ni : ℕ\nhi : IsSupported (↑↑i) s\... | [
216,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.nat_power_eq | [
{
"state_after": "no goals",
"state_before": "c : Cardinal\nh : ℵ₀ ≤ c\nn : ℕ\nhn : 2 ≤ n\n⊢ 2 ≤ ↑n",
"tactic": "assumption_mod_cast"
}
] | [
954,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.det_of_card_zero | [
{
"state_after": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nα β : Type v\ninst✝ : DecidableEq α\nM✝ : Matrix n n R\nh : IsEmpty n\nM : Matrix n n R\n⊢ det M = 1",
"state_before": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ :... | [
98,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure | [] | [
140,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.121444\ns : Multiset α\nf : α → β\n⊢ map f s = 0 ↔ s = 0",
"tactic": "rw [← Multiset.card_eq_zero, Multiset.card_map, Multiset.card_eq_zero]"
}
] | [
1239,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toDual_mul | [] | [
114,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | SemiconjBy.function_semiconj_mul_left | [
{
"state_after": "M : Type ?u.84938\nN : Type ?u.84941\nG : Type u_1\nH : Type ?u.84947\ninst✝ : Semigroup G\na b c : G\nh : SemiconjBy a b c\nj : G\n⊢ a * (b * j) = c * (a * j)",
"state_before": "M : Type ?u.84938\nN : Type ?u.84941\nG : Type u_1\nH : Type ?u.84947\ninst✝ : Semigroup G\na b c : G\nh : Semi... | [
240,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_nonpos_ae | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.297148\nE : Type ?u.297151\nF : Type ?u.297154\ninst✝ : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\ns : Set α\nhs : MeasurableSet s\nhf : ∀ᵐ (a : α) ∂μ, a ∈ s → f a ≤ 0\n⊢ (fun a => f a) ≤ᵐ[Measure.restrict μ s] 0",
"tactic": "rwa ... | [
769,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_le_lowerSemicontinuous_lintegral_ge | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : WeaklyRegular μ\nf : α → ℝ≥0∞\nhf : Measurable f\nε : ℝ≥0∞\nεpos : ε ≠ 0\nδ : ℕ → ℝ≥0∞\nδpos : ∀ (i : ℕ), 0 < δ i\nhδ : (∑' (i : ℕ), δ i) < ε\n⊢ ∃ g, (∀ (x : α... | [
200,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.disjSum_mono_left | [] | [
90,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_of_ae_restrict_of_ae_restrict_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.576854\nγ : Type ?u.576857\nδ : Type ?u.576860\nι : Type ?u.576863\nR : Type ?u.576866\nR' : Type ?u.576869\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t✝ t : S... | [
2857,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2848,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.sequence_mono | [] | [
2786,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2784,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius | [] | [
252,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na b : α\n⊢ destutter' R a [b] = if R a b then [a, b] else [a]",
"tactic": "split_ifs with h <;> simp! [h]"
}
] | [
64,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_def' | [] | [
219,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.add_product | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.59441\nδ : Type ?u.59444\na : α\nb : β\ns✝ : Multiset α\nt✝ : Multiset β\ns t : Multiset α\nu : Multiset β\n⊢ (s + t) ×ˢ u = s ×ˢ u + t ×ˢ u",
"tactic": "simp [SProd.sprod, product]"
}
] | [
280,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_compl_eq_card_compl | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.59809\nγ : Type ?u.59812\ninst✝⁴ : Finite α\np q : α → Prop\ninst✝³ : Fintype { x // p x }\ninst✝² : Fintype { x // ¬p x }\ninst✝¹ : Fintype { x // q x }\ninst✝ : Fintype { x // ¬q x }\nh : card { x // p x } = card { x // q x }\nval✝ : Fintype α\n⊢ card { ... | [
871,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.inclusion_right | [] | [
1062,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_le_prod_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.187458\nι : Sort ?u.187461\nκ : ι → Sort ?u.187466\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : LowerSet α\nt t₁ t₂ : LowerSet β\nx : α × β\n⊢ ↑s₁ ⊆ ↑s₂ ∧ ↑t₁ ⊆ ↑t₂ ∨ ↑s₁ = ∅ ∨ ↑t₁ = ∅ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨... | [
1732,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.symm_trans_apply | [] | [
903,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_replicate | [
{
"state_after": "case zero\nι : Type ?u.13701\nα : Type ?u.13704\nM : Type u_1\nN : Type ?u.13710\nP : Type ?u.13713\nM₀ : Type ?u.13716\nG : Type ?u.13719\nR : Type ?u.13722\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na✝ a : M\n⊢ prod (replicate Nat.zero a) = a ^ Nat.zero\n\ncas... | [
84,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_mem_Ico_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\nx y ε : α\nhx : 0 < x\nhy : 1 < y\n⊢ ∃ n, x ∈ Ico (y ^ n) (y ^ (n + 1))",
