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/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_eq_one_iff | [] | [
227,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_sdiff_diag | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.119528\nγ : Type ?u.119531\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\n⊢ s ×ˢ s \\ diag s = offDiag s",
"tactic": "rw [← diag_union_offDiag, union_comm, union_sdiff_self,\n sdiff_eq_self_of_disjoint (disjoint_diag_offDiag _)... | [
375,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finset.coe_einfsep | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34662\ninst✝¹ : EDist α\nx y : α\ns✝ t : Set α\ninst✝ : DecidableEq α\ns : Finset α\n⊢ einfsep ↑s = Finset.inf (Finset.offDiag s) (uncurry edist)",
"tactic": "simp_rw [einfsep_of_fintype, ← Finset.coe_offDiag, Finset.toFinset_coe]"
... | [
191,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | AddSubmonoid.toSubmonoid'_closure | [] | [
118,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.toLex_strictMono | [
{
"state_after": "ι : Type u_1\nβ : ι → Type u_2\nr : ι → ι → Prop\ns : {i : ι} → β i → β i → Prop\ninst✝² : LinearOrder ι\ninst✝¹ : IsWellOrder ι fun x x_1 => x < x_1\ninst✝ : (i : ι) → PartialOrder (β i)\nx y : (i : ι) → β i\ni✝ : ι\na✝ : β i✝\na b : (i : ι) → β i\nh : a < b\ni : ι\nhi : i ∈ {i | a i ≠ b i}\n... | [
140,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_mul_C | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ ↑(coeff R n) (φ * ↑(C σ R) a) = ↑(coeff R n) φ * a",
"tactic": "simpa using coeff_add_mul_monomial n 0 φ a"
}
] | [
449,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_le_iff' | [] | [
362,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | snd_integral | [] | [
1197,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Data/List/Basic.lean | List.get?_length | [] | [
1249,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_zero | [] | [
56,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_le_of_le_one' | [] | [
742,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | span_gcd | [
{
"state_after": "case mk.intro\nR : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : GCDMonoid R\nx y d : R\nhd : Ideal.span {x, y} = Submodule.span R {d}\n⊢ Ideal.span {gcd x y} = Ideal.span {x, y}",
"state_before": "R : Type u\nM : Type v\ninst✝³ : Co... | [
374,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal (2 • θ) = 2 * toReal θ - 2 * π ↔ π / 2 < toReal θ",
"tactic": "rw [two_zsmul, ← two_nsmul, two_nsmul_toReal_eq_two_mul_sub_two_pi]"
}
] | [
709,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_lt_ofReal_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.806824\nβ : Type ?u.806827\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nh : 0 < q\n⊢ ENNReal.ofReal p < ENNReal.ofReal q ↔ p < q",
"tactic": "rw [ENNReal.ofReal, ENNReal.ofReal, coe_lt_coe, Real.toNNReal_lt_toNNReal_iff h]"
}
] | [
2105,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2104,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_union_inter | [] | [
2149,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2148,
1
] |
Mathlib/Analysis/Complex/RemovableSingularity.lean | Complex.tendsto_limUnder_of_differentiable_on_punctured_nhds_of_isLittleO | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nhd : ∀ᶠ (x : ℂ) in 𝓝 c, x ∈ {c}ᶜ → DifferentiableAt ℂ f x\nho : (fun z => f z - f c) =o[𝓝[{c}ᶜ] c] fun z => (z - c)⁻¹\n⊢ Tendsto f (𝓝[{c}ᶜ] c) (𝓝 (limUnder (𝓝[{c}ᶜ] c) f))",
... | [
128,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_pi_apply | [] | [
847,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.union_mem_sup | [] | [
563,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | fderivInnerClm_apply | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
src/lean/Init/Core.lean | Quot.indBeta | [] | [
1222,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1218,
11
] |
Mathlib/Data/PNat/Interval.lean | PNat.map_subtype_embedding_Ioc | [] | [
56,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.frequently_mem | [] | [
1976,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1974,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_map_eq_of_injective | [] | [
568,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/RingTheory/FiniteType.lean | Algebra.FiniteType.iff_quotient_mvPolynomial'' | [
{
"state_after": "case mp\nR : Type u_1\nA : Type u\nB : Type ?u.54036\nM : Type ?u.54039\nN : Type ?u.54042\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\n⊢ Fi... | [
164,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | isClosedMap_mul_right | [] | [
140,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\n⊢ Set.Infinite (s ∪ t) ↔ Set.Infinite s ∨ Set.Infinite t",
