file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Lattice.lean | Set.subset_sUnion_of_mem | [] | [
1044,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.const | [] | [
422,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | RingHom.map_sum | [] | [
271,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.divMonomial_add | [] | [
81,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/LinearAlgebra/Ray.lean | units_smul_eq_self_iff | [
{
"state_after": "case h\nR : Type u_1\ninst✝³ : LinearOrderedCommRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : NoZeroSMulDivisors R M\nu : Rˣ\nv : M\nhv : v ≠ 0\n⊢ u • rayOfNeZero R v hv = rayOfNeZero R v hv ↔ 0 < ↑u",
"state_before": "R : Type u_1\ninst✝³ : LinearOrderedCommR... | [
581,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.to_nat_inj | [] | [
370,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Order/MinMax.lean | le_of_max_le_left | [] | [
280,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_sup_map_of_injective | [] | [
414,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_le_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.549373\nι : Type ?u.549376\ninst✝¹ : PseudoMetricSpace α\nγ : Type w\ninst✝ : MetricSpace γ\nx y : γ\n⊢ dist x y ≤ 0 ↔ x = y",
"tactic": "simpa [le_antisymm_iff, dist_nonneg] using @dist_eq_zero _ _ x y"
}
] | [
2865,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2864,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_dvd_right | [] | [
164,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_mul | [] | [
253,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ici_of_le | [] | [
1207,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_σ_succ' | [
{
"state_after": "n : ℕ\ni : Fin (n + 1)\n⊢ δ (Fin.succ i) ≫ σ i = 𝟙 [n]",
"state_before": "n : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nH : j = Fin.succ i\n⊢ δ j ≫ σ i = 𝟙 [n]",
"tactic": "subst H"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\ni : Fin (n + 1)\n⊢ δ (Fin.succ i) ≫ σ i... | [
308,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.cast_refl | [] | [
119,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.span_singleton_sup_ker_eq_top | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.366237\nR₂ : Type ?u.366240\nK : Type u_1\nM : Type ?u.366246\nM₂ : Type ?u.366249\nV : Type u_2\nS : Type ?u.366255\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : V →ₗ[K] K\nx : V\nhx : ↑f x ≠ 0\ny : V\nx✝ : y ∈ ⊤\n⊢ y - (↑f y *... | [
1002,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_mono | [] | [
808,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_C | [] | [
1442,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.26167\ninst✝ : CompleteBooleanAlgebra α\na b : α\ns : Set α\nf : ι → α\n⊢ iSup fᶜᶜ = (⨅ (i : ι), f iᶜ)ᶜ",
"tactic": "simp [compl_iInf]"
}
] | [
304,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.filter_dvd_eq_properDivisors | [
{
"state_after": "case a\nn : ℕ\nh : n ≠ 0\na✝ : ℕ\n⊢ a✝ ∈ filter (fun x => x ∣ n) (range n) ↔ a✝ ∈ properDivisors n",
"state_before": "n : ℕ\nh : n ≠ 0\n⊢ filter (fun x => x ∣ n) (range n) = properDivisors n",
"tactic": "ext"
},
{
"state_after": "case a\nn : ℕ\nh : n ≠ 0\na✝ : ℕ\n⊢ a✝ ∣ n → a✝ ... | [
74,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.toDual_apply | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | inv_mul_eq_one₀ | [] | [
56,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.of_le | [
{
"state_after": "case intro.mk.mk\nR : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.125264\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nN : Submonoid R\nh₁ : M ≤ N\nh₂ : ∀ (r : R), r ∈ N → IsUnit (↑(algebraMap R S) r)\ns :... | [
150,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix'_toBilin' | [] | [
213,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.ext | [] | [
82,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.decompId | [
{
"state_after": "case h\nC : Type u_1\ninst✝ : Category C\nP : Karoubi C\n⊢ (𝟙 P).f = (decompId_i P ≫ decompId_p P).f",
