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/SetTheory/Ordinal/Topology.lean | Ordinal.isLimit_of_mem_frontier | [
{
"state_after": "s : Set Ordinal\na : Ordinal\nha :\n (∀ (o : Set Ordinal), IsOpen o → a ∈ o → Set.Nonempty (o ∩ s)) ∧\n ∀ (o : Set Ordinal), IsOpen o → a ∈ o → Set.Nonempty (o ∩ sᶜ)\n⊢ IsLimit a",
"state_before": "s : Set Ordinal\na : Ordinal\nha : a ∈ frontier s\n⊢ IsLimit a",
"tactic": "simp onl... | [
185,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.NullMeasurableSet.image | [
{
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1374,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_induction | [] | [
1361,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_comap_mul | [] | [
1827,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1824,
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffWithinAt.norm | [] | [
193,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Computability/DFA.lean | DFA.eval_nil | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.isPiSystem_measurableSet | [] | [
76,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
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Mathlib/Data/Finset/Prod.lean | Finset.product_inter_product | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.766... | [
259,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
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Mathlib/Analysis/Convex/Uniform.lean | exists_forall_closed_ball_dist_add_le_two_sub | [
{
"state_after": "E : Type u_1\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : UniformConvexSpace E\nε : ℝ\ninst✝ : NormedSpace ℝ E\nhε : 0 < ε\nhε' : 0 < ε / 3\n⊢ ∃ δ, 0 < δ ∧ ∀ ⦃x : E⦄, ‖x‖ ≤ 1 → ∀ ⦃y : E⦄, ‖y‖ ≤ 1 → ε ≤ ‖x - y‖ → ‖x + y‖ ≤ 2 - δ",
"state_before": "E : Type u_1\ninst✝² : SeminormedAddCommGro... | [
113,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_eq_right_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nV : Type u_3\nV' : Type ?u.95650\nP : Type u_1\nP' : Type ?u.95656\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\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... | [
174,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.mkContinuous_coe | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.prod_top | [
{
"state_after": "no goals",
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"tactic": "simp [mem_prod, MonoidHom.coe_fst]"
}
] | [
1121,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
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Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingFaceMapComplex.map_f | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.integrableOn_Icc | [] | [
281,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_bsup | [
{
"state_after": "no goals",
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1471,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.mem_support_bind_iff | [
{
"state_after": "no goals",
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"tactic": "simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq, exists_prop]"
}
] | [
130,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prod_top | [] | [
1240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.716015\nG : Type ?u.716018\n𝕜 : Type ?u.716021\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : NormedSpace ℝ F'\ninst✝² ... | [
820,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.unitors_equal | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\n⊢ (λ_ (𝟙 a)).hom = (ρ_ (𝟙 a)).hom",
"tactic": "rw [← whiskerLeft_iff, ← cancel_epi (α_ _ _ _).hom, ← cancel_mono (ρ_ _).hom, triangle, ←\n rightUnitor_comp, rightUnitor_naturality]"
}
] | [
486,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Analysis/PSeries.lean | ENNReal.le_tsum_condensed | [
{
"state_after": "f : ℕ → ℝ≥0∞\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m\n⊢ (⨆ (i : ℕ), ∑ a in Finset.range (2 ^ i), f a) ≤ f 0 + ∑' (k : ℕ), 2 ^ k * f (2 ^ k)",
"state_before": "f : ℕ → ℝ≥0∞\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m\n⊢ (∑' (k : ℕ), f k) ≤ f 0 + ∑' (k : ℕ), 2 ^ k * f (2 ^ k)",
"ta... | [
105,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nβ₂ : Type ?u.165662\nγ : Type u_2\nι : Sort ?u.165668\nι' : Sort ?u.165671\nκ : ι → Sort ?u.165676\nκ' : ι' → Sort ?u.165681\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nf : β × γ → α\nc : α\n⊢ (⨆ (x : β × γ), f x) ≤ c ↔ (⨆ ... | [
1549,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1548,
1
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Mathlib/Data/Rat/NNRat.lean | NNRat.toNNRat_mono | [] | [