"tactic": "simp only [Set.Infinite, finite_union, not_and_or]"
}
] | [
1317,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.factorization_pow | [
{
"state_after": "no goals",
"state_before": "p k : ℕ\nhp : Prime p\n⊢ Nat.factorization (p ^ k) = single p k",
"tactic": "simp [hp]"
}
] | [
286,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.symmDiff | [] | [
216,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
11
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.quotientSubgroupOfEmbeddingOfLe_apply_mk | [] | [
701,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.ext | [] | [
481,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | measurableSet_eq | [] | [
288,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.trans_eventuallyLE | [] | [
155,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/BigOperators/NatAntidiagonal.lean | Finset.Nat.prod_antidiagonal_eq_prod_range_succ | [] | [
76,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_apply_of_mem_supported | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u_3\nN : Type ?u.286502\nP : Type ?u.286505\nR : Type u_2\nS : Type ?u.286511\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoi... | [
554,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.abs_mem_subalgebra_closure | [
{
"state_after": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf : { x // x ∈ A }\nf' : C(X, ↑(Set.Icc (-‖↑f‖) ‖↑f‖)) := attachBound ↑f\n⊢ abs ↑f ∈ Subalgebra.topologicalClosure A",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpa... | [
119,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Int/Basic.lean | Int.toNat_coe_nat | [] | [
295,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
9
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_iff_pairwise | [] | [
105,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_const_mul_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : Field β\ninst✝ : ContinuousMul β\nc : β\nhc0 : c ≠ 0\nh : SuperpolynomialDecay l k fun n => c * f n\nx : α\n⊢ c⁻¹ * (c * f x) = f x",
"tactic": "simp [← mul_ass... | [
212,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Grade.lean | grade_injective | [] | [
175,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/Hom/Group.lean | map_div' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.45321\nβ : Type ?u.45324\nM : Type ?u.45327\nN : Type ?u.45330\nP : Type ?u.45333\nG : Type u_1\nH : Type u_2\nF : Type u_3\ninst✝⁴ : MulOneClass M\ninst✝³ : MulOneClass N\ninst✝² : DivInvMonoid G\ninst✝¹ : DivInvMonoid H\ninst✝ : MonoidHomClass F G ... | [
421,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_mul | [] | [
193,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_map_eq_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.582453\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.582462\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nH : Subgroup G\nh : ker f ≤ H\n⊢ comap f (map f H) = H",
"tactic": "rwa [comap_map_eq, sup_eq_left]... | [
3064,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3063,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_map_vecMul | [
{
"state_after": "case h\nι : Type u_3\nι' : Type u_4\nκ : Type ?u.263788\nκ' : Type ?u.263791\nR : Type u_2\nM : Type ?u.263797\ninst✝⁸ : CommSemiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nR₂ : Type ?u.263984\nM₂ : Type ?u.263987\ninst✝⁵ : CommRing R₂\ninst✝⁴ : AddCommGroup M₂\ninst✝³ : Module R₂ M... | [
128,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.transpose | [] | [
78,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.normUnit_content | [
{
"state_after": "case pos\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nhp0 : content p = 0\n⊢ normUnit (content p) = 1\n\ncase neg\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nhp0 : ¬content p = 0\n⊢ normU... | [
186,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.IsComplement.existsUnique | [] | [
88,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_iSup_homogeneousIdeal | [] | [
260,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_re_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.367192\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y : F\n⊢ ↑re (inner x y) = ↑re (inner y x)",
"tactic": "rw [← inner_conj_symm, conj_re]"
}
] | [
234,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.splits_domain | [] | [
74,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_eq_of_mem_sphere' | [] | [
708,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_nat_pow_near | [
{