"state_before": "C : Type u_1\ninst✝ : Category C\nP : Karoubi C\n⊢ 𝟙 P = decompId_i P ≫ decompId_p P",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "... | [
279,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.insert_le_iff | [
{
"state_after": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nK : IntermediateField F E\n⊢ F⟮α⟯ ≤ K ↔ α ∈ K",
"state_before": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nK : IntermediateFie... | [
570,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.dist_eq_glueDist | [
{
"state_after": "no goals",
"state_before": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\np q : X ⊕ Y\nx : X\ny : Y\n⊢ Sum.dist p q = glueDist (fun x_1 => Nonempty.some (_ : Nonempty X)) (fun x => Nonempty.some (_ : Nonempty Y)) 1 p q",
"tactic": "cases p <;> cases... | [
215,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.hasFiniteIntegral_coeFn | [] | [
1279,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.h_apply_fromCoset | [
{
"state_after": "A B : GroupCat\nf : A ⟶ B\nx : ↑B\n⊢ ↑((τ.symm.trans (↑g x)).trans τ)\n (fromCoset\n { val := (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier,\n property :=\n (_ :\n ∃ y,\n Function.swap leftCoset (MonoidHom.range f).toSubmonoi... | [
271,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit1_le_bit0_iff | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nh : bit1 m ≤ bit0 n\n⊢ m < n",
"tactic": "rwa [m.bit1_eq_succ_bit0, succ_le_iff, bit0_lt_bit0] at h"
}
] | [
735,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.subset | [] | [
50,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypePreimage_symm_apply_coe_pos | [] | [
644,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | neg_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.114231\nM : Type ?u.114234\ninst✝¹ : Monoid R\ninst✝ : HasDistribNeg R\na : R\n⊢ (-a) ^ 2 = a ^ 2",
"tactic": "simp [sq]"
}
] | [
221,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.Squarefree.ext_iff | [
{
"state_after": "n m : ℕ\nhn : Squarefree n\nhm : Squarefree m\nh : ∀ (p : ℕ), Prime p → (p ∣ n ↔ p ∣ m)\np : ℕ\n⊢ ↑(factorization n) p = ↑(factorization m) p",
"state_before": "n m : ℕ\nhn : Squarefree n\nhm : Squarefree m\n⊢ n = m ↔ ∀ (p : ℕ), Prime p → (p ∣ n ↔ p ∣ m)",
"tactic": "refine' ⟨by rintro... | [
83,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.flip | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ν ≤ n\n⊢ Polynomial.comp (bernsteinPolynomial R n ν) (1 - X) = bernsteinPolynomial R n (n - ν)",
"tactic": "simp [bernsteinPolynomial, h, tsub_tsub_assoc, mul_right_comm]"
}
] | [
84,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.comp_continuousOn | [] | [
355,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/RingTheory/Prime.lean | mul_eq_mul_prime_pow | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst✝ : CancelCommMonoidWithZero R\np : R\nn : ℕ\nhp : Prime p\nt u : Finset ℕ\nb c : R\nhtus : t ∪ u = range n\nhtu : Disjoint t u\nhx : (b * ∏ i in t, p) * (c * ∏ i in u, p) = b * c * p ^ n\n⊢ ∃ i j b_1 c_1, i + j = n ∧ b * ... | [
60,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_biUnion | [] | [
2079,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2077,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_eq_iSup_orderOf | [
{
"state_after": "G : Type u\ninst✝ : CommMonoid G\nh : ∀ (g : G), 0 < orderOf g\n⊢ exponent G = sSup (Set.range fun g => orderOf g)",
"state_before": "G : Type u\ninst✝ : CommMonoid G\nh : ∀ (g : G), 0 < orderOf g\n⊢ exponent G = ⨆ (g : G), orderOf g",
"tactic": "rw [iSup]"
},
{
"state_after": ... | [
326,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.mul_X_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp (p * X) r = comp p r * r",
"tactic": "induction p using Polynomial.induction_on' with\n| h_add p q hp hq =>\n simp only [hp, hq, add_mul, add_comp]\n|... | [
596,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_sInf | [] | [
242,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioc_pred_right | [] | [
756,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.comp_sub | [] | [