185,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Set/Intervals/UnorderedInterval.lean | Set.uIcc_prod_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Lattice α\ninst✝ : Lattice β\na✝ a₁ a₂ b✝ b₁ b₂ c x : α\na b : α × β\n⊢ [[a, b]] = [[a.fst, b.fst]] ×ˢ [[a.snd, b.snd]]",
"tactic": "simp"
}
] | [
152,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Init/Logic.lean | imp_of_if_pos | [
{
"state_after": "a b c✝ d : Prop\np : ?m.27950\nc t e : Prop\ninst✝ : Decidable c\nh : if c then t else e\nhc : c\nthis : t\n⊢ t",
"state_before": "a b c✝ d : Prop\np : ?m.27950\nc t e : Prop\ninst✝ : Decidable c\nh : if c then t else e\nhc : c\n⊢ t",
"tactic": "have := if_pos hc ▸ h"
},
{
"sta... | [
357,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
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Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝² : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμs_lim : Tendsto μs F (𝓝 μ)\nnonzero : μ ≠ 0\nf : Ω →ᵇ ℝ≥0\nlim_mass : Tendsto (fun i => mass (μs ... | [
457,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.inv | [] | [
465,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_inv_of_invertible | [] | [
346,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Order/ModularLattice.lean | wellFounded_gt_exact_sequence | [] | [
284,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_sub | [
{
"state_after": "no goals",
"state_before": "K : Type ?u.1561683\nF : Type ?u.1561686\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.1561698\nΓ''₀ : Type ?u.1561701\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuatio... | [
303,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_equiv_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ (-x ≈ y) ↔ (x ≈ -y)",
"tactic": "rw [← neg_neg y, neg_equiv_neg_iff, neg_neg]"
}
] | [
1355,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_zero | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.image_eq_of_mapsTo | [] | [
865,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_withDensity_iff | [
{
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910,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
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Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.lt_zero_iff | [
{
"state_after": "case refine'_1\nn : WithBot ℕ\n⊢ none < 0 ↔ none = ⊥\n\ncase refine'_2\nn : WithBot ℕ\n⊢ ∀ (val : ℕ), some val < 0 ↔ some val = ⊥",
"state_before": "n : WithBot ℕ\n⊢ n < 0 ↔ n = ⊥",
"tactic": "refine' Option.casesOn n _ _"
},
{
"state_after": "case refine'_2\nn : WithBot ℕ\n⊢ ∀... | [
72,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_ite_one_zero | [
{
"state_after": "case inl\nF✝ : Type ?u.83334\nα : Type u_2\nβ : Type u_3\nγ : Type ?u.83343\nx✝¹ : NonAssocSemiring α\nx✝ : NonAssocSemiring β\nf✝ : α →+* β\nx y : α\nF : Type u_1\ninst✝¹ : RingHomClass F α β\nf : F\np : Prop\ninst✝ : Decidable p\nh : p\n⊢ ↑f (if p then 1 else 0) = 1\n\ncase inr\nF✝ : Type ?u... | [
595,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.proj_map_nth | [
{
"state_after": "ι : Type u_1\nΓ : ι → Type u_2\ninst✝ : (i : ι) → Inhabited (Γ i)\ni : ι\nL : ListBlank ((i : ι) → Γ i)\nn : ℕ\n⊢ PointedMap.f (proj i) (ListBlank.nth L n) = ListBlank.nth L n i",
"state_before": "ι : Type u_1\nΓ : ι → Type u_2\ninst✝ : (i : ι) → Inhabited (Γ i)\ni : ι\nL : ListBlank ((i :... | [
438,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_eq_bot | [] | [
1063,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_toAddSubgroup | [] | [
446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.coe_finsetBasisIndex | [] | [
85,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
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Mathlib/Data/List/Basic.lean | List.reduceOption_length_le | [
{
"state_after": "case nil\nι : Type ?u.350604\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ length (reduceOption []) ≤ length []\n\ncase cons\nι : Type ?u.350604\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nhd : Option α\ntl : List (Option α)\nhl : length (reduceOption ... | [
3453,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3448,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | eq_of_derivWithin_eq | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.54298\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → E\na b : ℝ\nf' g : ℝ → E\nfdiff : DifferentiableOn ℝ f (Icc a b)\ngdiff : DifferentiableOn ℝ g (Icc a b)\nhderiv : EqOn (derivWithin f (Icc ... | [
436,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_eq_iSup | [] | [