"state_after": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\nx y : α\nhx : 1 ≤ x\nhy : 1 < y\nh : ∃ n, x < y ^ n\n⊢ ∃ n, y ^ n ≤ x ∧ x < y ^ (n + 1)",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\nx y : α\nhx : 1 ≤ x\nhy : 1 < y\n⊢ ∃ n, y ^ n ≤ x... | [
190,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_ring' | [] | [
530,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_sup_hom' | [] | [
1318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumCompl_apply_symm_of_pos | [] | [
533,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.scanl_singleton | [
{
"state_after": "n : ℕ\nα : Type u_1\nβ : Type u_2\nf : β → α → β\nb : β\nv✝ : Vector α n\nv : Vector α 1\n⊢ scanl f b (head v ::ᵥ tail v) = b ::ᵥ f b (head (head v ::ᵥ tail v)) ::ᵥ nil",
"state_before": "n : ℕ\nα : Type u_1\nβ : Type u_2\nf : β → α → β\nb : β\nv✝ : Vector α n\nv : Vector α 1\n⊢ scanl f b ... | [
358,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_fintypeIoc | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Fintype.card ↑(Set.Ioc a b) = b - a",
"tactic": "rw [Fintype.card_ofFinset, card_Ioc]"
}
] | [
139,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodCongr_symm | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Computability/Reduce.lean | OneOneEquiv.le_congr_left | [] | [
255,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Order/Max.lean | not_isMax | [] | [
356,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Resp.Equiv.refl | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
11
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_iff_zero_or_omega_opow | [
{
"state_after": "case inl\n\n⊢ Principal (fun x x_1 => x + x_1) 0 ↔ 0 = 0 ∨ ∃ a, 0 = ω ^ a\n\ncase inr\no : Ordinal\nho : o ≠ 0\n⊢ Principal (fun x x_1 => x + x_1) o ↔ o = 0 ∨ ∃ a, o = ω ^ a",
"state_before": "o : Ordinal\n⊢ Principal (fun x x_1 => x + x_1) o ↔ o = 0 ∨ ∃ a, o = ω ^ a",
"tactic": "rcase... | [
242,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_bot_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58216\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\n⊢ Icc ⊥ ⊤ = univ",
"tactic": "simp"
}
] | [
1036,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeights_eq_one_of_nonempty | [] | [
827,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.116823\nE : Type u_1\nF : Type ?u.116829\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nc : E\n⊢ (∫ (x : α) in s... | [
448,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuous_finset_prod | [] | [
765,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.natDegree_cyclotomic' | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R\nn : ℕ\nh : IsPrimitiveRoot ζ n\n⊢ natDegree (∏ μ in primitiveRoots n R, (X - ↑C μ)) = Nat.totient n",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R\nn : ℕ\nh : IsPrimitiveRoot ζ n\n⊢ natDegree (cy... | [
119,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Maps.lean | Embedding.closure_eq_preimage_closure_image | [] | [
255,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.hom_inv_whiskerLeft | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng h : b ⟶ c\nη : g ≅ h\n⊢ f ◁ η.hom ≫ f ◁ η.inv = 𝟙 (f ≫ g)",
"tactic": "rw [← whiskerLeft_comp, hom_inv_id, whiskerLeft_id]"
}
] | [
200,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.inf_toSubalgebra | [
{
"state_after": "case h\nF : Type ?u.670328\nR : Type u_1\nA : Type u_2\nB : Type ?u.670337\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRing B\ninst✝ : StarModule ... | [
665,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Algebra/Regular/Pow.lean | IsLeftRegular.pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\na b : R\ninst✝ : Monoid R\nn : ℕ\nrla : IsLeftRegular a\n⊢ IsLeftRegular (a ^ n)",
"tactic": "simp only [IsLeftRegular, ← mul_left_iterate, rla.iterate n]"
}
] | [
34,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_lt_top | [] | [
295,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
9
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.add | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousAdd β\nhf : SuperpolynomialDecay l k f\nhg : SuperpolynomialDecay l k g\nz : ℕ\n⊢ Tendsto (fun a => k a ^ z * (f + g) a) l (𝓝 0)"... | [
89,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MulticospanIndex.multicospan_obj_left | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.fst | [] | [
347,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.isConjugateExponent_conjugateExponent | [] | [
127,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.Γ_obj | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_gcd_self_right_left | [] | [
162,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
161,
9