150,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/List/Basic.lean | List.map_drop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.219275\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : Type u_1\nβ : Type u_2\nf : α → β\ni : ℕ\n⊢ map f (drop i []) = drop i (map f [])",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : T... | [
2271,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2265,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.uniformContinuous_add | [] | [
44,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.edist_def | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1284348\nδ : Type ?u.1284351\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf g : { x // x ∈ Lp β 1 }\n⊢ (∫⁻ (a : α), ↑‖↑↑f a - ↑↑g a‖₊ ∂μ) = ∫⁻ (a : α), edist (↑↑f a) (↑↑... | [
1300,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Algebra/Group/Basic.lean | leftInverse_inv_mul_mul_right | [] | [
875,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.norm_mem_unitary_mul | [] | [
249,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.op_sum | [] | [
1790,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1788,
1
] |
Mathlib/Algebra/Module/GradedModule.lean | DirectSum.Gmodule.smul_def | [] | [
96,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.map_coe | [] | [
599,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | goldConj_neg | [
{
"state_after": "no goals",
"state_before": "⊢ ψ < 0",
"tactic": "linarith [one_sub_goldConj, one_lt_gold]"
}
] | [
123,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_module | [
{
"state_after": "k : Type u_2\nV1 : Type u_1\nP1 : Type ?u.405790\nV2 : Type ?u.405793\nP2 : Type ?u.405796\nV3 : Type ?u.405799\nP3 : Type ?u.405802\nV4 : Type ?u.405805\nP4 : Type ?u.405808\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ : AddCommGroup ... | [
526,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_sUnion | [] | [
1006,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_left_lt_of_lt_add | [
{
"state_after": "a b c : Int\nh✝ : a < b + c\nh : a + -b < b + c + -b\n⊢ a - b < c",
"state_before": "a b c : Int\nh : a < b + c\n⊢ a - b < c",
"tactic": "have h := Int.add_lt_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a < b + c\nh : a + -b < b + c ... | [
1077,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1075,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_spanningSetsIndex | [] | [
3517,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3515,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | pow_eq_one_iff_modEq | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\n⊢ x ^ n = 1 ↔ n ≡ 0 [MOD orderOf x]",
"tactic": "rw [modEq_zero_iff_dvd, orderOf_dvd_iff_pow_eq_one]"
}
] | [
275,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_neg | [
{
"state_after": "F : Type ?u.942371\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.942380\ninst✝³ : Monoid α\ninst✝² : AddGroup β\ninst✝¹ : DistribMulAction α β\ninst✝ : DecidableEq β\na : α\ns : Finset α\nt : Finset β\n⊢ s • image (fun x => -x) t = image (fun x => -x) (s • t)",
"state_before": "F : Type ?u.9423... | [
2151,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.zero_rpow_def | [
{
"state_after": "case inl\ny : ℝ\nH : 0 < y\n⊢ 0 ^ y = if 0 < y then 0 else if y = 0 then 1 else ⊤\n\ncase inr.inl\n\n⊢ 0 ^ 0 = if 0 < 0 then 0 else if 0 = 0 then 1 else ⊤\n\ncase inr.inr\ny : ℝ\nH : y < 0\n⊢ 0 ^ y = if 0 < y then 0 else if y = 0 then 1 else ⊤",
"state_before": "y : ℝ\n⊢ 0 ^ y = if 0 < y t... | [
341,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Set.toFinset_mul | [] | [
2206,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2204,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | exists_pos_bound_of_bound | [
{
"state_after": "case h\nV : Type u_1\nW : Type u_2\ninst✝¹ : SeminormedAddCommGroup V\ninst✝ : SeminormedAddCommGroup W\nf : V → W\nM : ℝ\nh : ∀ (x : V), ‖f x‖ ≤ M * ‖x‖\nx : V\n⊢ M ≤ max M 1",
"state_before": "V : Type u_1\nW : Type u_2\ninst✝¹ : SeminormedAddCommGroup V\ninst✝ : SeminormedAddCommGroup W... | [