287,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.finset_sup_apply_le | [
{
"state_after": "case intro\nR : Type ?u.518585\nR' : Type ?u.518588\n𝕜 : Type u_1\n𝕜₂ : Type ?u.518594\n𝕜₃ : Type ?u.518597\n𝕝 : Type ?u.518600\nE : Type u_2\nE₂ : Type ?u.518606\nE₃ : Type ?u.518609\nF : Type ?u.518612\nG : Type ?u.518615\nι : Type u_3\ninst✝¹⁸ : SeminormedRing 𝕜\ninst✝¹⁷ : SeminormedRi... | [
414,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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Mathlib/Analysis/PSeries.lean | Finset.sum_condensed_le' | [
{
"state_after": "case zero\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 1 < m → m ≤ n → f n ≤ f m\n⊢ ∑ k in range Nat.zero, 2 ^ k • f (2 ^ (k + 1)) ≤ ∑ k in Ico 2 (2 ^ Nat.zero + 1), f k\n\ncase succ\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 1 < ... | [
85,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_subtypeCongr | [
{
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"tact... | [
788,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.add | [] | [
384,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
8
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_eq | [] | [
99,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_sup | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_one | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\n⊢ logb b 1 = 0",
"tactic": "simp [logb]"
}
] | [
56,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | Finset.norm_prod_le | [
{
"state_after": "case mk.mk\nα✝ : Type ?u.121829\nβ : Type ?u.121832\nγ : Type ?u.121835\nι : Type u_2\ninst✝² : SeminormedRing α✝\nα : Type u_1\ninst✝¹ : NormedCommRing α\ninst✝ : NormOneClass α\nf : ι → α\nval✝ : Multiset ι\nl : List ι\nhl : Multiset.Nodup (Quot.mk Setoid.r l)\n⊢ ‖∏ i in { val := Quot.mk Set... | [
351,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.algebraMap_quotient_injective | [
{
"state_after": "case mk.mk\nR : Type u\nS : Type v\nF : Type w\ninst✝⁹ : CommRing R\ninst✝⁸ : CommRing S\nR₁ : Type ?u.1618416\nR₂ : Type ?u.1618419\nA : Type u_1\nB : Type ?u.1618425\ninst✝⁷ : CommSemiring R₁\ninst✝⁶ : CommSemiring R₂\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra R₁ A\ninst✝² :... | [
478,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Data/List/Func.lean | List.Func.get_add | [
{
"state_after": "case h1\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u\ninst✝ : AddMonoid α\nk : ℕ\nxs ys : List α\n⊢ default + default = default",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u\ninst✝ : AddMonoid α\nk : ℕ\nxs ys : List α\n⊢ get k (add xs ys) = get k xs + get k ys",
... | [
326,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.singleton_seq | [
{
"state_after": "no goals",
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1971,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1970,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_image | [
{
"state_after": "no goals",
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207,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_zero | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ x ^ 0 = 1",
"tactic": "simp [rpow_def]"
}
] | [
100,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_coe_le_norm | [
{
"state_after": "no goals",
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"tactic": "simp [dist_zero_right]"
}
] | [
822,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_mul_of_domain | [
{
"state_after": "case pos\nR✝ : Type ?u.361245\ninst✝² : Semiring R✝\nf✝ : R✝[X]\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : NoZeroDivisors R\nf g : R[X]\nf0 : f = 0\n⊢ reverse (f * g) = reverse f * reverse g\n\ncase neg\nR✝ : Type ?u.361245\ninst✝² : Semiring R✝\nf✝ : R✝[X]\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ :... | [
329,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/AlgebraicTopology/TopologicalSimplex.lean | SimplexCategory.continuous_toTopMap | [
{
"state_after": "x y : SimplexCategory\nf : x ⟶ y\ni : (CategoryTheory.forget SimplexCategory).obj y\n⊢ Continuous fun a =>\n ∑ j in Finset.filter (fun k => (CategoryTheory.forget SimplexCategory).map f k = i) Finset.univ, ↑a j",
"state_before": "x y : SimplexCategory\nf : x ⟶ y\n⊢ Continuous (toTopMap ... | [
86,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.map_monotone | [
{
"state_after": "α : Type ?u.180760\nβ : Type ?u.180763\nn d✝ k N : ℕ\nx✝ : Fin n → ℕ\nd : ℕ\nx y : Fin n → ℕ\nh : x ≤ y\n⊢ ∑ i : Fin n, x i * d ^ ↑i ≤ ∑ i : Fin n, y i * d ^ ↑i",
