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/Finite.lean | Set.not_infinite | [] | [
138,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Int/Units.lean | Int.isUnit_mul_self | [] | [
105,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.inv_I | [
{
"state_after": "no goals",
"state_before": "⊢ I⁻¹ = -I",
"tactic": "rw [inv_eq_one_div, div_I, one_mul]"
}
] | [
812,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
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Mathlib/Data/Finset/Sups.lean | Finset.infs_eq_empty | [] | [
320,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Data/List/Forall2.lean | List.Forall₂.flip | [] | [
55,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.map_id' | [] | [
1289,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Raised.dist_le' | [
{
"state_after": "α : Type ?u.244405\nn m : ℕ\nH : Raised n m\n⊢ Nat.dist n m ≤ 1",
"state_before": "α : Type ?u.244405\nn m : ℕ\nH : Raised n m\n⊢ Nat.dist m n ≤ 1",
"tactic": "rw [Nat.dist_comm]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.244405\nn m : ℕ\nH : Raised n m\n... | [
797,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right | [] | [
380,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
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Mathlib/Logic/Relation.lean | Equivalence.eqvGen_eq | [] | [
688,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.lt_succ_floor | [] | [
161,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.subset_support_append_right | [
{
"state_after": "V✝ : Type u\nV' : Type v\nV'' : Type w\nG✝ : SimpleGraph V✝\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nV : Type u\nG : SimpleGraph V\nu v w : V\np : Walk G u v\nq : Walk G v w\nh : V\n⊢ h ∈ support q → h ∈ support (append p q)",
"state_before": "V✝ : Type u\nV' : Type v\nV'' : Type w\nG✝... | [
625,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonneg | [] | [
744,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_pair_le_of_right_mem | [] | [
1370,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.cancel_right | [] | [
277,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_irrefl | [] | [
592,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
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Mathlib/Data/Nat/Basic.lean | Nat.findGreatest_eq | [
{
"state_after": "no goals",
"state_before": "m n✝ k : ℕ\nP Q : ℕ → Prop\ninst✝ : DecidablePred P\nb n : ℕ\nh : P (n + 1)\n⊢ Nat.findGreatest P (n + 1) = n + 1",
"tactic": "simp [Nat.findGreatest, h]"
}
] | [
897,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
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Mathlib/Analysis/NormedSpace/Pointwise.lean | infEdist_thickening | [
{
"state_after": "case inl\n𝕜 : Type ?u.220755\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx✝ y z : E\nδ ε : ℝ\nhδ : 0 < δ\ns : Set E\nx : E\nhs : infEdist x s < ENNReal.ofReal δ\n⊢ infEdist x (thickening δ s) = infEdist x s - E... | [
269,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommFold_eq_fold | [
{
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109,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_le_false | [] | [
708,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.span_iUnion | [] | [
734,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_zero | [] | [
318,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
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Mathlib/Order/Heyting/Basic.lean | sdiff_le_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.88914\nα : Type u_1\nβ : Type ?u.88920\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ b ≤ c ↔ a \\ c ≤ b",
"tactic": "rw [sdiff_le_iff, sdiff_le_iff']"
}
] | [
510,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
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Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.nonempty_algebraRat_iff | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : CommRing R\n⊢ Nonempty (Algebra ℚ R) → ∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I)\n\ncase mpr\nR : Type u_1\ninst✝ : CommRing R\n⊢ (∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I)) → Nonempty (Algebra ℚ R)",
"state_before": "R : Type u_1\ninst✝ : CommRing R\n⊢ Nonem... | [
296,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/List/Basic.lean | List.replicate_succ' | [] | [
445,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_pow | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.456883\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q a : MvPolynomial σ R\n⊢ totalDegree (a ^ Nat.zero) ≤ Nat.zero * totalDegree a\n\ncase succ\nR : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.456883\nr : R\ne : ℕ... | [
712,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mul_le_mul_left | [] | [
640,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/List/Lex.lean | Decidable.List.Lex.ne_iff | [
{