77,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ker_prod | [] | [
997,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_add_left | [] | [
126,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Algebra/Group/Basic.lean | one_div_mul_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33748\nG : Type ?u.33751\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ 1 / a * (1 / b) = 1 / (a * b)",
"tactic": "simp"
}
] | [
530,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.mkOfCompact_apply | [] | [
146,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.mem_support_C_mul_X_pow | [] | [
484,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_one | [
{
"state_after": "R : Type u\nS : Type ?u.92888\nA : Type v\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Ring A\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R S\ninst✝² : Algebra S A\ninst✝¹ : IsScalarTower R S A\ninst✝ : Nontrivial R\n⊢ IsAlgebraic R (↑(algebraMap R A) 1)",
"state_before": "R : Type u\nS... | [
116,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.ext | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.34908\nδ : Type ?u.34911\ne✝ : LocalEquiv α β\ne'✝ : LocalEquiv β γ\ne e' : LocalEquiv α β\nh : ∀ (x : α), ↑e x = ↑e' x\nhsymm : ∀ (x : β), ↑(LocalEquiv.symm e) x = ↑(LocalEquiv.symm e') x\nhs : e.source = e'.source\nA : ↑e = ↑e'\n⊢ e = e'",
"state_b... | [
564,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
11
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.pair_eq_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.392686\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α →ₘ[μ] β\ng : α →ₘ[μ] γ\n⊢ pair f g = mk (fun x => (↑f x, ↑g x))... | [
283,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.sum_card_slice_div_choose_le_one | [
{
"state_after": "𝕜 : Type u_2\nα : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\n𝒜 : Finset (Finset α)\ns : Finset α\nk : ℕ\ninst✝ : Fintype α\nh𝒜 : IsAntichain (fun x x_1 => x ⊆ x_1) ↑𝒜\n⊢ ∑ r in range (Fintype.card α + 1),\n ↑(card (𝒜 # (Fintype.card α - r))) / ↑(Nat.choose (Fintype.card α) (Fintype.ca... | [
222,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_zero_sub_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocMod hp 0 (a - b) = p - toIcoMod hp 0 (b - a)",
"tactic": "rw [← neg_sub, toIocMod_neg, neg_zero]"
}
] | [
765,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.ext | [] | [
224,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_singleton | [] | [
255,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_id | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type w\nN : Type ?u.100902\nP : Type u_1\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS✝ : Substructure L M\ns : Set M\nS : Substructure L P\n⊢ ∀ (x : P), x ∈ comap (Hom.id L P) S ↔ x ∈ S",
"tactic": "simp"
}
] | [
435,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.finset_sup_le_sum | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.507526\nR' : Type ?u.507529\n𝕜 : Type u_1\n𝕜₂ : Type ?u.507535\n𝕜₃ : Type ?u.507538\n𝕝 : Type ?u.507541\nE : Type u_2\nE₂ : Type ?u.507547\nE₃ : Type ?u.507550\nF : Type ?u.507553\nG : Type ?u.507556\nι : Type u_3\ninst✝¹⁸ : SeminormedRing 𝕜\nin... | [
407,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ico.mk_zero | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/PathConnected.lean | IsPathConnected.exists_path_through_family | [
{
"state_after": "X✝ : Type ?u.658803\nY : Type ?u.658806\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.658821\nF : Set X✝\nX : Type u_1\ninst✝ : TopologicalSpace X\nn : ℕ\ns : Set X\nh : IsPathConnected s\np : Fin (n + 1) → X\nhp : ∀ (i : Fin (n + 1)), p i ∈ s\np' : ℕ → X ... | [
1069,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.lfp_induction | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : CompleteLattice α\nf : α →o α\np : α → Prop\nstep : ∀ (a : α), p a → a ≤ ↑lfp f → p (↑f a)\nhSup : ∀ (s : Set α), (∀ (a : α), a ∈ s → p a) → p (sSup s)\ns : Set α := {a | a ≤ ↑lfp f ∧ p a}\n⊢ p (↑lfp f)",
"state_before": "α : Type u\nβ : Type v\n... | [
