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/Hom/Freiman.lean | FreimanHom.inv_comp | [] | [
374,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_iInter₂_subset | [] | [
402,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.card_eq_sum_ones | [] | [
47,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_iff_coprime | [
{
"state_after": "M : Type u_1\nN : Type ?u.2013558\nG : Type ?u.2013561\nR : Type ?u.2013564\nS : Type ?u.2013567\nF : Type ?u.2013570\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk l : ℕ\nζ : M\nf : F\nh✝ h : IsPrimitiveRoot ζ k\nh0 : 0 < k\ni : ℕ\n⊢ IsPrimitiveRoot (ζ ^ i) k →... | [
452,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_symm | [
{
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338,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/SubsetProperties.lean | compactSpace_of_finite_subfamily_closed | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.76247\nπ : ι → Type ?u.76252\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nh :\n ∀ {ι : Type u} (Z : ι → Set α),\n (∀ (i : ι), IsClosed (Z i)) → (⋂ (i : ι), Z i) = ∅ → ∃ t, (⋂ (i : ι) (_ : i ∈ t), ... | [
738,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
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Mathlib/Data/Set/Image.lean | Function.Injective.mem_range_iff_exists_unique | [] | [
1334,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_map_eq | [
{
"state_after": "G : Type u_1\nG' : Type ?u.565766\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.565775\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf : G →* N\nH : Subgroup G\n⊢ comap f (map f H) ≤ H ⊔ ker f",
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48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3014,
1
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Mathlib/Topology/Maps.lean | Inducing.map_nhds_eq | [] | [
105,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_update | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni : Fin n\ny : α (↑castSucc i)\nz : α (last n)\nj : Fin (n + 1)\n⊢ snoc (update p i y) x j = update (snoc p x) (↑castSucc i) y j",
"state_before": "m n : ℕ\nα : Fin (n... | [
528,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/WithBot.lean | WithBot.none_lt_some | [] | [
271,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCore_empty | [] | [
81,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.mulRight_symm | [
{
"state_after": "case H\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\na x✝ : G\n⊢ ↑(Homeomorph.symm (Homeomorph.mulRight a)) x✝ = ↑(Homeomorph.mulRight a⁻¹) x✝",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝... | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.inr_apply | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
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Mathlib/Analysis/Convex/Measure.lean | Convex.add_haar_frontier | [
{
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85,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
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Mathlib/Data/Nat/Cast/Basic.lean | ext_nat' | [
{
"state_after": "α : Type ?u.27138\nβ : Type ?u.27141\nA : Type u_1\nB : Type ?u.27147\nF : Type u_2\ninst✝² : AddMonoidWithOne B\ninst✝¹ : AddMonoid A\ninst✝ : AddMonoidHomClass F ℕ A\nf g : F\nh : ↑f 1 = ↑g 1\nn : ℕ\n⊢ ↑f n = ↑g n",
"state_before": "α : Type ?u.27138\nβ : Type ?u.27141\nA : Type u_1\nB :... | [
208,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Data/Int/ModEq.lean | Int.modEq_iff_dvd | [
{
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"state_before": "m n a b c d : ℤ\n⊢ a ≡ b [ZMOD n] ↔ n ∣ b - a",
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},
{
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"state_before": "m n a b c d : ℤ\n⊢ b % n = a % n ↔ n ∣ b - a",
"tactic": "simp [emod_eq_emod_... | [
99,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/Topology/List.lean | Vector.continuousAt_removeNth | [
{
"state_after": "α : Type u_1\nβ : Type ?u.68450\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nn : ℕ\ni : Fin (n + 1)\nl : List α\nhl : List.length l = n + 1\n⊢ Tendsto (fun x => ↑(removeNth i x)) (𝓝 { val := l, property := hl })\n (𝓝\n ↑(match { val := l, property := hl } with\n |... | [
223,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.min'_mem | [
{
"state_after": "F : Type ?u.332825\nα : Type u_1\nβ : Type ?u.332831\nγ : Type ?u.332834\nι : Type ?u.332837\nκ : Type ?u.332840\ninst✝ : LinearOrder α\ns : Finset α\nH : Finset.Nonempty s\nx : α\n⊢ inf s WithTop.some = inf s (WithTop.some ∘ fun x => x)",