"state_after": "case nil.nil\nα : Type u\ninst✝ : DecidableEq α\nl₁ l₂ : List α\nH✝ : length l₁ ≤ length l₂\nh✝ : l₁ ≠ l₂\nH : length [] ≤ length []\nh : [] ≠ []\n⊢ Lex (fun x x_1 => x ≠ x_1) [] []\n\ncase nil.cons\nα : Type u\ninst✝ : DecidableEq α\nl₁ l₂✝ : List α\nH✝ : length l₁ ≤ length l₂✝\nh✝ : l₁ ≠ l₂✝... | [
167,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_le_of_sum_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.206222\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nhs : Finset.Nonempty s\nf g : α → ℝ≥0∞\nHle : ∀ (i : α), i ∈ s → g i < f i\n⊢ ∑ i in s, g i < ∑ i in s, f i",
"state_before": "α : Type u_1\nβ : Type ?u.206222\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nhs : Fins... | [
1276,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
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] |
Mathlib/Computability/Reduce.lean | disjoin_le | [] | [
324,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_update_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\ninst✝¹⁵ : Semiring R\nM : Type u_3\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : Module R M\nN : Type u_2\ninst✝¹² : AddCommMonoid N\ninst✝¹¹ : Module R N\nP : Type ?u.411142\ninst✝¹⁰ : AddCommMonoid P\ninst✝⁹ : Module R P\nM' : Type ?u.411172\ninst✝⁸ : Ad... | [
680,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.commonNeighbors_eq | [] | [
1013,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Continuous.aemeasurable2 | [] | [
958,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.one_def | [] | [
396,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\n𝕜 : Type ?u.1636764\nE : Type u_1\nF : Type ?u.1636770\nA : Type ?u.1636773\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : CompleteSpace E\ninst✝² : NormedSpace ℝ E\nf : ℝ → E\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\na b z : ℝ\nu v ua... | [
550,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
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] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.map_zero | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.126220\nR : Type u_1\nR₁ : Type ?u.126226\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nQ : QuadraticForm R M\n⊢ ↑Q 0 = 0",
"tactic": "rw [← @zero_smul R _ _ _ _ (0 : M), map_smul, zero_mul, zero_mul]"
}
] | [
232,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/Algebra/GroupPower/Ring.lean | pow_eq_zero_iff | [
{
"state_after": "R : Type ?u.22317\nS : Type ?u.22320\nM : Type u_1\ninst✝¹ : MonoidWithZero M\ninst✝ : NoZeroDivisors M\na : M\nn : ℕ\nhn : 0 < n\n⊢ a = 0 → a ^ n = 0",
"state_before": "R : Type ?u.22317\nS : Type ?u.22320\nM : Type u_1\ninst✝¹ : MonoidWithZero M\ninst✝ : NoZeroDivisors M\na : M\nn : ℕ\nh... | [
69,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_of_aemeasurable_trim | [] | [
298,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnionIndex_of_mem | [] | [
385,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftMonoidWithZeroHom_apply | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : Field K\nL : Type u_1\ninst✝ : CommGroupWithZero L\nφ : K[X] →*₀ L\nhφ : K[X]⁰ ≤ Submonoid.comap φ L⁰\nf : RatFunc K\n⊢ ↑(liftMonoidWithZeroHom φ hφ) f = ↑φ (num f) / ↑φ (denom f)",
"tactic": "rw [← num_div_denom f, liftMonoidWithZeroHom... | [
1355,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoid.End.natCast_apply | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_sin | [] | [
225,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_add_single | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → AddZeroClass (β i)\ni : ι\nf : Π₀ (i : ι), β i\n⊢ ↑(erase i f + single i (↑f i)) i = ↑f i",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι →... | [
953,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_union_inter' | [
{
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787,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
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] |
Mathlib/Order/Basic.lean | LT.lt.lt_or_lt | [] | [
316,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.image_closure | [] | [
749,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.mem_cycleFactorsFinset_support_le | [
{
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"state_before": "ι : Type ?u.2746614\nα : Type u_1\nβ : Type ?u.2746620\ninst✝¹ : DecidableE... | [
1439,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.leftRel_r_eq_leftCosetEquivalence | [
{
"state_after": "case h.h.a\nα : Type u_1\ninst✝ : Group α\ns : Subgroup α\nx✝¹ x✝ : α\n⊢ Setoid.r x✝¹ x✝ ↔ LeftCosetEquivalence (↑s) x✝¹ x✝",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ Setoid.r = LeftCosetEquivalence ↑s",
"tactic": "ext"
},
{
"state_after": "case h.h.a\n... | [
348,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Finset/Slice.lean | Finset.sum_card_slice | [
{
"state_after": "α : Type u_1\nι : Sort ?u.15793\nκ : ι → Sort ?u.15798\n𝒜 : Finset (Finset α)\nA A₁ A₂ : Finset α\nr r₁ r₂ : ℕ\ninst✝ : Fintype α\nthis : DecidableEq α := Classical.decEq α\n⊢ ∑ r in Iic (Fintype.card α), card (𝒜 # r) = card 𝒜",