111,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integral_exp_Iic_zero | [] | [
53,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.associator_naturality_aux | [
{
"state_after": "case H\nR : Type u\ninst✝¹² : CommRing R\nX₁ : Type u_1\nX₂ : Type u_2\nX₃ : Type u_3\ninst✝¹¹ : AddCommMonoid X₁\ninst✝¹⁰ : AddCommMonoid X₂\ninst✝⁹ : AddCommMonoid X₃\ninst✝⁸ : Module R X₁\ninst✝⁷ : Module R X₂\ninst✝⁶ : Module R X₃\nY₁ : Type u_4\nY₂ : Type u_5\nY₃ : Type u_6\ninst✝⁵ : AddC... | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
9
] |
Mathlib/Topology/ContinuousOn.lean | mem_closure_pi | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.191155\nβ : Type ?u.191158\nγ : Type ?u.191161\nδ : Type ?u.191164\ninst✝¹ : TopologicalSpace α✝\nι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → TopologicalSpace (α i)\nI : Set ι\ns : (i : ι) → Set (α i)\nx : (i : ι) → α i\n⊢ x ∈ closure (Set.pi ... | [
415,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.linearProjOfIsCompl_comp_subtype | [] | [
195,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_vsub_const_eq_affineCombination_vsub | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_3\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.344641\ns₂ : Finset ι₂\nw : ι → k\np₁ : ι → P\np₂ : P\nh : ∑ i in s, w i = 1\n⊢ ∑ i in s, w i • ... | [
525,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_add_nat | [
{
"state_after": "F : Type ?u.146654\nα : Type u_1\nβ : Type ?u.146660\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\nm : ℕ\n⊢ a + ↑m - ↑⌊a + ↑m⌋ = fract a",
"state_before": "F : Type ?u.146654\nα : Type u_1\nβ : Type ?u.146660\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\... | [
829,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.CostructuredArrow.isSeparating_proj_preimage | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nS : C ⥤ D\nT : D\n𝒢 : Set C\nh𝒢 : IsSeparating 𝒢\nX Y : CostructuredArrow S T\nf g : X ⟶ Y\nhfg : ∀ (G : CostructuredArrow S T), G ∈ (proj S T).toPrefunctor.obj ⁻¹' 𝒢 → ∀ (h : G ⟶ X), h ≫ f = h ≫ g\nG : C\nhG : G ∈ 𝒢\nh : ... | [
379,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_mul | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_map_equiv | [] | [
1329,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_nil | [] | [
3867,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3866,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode₂_encode | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.7117\ninst✝ : Encodable α\na a✝ : α\n⊢ a✝ ∈ decode₂ α (encode a) ↔ a✝ ∈ some a",
"state_before": "α : Type u_1\nβ : Type ?u.7117\ninst✝ : Encodable α\na : α\n⊢ decode₂ α (encode a) = some a",
"tactic": "ext"
},
{
"state_after": "no goals",
... | [
211,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Computability/EpsilonNFA.lean | NFA.toεNFA_εClosure | [
{
"state_after": "case h\nα : Type u\nσ σ' : Type v\nM✝ : εNFA α σ\nS✝ : Set σ\nx : List α\ns : σ\na✝ : α\nM : NFA α σ\nS : Set σ\na : σ\n⊢ a ∈ εNFA.εClosure (toεNFA M) S ↔ a ∈ S",
"state_before": "α : Type u\nσ σ' : Type v\nM✝ : εNFA α σ\nS✝ : Set σ\nx : List α\ns : σ\na : α\nM : NFA α σ\nS : Set σ\n⊢ εNFA... | [
192,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/CharP/Basic.lean | add_pow_char | [] | [
277,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.aestronglyMeasurable_coeFn | [] | [
1291,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_subset_right | [] | [
249,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.continuousWithinAt | [] | [
539,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.Iio_eq_finset_subtype | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.map_eq_zero_iff | [] | [
510,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_biUnion | [] | [
666,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.iff_continuous | [] | [
120,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.exp.coev_ev | [] | [
145,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.const_mul | [] | [
118,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
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