"tactic": "classical exact\n let ⟨N, hN⟩ := pow_unbounded_of_one_lt x⁻¹ hy\n have he : ∃ m : ℤ, y ^ m ≤ x :=\n... | [
218,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.antidiagonal_succ_succ' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ¬(n + 2, 0) ∈\n map\n (Function.Embedding.prodMap { toFun := Nat.succ, inj' := Nat.succ_injective }\n { toFun := Nat.succ, inj' := Nat.succ_injective })\n (antidiagonal n)",
"tactic": "simp"
},
{
"state_after": "n... | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_mul_singleton | [] | [
1912,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1911,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | norm_mk_eq_zero | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.361198\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nhS : IsClosed ↑S\nm : M\nh : ‖↑(mk' S) m‖ = 0\n⊢ m ∈ S",
"tactic": "rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h"
}
] | [
229,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | Fintype.linearIndependent_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.36281\nR : Type u_1\nK : Type ?u.36287\nM : Type u_2\nM' : Type ?u.36293\nM'' : Type ?u.36296\nV : Type u\nV' : Type ?u.36301\nv : ι → M\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M... | [
169,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_sup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.101691\nβ₂ : Type ?u.101694\nγ : Type ?u.101697\nι : Sort u_1\nι' : Sort ?u.101703\nκ : ι → Sort ?u.101708\nκ' : ι' → Sort ?u.101713\ninst✝¹ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b : α\ninst✝ : Nonempty ι\nf : ι → α\na : α\n⊢ (⨆ (x ... | [
1250,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_one_eq_bot | [
{
"state_after": "case intro.intro\nG : Type u_2\nG' : Type ?u.252260\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.252269\ninst✝² : AddGroup A\nH K : Subgroup G\nk : Set G\nN : Type u_1\ninst✝¹ : Group N\nP : Type ?u.252296\ninst✝ : Group P\ny : G\nleft✝ : y ∈ ↑K\n⊢ ↑1 y ∈ ⊥",
"state_before": "G : Type... | [
1452,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | not_small_ordinal | [] | [
2142,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2141,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | Measurable.comp_aemeasurable | [] | [
728,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_comap | [] | [
256,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsLowerSet.inv | [] | [
99,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ici_iSup₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.115994\nγ : Type ?u.115997\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : CompleteLattice α\nf : (i : ι) → κ i → α\n⊢ Ici (⨆ (i : ι) (j : κ i), f i j) = ⨆ (i : ι) (j : κ i), Ici (f i j)",
"tactic": "simp_rw [Ici_iSup]"
}
] | [
1154,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_neg_one | [] | [
584,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.induction | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : Ordnode α\nhl : Sized t\nC : Ordnode α → Prop\nH0 : C nil\nH1 : ∀ (l : Ordnode α) (x : α) (r : Ordnode α), C l → C r → C (Ordnode.node' l x r)\n⊢ C t",
"tactic": "induction t with\n| nil => exact H0\n| node _ _ _ _ t_ih_l t_ih_r =>\n rw [h... | [
132,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.star_apply | [] | [
2348,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2347,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_integral_norm_Ioc | [] | [
546,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_eq_zero_iff | [] | [
351,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.coeFn_smul_apply | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_2\ninst✝⁵ : MeasurableSpace Ω\nR : Type u_1\ninst✝⁴ : SMul R ℝ≥0\ninst✝³ : SMul R ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0 ℝ≥0\nc : R\nμ : FiniteMeasure Ω\ns : Set Ω\n⊢ (fun s => ENNReal.... | [
270,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_bot | [] | [
1204,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.evaln_bound | [
{
"state_after": "no goals",
"state_before": "c : Code\nn x : ℕ\nh : x ∈ evaln 0 c n\n⊢ n < 0",
"tactic": "simp [evaln] at h"
},
{
"state_after": "k : ℕ\nc : Code\nn x : ℕ\nh : x ∈ evaln (k + 1) c n\n⊢ ∀ {o : Option ℕ},\n (x ∈ do\n guard (n ≤ k)\n o) →\n n < k + 1",
"st... | [
783,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.toFun_eq_coe | [] | [
75,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast?_cons_cons | [] | [
773,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_single_iff | [
{
"state_after": "case mp\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i j : ι\nxi : β i\nxj : β j\n⊢ single i xi = single j xj → i = j ∧ HEq xi xj ∨ xi = 0 ∧ xj = 0\n\ncase mpr\nι : Type u\... | [
682,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.prodIsoProd_hom_apply | [
{