"state_before": "α : Type u_1\nι : Sort ?u.15793\nκ : ι → ... | [
180,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.supp_eq | [
{
"state_after": "case h\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nx : F α\nx✝ : α\n⊢ x✝ ∈ supp x ↔ x✝ ∈ {u | ∀ (a : (P F).A) (f : PFunctor.B (P F) a → α), abs { fst := a, snd := f } = x → u ∈ f '' univ}",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\n... | [
629,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_smul_set_iff_inv_smul_mem₀ | [] | [
1018,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkFunctor_obj | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | MeasureTheory.Measure.ext_of_Iic | [
{
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757,
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746,
1
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Mathlib/Data/List/Cycle.lean | Cycle.map_coe | [] | [
724,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.inv_subtypePerm | [] | [
398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ioc_right | [
{
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"tactic": "simpa using image_update_Ioc f i (f i) b"
}
] | [
188,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.ofCoreEq_toCore | [] | [
374,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Filter.Tendsto.dist | [] | [
1815,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1812,
11
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_ofNat | [] | [
371,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_preimage_of_injective | [
{
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"state_before": "α β : Type u\nf : α → β\ns : Set β\nh : Injective f\n⊢ (#↑(f ⁻¹' s)) ≤ (#↑s)",
"tactic": "rw [← lift_id (#↑(f ⁻¹' s)), ← lift_id (#↑(s))]"
},
{
"state_after": "no goals",
... | [
2193,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2190,
1
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Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | orderOf_eq_card_of_forall_mem_zpowers | [
{
"state_after": "no goals",
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"tactic": "classical\n rw [orderOf_eq_card_zpowers]\n apply Fintype.card_of_finset'\n simpa using hx"
},
{
"state_after": ... | [
154,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | List.aestronglyMeasurable_prod' | [
{
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1381,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.restrictScalars_eq_bot_iff | [
{
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... | [
82,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_inf_map_of_injective | [] | [
402,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.MeasurePreserving.integrable_comp_emb | [] | [
634,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.mono_of_zero_of_map_zero | [] | [
326,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Order/Filter/Lift.lean | Filter.HasBasis.lift | [
{
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71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_C_mul_X_pow | [
{
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"tactic": "rw [roots_C_mul _ ha, roots_X_pow]"
}
] | [
723,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
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Mathlib/Order/LocallyFinite.lean | Finset.mem_Ioc | [] | [
338,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coeSubtype | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.leftUnitor_conjugation | [
{
"state_after": "no goals",
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"tactic": "rw [← leftUnitor_naturality_assoc, Iso.hom... | [
258,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_injective_of_injective | [] | [
400,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.norm_indicatorConstLp | [
{
"state_after": "no goals",
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752,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_pi_le_iff | [
{
"state_after": "no goals",
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489,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.liftOn_mk | [
{
"state_after": "no goals",
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125,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Fintype/Perm.lean | mem_permsOfList_iff | [] | [
102,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_preimage_eq | [] | [
495,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | smul_algebra_smul_comm | [] | [
916,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Data/List/Basic.lean | List.dropWhile_nthLe_zero_not | [
{
"state_after": "case nil\nι : Type ?u.385620\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\nhl✝ : 0 < length (dropWhile p l)\nhl : 0 < length (dropWhile p [])\n⊢ ¬p (nthLe (dropWhile p []) 0 hl) = true\n\ncase cons\nι : Type ?u.385620\nα : Type u\nβ : Type v\nγ : Ty... | [