"state_before": "F : Type ?u.332825\nα : Type u_1\... | [
1325,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
1
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Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.abs_edgeDensity_sub_edgeDensity_le_one_sub_mul | [
{
"state_after": "𝕜 : Type ?u.36968\nι : Type ?u.36971\nκ : Type ?u.36974\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nhs : s₂ ⊆ s₁\nht : t₂ ⊆ t₁\nhs₂ : Finset.Nonempty s₂\nht₂... | [
215,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.extend_restrict | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nx : FamilyOfElements P (generate R).arrows\nt : FamilyOfElements.SieveCompatible x\n⊢ FamilyOfElements.sieveExtend (FamilyOfElements.restrict (_ : R ≤ (generate R).arrows... | [
256,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Order/BoundedOrder.lean | not_isMax_bot | [] | [
420,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.div_nat_pos | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] ↑padicNormE\nn : ℕ\n⊢ 0 < ↑n + 1",
"tactic": "exact_mod_cast succ_pos _"
}
] | [
683,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
9
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_toList | [] | [
68,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
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Mathlib/Geometry/Manifold/Instances/Real.lean | range_quadrant | [] | [
101,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.pow_dvd_pow_iff | [
{
"state_after": "a b n : ℕ\nn0 : 0 < n\nh : a ^ n ∣ b ^ n\n⊢ a ∣ b",
"state_before": "a b n : ℕ\nn0 : 0 < n\n⊢ a ^ n ∣ b ^ n ↔ a ∣ b",
"tactic": "refine' ⟨fun h => _, fun h => pow_dvd_pow_of_dvd h _⟩"
},
{
"state_after": "case inl\na b n : ℕ\nn0 : 0 < n\nh : a ^ n ∣ b ^ n\ng0 : gcd a b = 0\n⊢ a... | [
268,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.inf_eq_add | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_def | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Topology/Sequences.lean | isSeqClosed_iff | [] | [
113,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_tanh | [] | [
715,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_top | [] | [
1440,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.xgcd_zero_left | [
{
"state_after": "no goals",
"state_before": "s t : ℤ\nr' : ℕ\ns' t' : ℤ\n⊢ xgcdAux 0 s t r' s' t' = (r', s', t')",
"tactic": "simp [xgcdAux]"
}
] | [
58,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_Ioo | [] | [
745,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.rescale_mk | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : CommSemiring R\nf : ℕ → R\na : R\nn✝ : ℕ\n⊢ ↑(coeff R n✝) (↑(rescale a) (mk f)) = ↑(coeff R n✝) (mk fun n => a ^ n * f n)",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nf : ℕ → R\na : R\n⊢ ↑(rescale a) (mk f) = mk fun n => a ^ n * f n",
"tactic":... | [
1787,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nE : Type ?u.60121\nF : Type u_2\n𝕜 : Type u_1\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedField 𝕜\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : SMulCommClass ℝ 𝕜 F\nc : 𝕜\ns : Set α\nx : ... | [
233,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Real/NNReal.lean | Set.OrdConnected.preimage_coe_nnreal_real | [] | [
1022,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
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Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.degrees_indicator | [
{
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"state_before": "K : Type u_2\nσ : Type u_1\ninst✝² : Fintype K\ninst✝¹ : Fintype σ\... | [
93,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Image.lift_fac | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nα β : Type u\nf : α ⟶ β\nF' : MonoFactorisation f\nx : Image f\n⊢ (lift F' ≫ F'.m) x = ι f x",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nα β : Type u\nf : α ⟶ β\nF' : MonoFactorisation f\n⊢ lift F' ≫ F'.m = ι f",
"tactic": "funex... | [
529,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_one_le_iff | [] | [
846,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
846,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_toReal | [
{
"state_after": "case intro\nx : ℝ\nhx : ↑x ≠ ⊤\nh'x : ↑x ≠ ⊥\n⊢ ↑(toReal ↑x) = ↑x",
"state_before": "x : EReal\nhx : x ≠ ⊤\nh'x : x ≠ ⊥\n⊢ ↑(toReal x) = x",