"state_after": "case h₁\nJ : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\nx : ↑(X ⨯ Y)\n⊢ ((forget TopCat).map (prodIsoProd X Y).hom x).fst =\n ((forget TopCat).map prod.fst x, (forget TopCat).map prod.snd x).fst\n\ncase h₂\nJ : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\nx : ↑(X ⨯ Y)\n⊢ ((forget TopC... | [
227,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.exists_eq_add_of_le' | [] | [
290,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.ker_eq_lift_of_injective | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.sin_arccos | [
{
"state_after": "case pos\nx : ℝ\nhx₁ : -1 ≤ x\n⊢ sin (arccos x) = sqrt (1 - x ^ 2)\n\ncase neg\nx : ℝ\nhx₁ : ¬-1 ≤ x\n⊢ sin (arccos x) = sqrt (1 - x ^ 2)",
"state_before": "x : ℝ\n⊢ sin (arccos x) = sqrt (1 - x ^ 2)",
"tactic": "by_cases hx₁ : -1 ≤ x"
},
{
"state_after": "case neg\nx : ℝ\nhx₁ ... | [
429,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.Iic_pure | [] | [
431,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | zpow_eq_mod_card | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Fintype G\nn : ℤ\n⊢ x ^ n = x ^ (n % ↑(Fintype.card G))",
"tactic": "rw [zpow_eq_mod_orderOf, ← Int.emod_emod_of_dvd n (Int.coe_nat_dvd.2 orderOf_dvd_card_univ... | [
961,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.red | [
{
"state_after": "case nil\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\n⊢ Red [] (reduce [])\n\ncase cons\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\nhd1 : α × Bool\ntl1 : List (α × Bool)\nih : Red tl1 (reduce tl1)\n⊢ Red (hd1 :: tl1) (reduce (hd1 :: tl1))",
... | [
1148,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_inf_comap_of_surjective | [] | [
1588,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1587,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.unop | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nA✝ B✝ B' X✝ Y✝ Y' : C\ni✝ : A✝ ⟶ B✝\ni' : B✝ ⟶ B'\np✝ : X✝ ⟶ Y✝\np' : Y✝ ⟶ Y'\nA B X Y : Cᵒᵖ\ni : A ⟶ B\np : X ⟶ Y\nh : HasLiftingProperty i p\nf : Y.unop ⟶ B.unop\ng : X.unop ⟶ A.unop\nsq : CommSq f p.unop i.unop g\n⊢ CommSq.HasLift (_ : CommSq g.op i.unop.op... | [
69,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.denseRange_coe₃ | [] | [
491,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Order/RelClasses.lean | eq_empty_relation | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nr✝ : α → α → Prop\ns : β → β → Prop\nr : α → α → Prop\ninst✝¹ : IsIrrefl α r\ninst✝ : Subsingleton α\n⊢ ∀ (a b : α), r a b = EmptyRelation a b",
"tactic": "simpa using not_rel_of_subsingleton r"
}
] | [
157,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.map_lift_mapBiprod | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁶ : Category C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : HasZeroMorphisms C\ninst✝³ : HasZeroMorphisms D\nF : C ⥤ D\ninst✝² : PreservesZeroMorphisms F\nX Y : C\ninst✝¹ : HasBinaryBiproduct X Y\ninst✝ : PreservesBinaryBiproduct X Y F\nW : C\nf... | [
453,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/CategoryTheory/Limits/FunctorCategory.lean | CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : HasColimitsOfShape J C\nF : J ⥤ K ⥤ C\nj : J\nk : K\n⊢ colimit.ι (F ⋙ (evaluation K C).obj k) j ≫ (preservesColimitIso ((evaluation K C).obj k) F).inv ... | [
285,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_empty | [
{
"state_after": "ι : Type ?u.4271\nα : Type u_1\nβ : Type ?u.4277\ninst✝ : Bornology α\ns t : Set α\nx : α\n⊢ univ ∈ cobounded α",
"state_before": "ι : Type ?u.4271\nα : Type u_1\nβ : Type ?u.4277\ninst✝ : Bornology α\ns t : Set α\nx : α\n⊢ IsBounded ∅",
"tactic": "rw [isBounded_def, compl_empty]"
},... | [
176,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.natAbs_inj_of_nonneg_of_nonneg | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\nha : 0 ≤ a\nhb : 0 ≤ b\n⊢ natAbs a = natAbs b ↔ a = b",
"tactic": "rw [← sq_eq_sq ha hb, ← natAbs_eq_iff_sq_eq]"
}
] | [
65,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.moveRight | [] | [
273,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Vector.lean | Vector.eq | [] | [
204,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
11
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.localInverse_apply_image | [] | [
638,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_one_lt_of_le | [] | [
1259,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1258,
1
] |
Std/Data/List/Basic.lean | List.takeD_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : Nat\na : α\n⊢ takeD n [] a = replicate n a",
"tactic": "induction n <;> simp [*]"
}
] | [
592,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
592,
9
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | interior_smul₀ | [] | [
338,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.coe_inf | [] | [
835,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
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