3620,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3613,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.eq_zero_iff_ae_eq_zero | [
{
"state_after": "case mp\nα : Type u_1\nE : Type u_2\nF : Type ?u.414402\nG : Type ?u.414405\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : { x // x ∈ Lp E p }\n⊢ f = 0 → ↑↑f =ᵐ[μ] 0\n\ncase mpr\nα : T... | [
345,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.comp_id | [] | [
172,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.Prod.continuous_inv_fun | [
{
"state_after": "B : Type u_3\ninst✝⁶ : TopologicalSpace B\nF₁ : Type u_2\ninst✝⁵ : TopologicalSpace F₁\nE₁ : B → Type u_5\ninst✝⁴ : TopologicalSpace (TotalSpace E₁)\nF₂ : Type u_1\ninst✝³ : TopologicalSpace F₂\nE₂ : B → Type u_4\ninst✝² : TopologicalSpace (TotalSpace E₂)\ne₁ : Trivialization F₁ TotalSpace.pro... | [
222,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuousOn_primitive_interval | [] | [
1229,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq_of_equiv | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : ¬f ≈ 0\nhg : ¬g ≈ 0\nhfg : f ≈ g\nh : ¬padicNorm p (↑f (stationaryPoint hf)) = padicNorm p (↑g (stationaryPoint hg))\n⊢ False",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : ¬f ≈ 0\nhg : ¬g ≈ 0\nhfg : f ≈ g\n⊢... | [
361,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
9
] |
Mathlib/Analysis/SpecialFunctions/PolynomialExp.lean | Polynomial.tendsto_div_exp_atTop | [
{
"state_after": "no goals",
"state_before": "p : ℝ[X]\n⊢ Tendsto (fun x => eval x p / exp x) atTop (𝓝 0)",
"tactic": "induction p using Polynomial.induction_on' with\n| h_monomial n c => simpa [exp_neg, div_eq_mul_inv, mul_assoc]\n using tendsto_const_nhds.mul (tendsto_pow_mul_exp_neg_atTop_nhds_0 n)... | [
31,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_mul_mod | [
{
"state_after": "no goals",
"state_before": "x k n : Nat\nh₁ : n * k ≤ x\n⊢ (x - n * k) % n = x % n",
"tactic": "match k with\n| 0 => rw [Nat.mul_zero, Nat.sub_zero]\n| succ k =>\n have h₂ : n * k ≤ x := Nat.le_trans (le_add_right _ n) h₁\n have h₄ : x - n * k ≥ n := by\n apply Nat.le_of_add_le_ad... | [
541,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
532,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_bind₂ | [] | [
244,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.map_comp | [] | [
151,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.rep_nonzero | [] | [
83,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_inv_smul_measure | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.850036\nδ : Type ?u.850039\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ⊤\n⊢ c⁻¹ ≠ 0",
"tac... | [
579,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.isoOfComponents_app | [
{
"state_after": "case w\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC C₁ C₂ C₃ : HomologicalComplex V c\nf : (i : ι) → X C₁ i ≅ X C₂ i\nhf : ∀ (i j : ι), ComplexShape.Rel c i j → (f i).hom ≫ d C₂ i j = d C₁ i j ≫ (f j).hom\ni : ι\n⊢ (isoApp (isoOfComponents f... | [
512,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Analysis/Complex/Arg.lean | Complex.sameRay_of_arg_eq | [] | [
61,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.mem_span | [
{
"state_after": "K : Type u_2\nV : Type u_1\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nS : Set (ℙ K V)\nu : ℙ K V\n⊢ u ∈ span S ↔ ∀ (W : Subspace K V), span S ≤ W → u ∈ W",
"state_before": "K : Type u_2\nV : Type u_1\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nS : S... | [
207,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.closedBall_mul | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx✝ y : E\nhs : IsCompact s\nhδ : 0 ≤ δ\nx : E\n⊢ closedBall x δ * s = x • cthickening δ s",
"tactic": "rw [mul_comm, hs.mul_closedBall hδ]"
}
] | [
299,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.continuous | [] | [
305,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
11
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_smul_vsub_vadd_left | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.383102\nP : Type u_3\nP' : Type ?u.383108\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx p₁ p₂ : P\... | [
750,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_one | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwiseDisjoint_singleton | [] | [
268,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/Convex/KreinMilman.lean | closure_convexHull_extremePoints | [
{
"state_after": "E : Type u_1\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : T2Space E\ninst✝² : TopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhscomp : IsCompact s\nhAconv : Convex ℝ s\n⊢ s ⊆ closure (↑(convexHull ℝ).toOrder... | [
109,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Tactic/NormNum/IsCoprime.lean | Tactic.NormNum.isInt_isCoprime | [] | [
30,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_eq_empty | [] | [
368,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
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