"tactic": "lift x to ℝ using ⟨hx, h'x⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nx : ℝ\nhx : ↑x ≠ ⊤\nh'x : ↑x ≠ ⊥... | [
415,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | ext | [] | [
97,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_add_pi_mul_I | [] | [
1393,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | LowerSet.one_mul | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns✝ t : Set α\na : α\ns : LowerSet α\n⊢ (⋃ (a : α) (_ : a ∈ Set.Iic 1), a • ↑s) ⊆ ↑s",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns✝ t : Set α\na : α\ns : LowerSet α\n⊢ Set.Iic 1 * ↑s ⊆ ↑s",
"tactic": "rw [← smul_eq_mul, ← Set.iU... | [
248,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
9
] |
Mathlib/Data/Nat/Interval.lean | Nat.Iio_eq_range | [
{
"state_after": "case h.a\na b✝ c b x : ℕ\n⊢ x ∈ Iio b ↔ x ∈ range b",
"state_before": "a b c : ℕ\n⊢ Iio = range",
"tactic": "ext (b x)"
},
{
"state_after": "no goals",
"state_before": "case h.a\na b✝ c b x : ℕ\n⊢ x ∈ Iio b ↔ x ∈ range b",
"tactic": "rw [mem_Iio, mem_range]"
}
] | [
85,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.top_le | [] | [
317,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Bool/Count.lean | List.Chain'.two_mul_count_bool_eq_ite | [
{
"state_after": "case pos\nl : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bool\nh2 : Even (length l)\n⊢ 2 * count b l =\n if Even (length l) then length l else if (some b == head? l) = true then length l + 1 else length l - 1\n\ncase neg\nl : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nb : Bo... | [
120,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_im | [] | [
345,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | inv_mul_mul_self | [
{
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368,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/Order/Module.lean | lt_of_smul_lt_smul_of_nonpos | [
{
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"state_before": "k : Type u_2\nM : Type u_1\nN : Type ?u.22212\ninst✝³ : OrderedRi... | [
73,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.derivWithin | [
{
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2129,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2121,
11
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Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.id_apply | [
{
"state_after": "no goals",
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332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | exists_Ioo_extr_on_Icc | [
{
"state_after": "f f' : ℝ → ℝ\na b : ℝ\nhab : a < b\nhfc : ContinuousOn f (Icc a b)\nhfI : f a = f b\nne : Set.Nonempty (Icc a b)\n⊢ ∃ c, c ∈ Ioo a b ∧ IsExtrOn f (Icc a b) c",
"state_before": "f f' : ℝ → ℝ\na b : ℝ\nhab : a < b\nhfc : ContinuousOn f (Icc a b)\nhfI : f a = f b\n⊢ ∃ c, c ∈ Ioo a b ∧ IsExtrO... | [
287,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.div_apply | [] | [
1688,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.pointwise_smul_toAddSubmonoid | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_finset_sup | [] | [
149,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.nsmul_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.91193\nγ : Type ?u.91196\na : α\nn : ℕ\n⊢ n • {a} = replicate n a",
"tactic": "rw [← replicate_one, nsmul_replicate, mul_one]"
}
] | [
965,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | finrank_span_finset_le_card | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
321,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.pop_data | [] | [
188,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
188,
9
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_le_iff_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a * b⁻¹ ≤ c ↔ a ≤ b * c",
"tactic": "rw [← inv_mul_le_iff_le_mul, mul_comm]"
}
] | [
536,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\n⊢ 𝟙 X ⊗ (ρ_ Y).inv = (ρ_ (X ⊗ Y)).inv ≫ (α_ X Y tensorUnit').hom",
"tactic": "coherence"
}
] | [
50,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_sphere' | [
{
"state_after": "case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nhc : c ≠ 0\nx : E\nr : ℝ\ny : E\n⊢ y ∈ c • sphere x r ↔ y ∈ sphere (c • x) (‖c‖ * r)",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NormedField 𝕜\ni... | [
107,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Nat/Factorial/DoubleFactorial.lean | Nat.doubleFactorial_two_mul | [
{
"state_after": "n : ℕ\n⊢ (2 * n + 2) * (2 ^ n * n !) = 2 ^ n * 2 * ((n + 1) * n !)",
"state_before": "n : ℕ\n⊢ (2 * (n + 1))‼ = 2 ^ (n + 1) * (n + 1)!",