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.comp_ite | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nP : Prop\ninst✝ : Decidable P\nX Y Z : C\nf : X ⟶ Y\ng g' : Y ⟶ Z\n⊢ (f ≫ if P then g else g') = if P then f ≫ g else f ≫ g'",
"tactic": "aesop"
}
] | [
243,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_l_eq | [] | [
772,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_insert | [] | [
902,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Algebra/Ring/Units.lean | Units.divp_sub | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : Ring α\na✝ b✝ a b : α\nu : αˣ\n⊢ b = b * ↑u * ↑u⁻¹",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : Ring α\na✝ b✝ a b : α\nu : αˣ\n⊢ a /ₚ u - b = (a - b * ↑u) /ₚ u",
"tactic": "simp only [divp, sub_mul, s... | [
91,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | LinearOrderedField.smul_Iio | [
{
"state_after": "case h\nα : Type ?u.63203\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\nx : K\n⊢ x ∈ r • Iio a ↔ x ∈ Iio (r • a)",
"state_before": "α : Type ?u.63203\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\n⊢ r • Iio a = Iio (r • a)",
"tactic": "ext x"
... | [
267,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.nhds_le | [] | [
379,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff_ne_bot | [] | [
880,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_zsmul_eq | [] | [
245,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.pmap | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nR S✝ T : α → α → Prop\na : α\nl✝ l : List α\nhl : Pairwise R l\np : α → Prop\nf : (a : α) → p a → β\nh : ∀ (x : α), x ∈ l → p x\nS : β → β → Prop\nhS : ∀ ⦃x : α⦄ (hx : p x) ⦃y : α⦄ (hy : p y), R x y → S (f x hx) (f y hy)\n⊢ ∀ {a b : α}, a ∈ l → b ∈ l → R a b → ∀ (h₁... | [
250,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_subtype' | [] | [
1207,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.embedding_of_pullback_embeddings | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\ng : Y ⟶ S\nH₁ : Embedding ((forget TopCat).map f)\nH₂ : Embedding ((forget TopCat).map g)\ne_2✝ : (forget TopCat).obj ((cospan f g).obj WalkingCospan.one) = (forget TopCat).obj S\n⊢ (forget TopCat)... | [
313,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.comap_unop_mul | [
{
"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\n⊢ comap (↑(LinearEquiv.symm (opLinearEquiv R))) (M * N) =\n comap (↑(LinearEquiv.symm (opLinearEquiv R))) N ... | [
300,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Set/Sups.lean | Set.image_subset_sups_right | [] | [
102,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Ioo_left | [] | [
497,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_eq_right₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11641\nM₀ : Type u_1\nG₀ : Type ?u.11647\nM₀' : Type ?u.11650\nG₀' : Type ?u.11653\nF : Type ?u.11656\nF' : Type ?u.11659\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\nhb : b ≠ 0\n⊢ a * b = b ↔ a = 1",
"tactic": "rw [Iff.comm, ← mul_left_inj' hb,... | [
208,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_left_of_right_le'' | [] | [
1102,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.tensorObj_map | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.hasIntegral_const | [] | [
318,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftAlgHom_injective | [] | [
971,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_refl_apply | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.13387\nX : Type u_1\nY : Type ?u.13393\nZ : Type ?u.13396\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS A B C : DiscreteQuotient X\na : Quotient A.toSetoid\n⊢ ofLE (_ : A ≤ A) a = a",
"tactic": "simp"
... | [
221,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.mod_mul_left_div_self | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k✝ l m n k : ℕ\n⊢ m % (k * n) / n = m / n % k",
"tactic": "rw [mul_comm k, mod_mul_right_div_self]"
}
] | [
480,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Iic_iff_integrableOn_Iio | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4685922\nE : Type u_2\nF : Type ?u.4685928\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ 0 ≠ ⊤",
"state_before": "α : ... | [
709,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Data/List/Zip.lean | List.get?_zip_with_eq_some | [
{
"state_after": "case nil\nα✝ : Type u\nβ✝ : Type ?u.112193\nγ✝ : Type ?u.112196\nδ : Type ?u.112199\nε : Type ?u.112202\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\nz : γ\nl₂ : List β\ni : ℕ\n⊢ get? (zipWith f [] l₂) i = some z ↔ ∃ x y, get? [] i = some x ∧ get? l₂ i = some y ∧ f x y = z\n\ncase ... | [
386,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
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