"tactic": "rw [mul_add, mul_one, doubleFactorial_add_two, factorial, pow_succ, doubleFactorial_two_mul _,\n succ_eq_add_one]"
},
{
"state_af... | [
61,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Real.lean | dist_le_tsum_dist_of_tendsto₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PseudoMetricSpace α\nf : ℕ → α\na : α\nh : Summable fun n => dist (f n) (f (Nat.succ n))\nha : Tendsto f atTop (𝓝 a)\n⊢ dist (f 0) a ≤ ∑' (n : ℕ), dist (f n) (f (Nat.succ n))",
"tactic": "simpa only [zero_add] using dist_le_tsum_dist_o... | [
98,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inter_smul_subset | [] | [
1395,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1394,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.lower_bound_le_one | [
{
"state_after": "case inl\nα : Type ?u.881020\nβ : Type ?u.881023\nn d k : ℕ\nx : Fin n → ℕ\nhN : 1 ≤ 1\nhN' : 1 ≤ 4096\n⊢ ↑1 * exp (-4 * Real.sqrt (log ↑1)) ≤ 1\n\ncase inr\nα : Type ?u.881020\nβ : Type ?u.881023\nn d k N : ℕ\nx : Fin n → ℕ\nhN✝ : 1 ≤ N\nhN' : N ≤ 4096\nhN : 1 < N\n⊢ ↑N * exp (-4 * Real.sqrt ... | [
549,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_self_mul_compl | [] | [
440,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_get? | [
{
"state_after": "ι : Type ?u.431551\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ List α → ℕ → True",
"state_before": "ι : Type ?u.431551\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ ∀ (l : List α) (n : ℕ), get? (enum l) n = (fun a => (n, a)) <$> get? l n",
"t... | [
3832,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3831,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.seqRight_eq | [
{
"state_after": "case h\nm : Type u_1 → Type u_2\nσ α β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : StateT σ m α\ny : StateT σ m β\n⊢ ∀ (s : σ), run (SeqRight.seqRight x fun x => y) s = run (Seq.seq (const α id <$> x) fun x => y) s",
"state_before": "m : Type u_1 → Type u_2\nσ α β : Type u_1\n... | [
292,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
288,
1
] |
Mathlib/Data/List/Basic.lean | List.map_erase | [
{
"state_after": "ι : Type ?u.425891\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nfinj : Injective f\na : α\nl : List α\nthis : Eq a = Eq (f a) ∘ f\n⊢ map f (List.erase l a) = List.erase (map f l) (f a)",
"state_before": "ι : Type... | [
3746,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3743,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_lt_top | [] | [
343,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Algebra/Parity.lean | Even.add_odd | [
{
"state_after": "case intro.intro\nF : Type ?u.81616\nα : Type u_1\nβ : Type ?u.81622\nR : Type ?u.81625\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n : α\n⊢ Odd (m + m + (2 * n + 1))",
"state_before": "F : Type ?u.81616\nα : Type u_1\nβ : Type ?u.81622\nR : Type ?u.81625\ninst✝¹ : Semiring α\ninst✝ : Semi... | [
332,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.terminal.hom_ext | [] | [
251,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Order/Heyting/Hom.lean | map_hnot | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.37721\nδ : Type ?u.37724\ninst✝² : CoheytingAlgebra α\ninst✝¹ : CoheytingAlgebra β\ninst✝ : CoheytingHomClass F α β\nf : F\na : α\n⊢ ↑f (￢a) = ￢↑f a",
"tactic": "rw [← top_sdiff', ← top_sdiff', map_sdiff,... | [
208,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.closedEmbedding | [] | [
214,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.lift_comp_of | [] | [
546,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_equivSentence_symm_con | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.257040\nP : Type ?u.257043\ninst✝⁴ : Structure L M\ninst✝³ : Structure L N\ninst✝² : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\ninst✝¹ : Structure (L[[α]]) M\ninst✝ : LHom.IsExpansionOn (lhomWithConstants L α) M\nφ : Sentence (L[[α]])\n... | [
745,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.extendDomain | [
{
"state_after": "case intro.intro\nι : Type ?u.344602\nα : Type u_2\nβ : Type u_1\nf✝ g : Perm α\nx y : α\np : β → Prop\ninst✝ : DecidablePred p\nf : α ≃ Subtype p\na : α\nha : ↑g a ≠ a\nha' : ∀ ⦃y : α⦄, ↑g y ≠ y → SameCycle g a y\n⊢ IsCycle (extendDomain g f)",
"state_before": "ι : Type ?u.344602\nα : Typ... | [
337,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
11
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_smul_deriv'' | [
{
"state_after": "ι : Type ?u.1904826\n𝕜 : Type ?u.1904829\nE : Type u_1\nF : Type ?u.1904835\nA : Type ?u.1904838\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝¹ : ℝ → E\ng' g✝ φ : ℝ → ℝ\nf✝ f'✝ : ℝ → E\na b : ℝ\nf f' : ℝ → ℝ\ng : ℝ → E\nhf : ContinuousOn f [[a, b]]\nhff... | [
1407,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_cast | [
{
"state_after": "case mk.refl\nR : Type u_1\ninst✝ : Ring R\nm : ℤ\n⊢ IsInt (↑↑m) m",
"state_before": "R : Type u_1\ninst✝ : Ring R\nn m : ℤ\n⊢ IsInt n m → IsInt (↑n) m",
"tactic": "rintro ⟨⟨⟩⟩"
},
{
"state_after": "no goals",
"state_before": "case mk.refl\nR : Type u_1\ninst✝ : Ring R\nm :... | [
87,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearMap.toPMap_apply | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Order/Chain.lean | IsChain.mono_rel | [] | [
81,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_self_le_mul_self | [] | [
1234,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1233,
11
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.mem_rootsOfUnity | [] | [
488,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
11
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_isOpenMap_iff' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.72743\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\nf : β → γ\n⊢ IsOpenMap (f ∘ ↑h) → IsOpenMap f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ... | [
447,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_eq_zero | [
{
"state_after": "d : ℤ\nh_nonsquare : ∀ (n : ℤ), d ≠ n * n\na : ℤ√d\nha : norm a = 0\n⊢ a.re = 0.re ∧ a.im = 0.im",
"state_before": "d : ℤ\nh_nonsquare : ∀ (n : ℤ), d ≠ n * n\na : ℤ√d\n⊢ norm a = 0 ↔ a = 0",
"tactic": "refine' ⟨fun ha => ext.mpr _, fun h => by rw [h, norm_zero]⟩"
},
{
"state_af... | [
1026,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.morphismProperty_is_top' | [] | [
268,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Std/Data/List/Lemmas.lean | List.foldl_map | [
{
"state_after": "no goals",
"state_before": "β₁ : Type u_1\nβ₂ : Type u_2\nα : Type u_3\nf : β₁ → β₂\ng : α → β₂ → α\nl : List β₁\ninit : α\n⊢ foldl g init (map f l) = foldl (fun x y => g x (f y)) init l",
"tactic": "induction l generalizing init <;> simp [*]"
}
] | [
1411,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1409,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | coe_gramSchmidtBasis | [] | [
262,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/Connected.lean | connectedComponent_eq_iff_mem | [] | [
678,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.ext | [] | [
385,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.values_eq_on_of_interpolate_eq | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\nhvs : Set.InjOn v ↑s\nhrr' : ↑(interpolate s v) r = ↑(interpolate s v) r'\nx✝ : ι\nhi : x✝ ∈ s\n⊢ r x✝ = r' x✝",
"tactic": "rw [← eval_interpolate_a... | [
361,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toLex_mul | [] | [
254,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.sup | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.278636\nι : Type ?u.278639\ninst✝⁴ : Countable ι\nm0 : MeasurableSpace α\nμ : Measure α\nf g : α → β\ninst✝³ : TopologicalSpace β\ninst✝² : Zero β\ninst✝¹ : SemilatticeSup β\ninst✝ : ContinuousSup β\nhf : FinStronglyMeasurable f μ\nhg : FinStronglyMeasur... | [
1116,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
11
] |
Mathlib/Order/Basic.lean | lt_of_not_le | [] | [
472,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Rel.lean | Rel.core_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.23811\nr : Rel α β\n⊢ ∀ (x : α), x ∈ core r Set.univ ↔ x ∈ Set.univ",
"tactic": "simp [mem_core]"
}
] | [
236,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Order/Basic.lean | Pi.le_def | [] | [
798,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_union | [] | [
370,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.closure_setOf_re_lt | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ closure {z | z.re < a} = {z | z.re ≤ a}",
"tactic": "simpa only [closure_Iio] using closure_preimage_re (Iio a)"
}
] | [
118,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/RelClasses.lean | IsTotal.isTrichotomous | [] | [
128,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Data/Complex/Basic.lean | Complex.I_zpow_bit1 | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ I ^ bit1 n = (-1) ^ n * I",
"tactic": "rw [zpow_bit1', I_mul_I]"
}
] | [
776,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
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