"state_before": "α : Type ?u.180760\nβ : Type ?u.180763\nn d✝ k N : ℕ\nx✝ : Fin n → ℕ\nd : ℕ\nx y : Fin n → ℕ\nh : x ≤ y\n⊢ ↑(m... | [
140,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesEpimorphisms.of_iso | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF G : C ⥤ D\ninst✝ : PreservesEpimorphisms F\nα : F ≅ G\nX Y : C\nf : X ⟶ Y\nh : Epi f\nthis : Epi (F.map f ≫ (α.app Y).hom)\n⊢ Epi (G.map f)",
"state_before": "C : Type u₁\ninst✝³ : Categ... | [
142,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.smul_sup | [] | [
258,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.symm_cast | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : n = m\n⊢ OrderIso.symm (cast h) = cast (_ : m = n)",
"tactic": "simp"
}
] | [
1067,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/NumberTheory/Primorial.lean | primorial_succ | [
{
"state_after": "n : ℕ\nhn1 : n ≠ 1\nhn : Odd n\n⊢ filter Nat.Prime (range (n + 1 + 1)) = filter Nat.Prime (range (n + 1))",
"state_before": "n : ℕ\nhn1 : n ≠ 1\nhn : Odd n\n⊢ (n + 1)# = n#",
"tactic": "refine prod_congr ?_ fun _ _ ↦ rfl"
},
{
"state_after": "n : ℕ\nhn1 : n ≠ 1\nhn : Odd n\n⊢ N... | [
52,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_units_inv | [
{
"state_after": "no goals",
"state_before": "f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\n⊢ τ ↑f⁻¹ + τ ↑f = 0",
"tactic": "simp [← translationNumber_mul_of_commute (Commute.refl _).units_inv_left]"
}
] | [
741,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_mul_self | [] | [
206,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Disjoint.exists_uniform_thickening | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.74705\ninst✝ : UniformSpace α\nA B : Set α\nhA : IsCompact A\nhB : IsClosed B\nh : Disjoint A B\nthis : Bᶜ ∈ 𝓝ˢ A\n⊢ ∃ V, V ∈ 𝓤 α ∧ Disjoint (⋃ (x : α) (_ : x ∈ A), ball x V) (⋃ (x : α) (_ : x ∈ B), ball x V)",
"state_before... | [
847,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_inter_Ioo_of_left_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.188656\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\nh : b₁ < b₂\nx : α\n⊢ x ∈ Ioc a₁ b₁ ∩ Ioo a₂ b₂ ↔ x ∈ Ioc (max a₁ a₂) b₁",
"tactic": "simp [and_assoc, @and_left_comm (x ≤ _), and_iff_left_i... | [
1797,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1795,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_injective | [] | [
82,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.coeff_mul_mirror | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\n⊢ (Finset.sum (Finset.range (Nat.succ (natDegree p + natTrailingDegree p))) fun k =>\n coeff p (k, natDegree p + natTrailingDegree p - k).fst *\n coeff (mirror p) (k, natDegree p + natTrailingDegree p - k).snd) =\n sum p fun n x => x... | [
172,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma0_det | [
{
"state_after": "no goals",
"state_before": "N✝ N : ℕ\nA : { x // x ∈ Gamma0 N }\n⊢ ↑(det ↑↑A) = 1",
"tactic": "simp [A.1.property]"
}
] | [
121,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_symm | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.coe_zero | [] | [
148,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_mul_unit_left_left | [] | [
252,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.bipartiteBelow_swap | [] | [
59,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearEquiv_toLinearMap | [] | [
890,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_add_right_eq_add | [
{
"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 c : α\n⊢ toIocMod hp a (b + c) = toIocMod hp (a - c) b + c",
"tactic": "simp_rw [toIocMod, toIocDiv_sub_eq_toIocDiv_add', sub_add_eq_add_sub]"
... | [
545,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Order/RelClasses.lean | extensional_of_trichotomous_of_irrefl | [] | [
184,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_prod_of_subset_of_one_le' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.20233\nβ : Type ?u.20236\nM : Type ?u.20239\nN : Type u_2\nG : Type ?u.20245\nk : Type ?u.20248\nR : Type ?u.20251\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf g : ι → N\ns t : Finset ι\nh : s ⊆ t\nhf : ∀ (i : ι), i ∈ t → ¬i ∈... | [
166,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | isBoundedBilinearMapApply | [] | [
468,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.isConnected_setOf_sOppSide | [
{
"state_after": "case intro\nR : Type ?u.503618\nV : Type u_1\nV' : Type ?u.503624\nP : Type u_2\nP' : Type ?u.503630\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nx : P\nhx : ¬x ∈ s\np : P\nhp : p ∈ ↑s\n⊢ IsConn... | [
936,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sq_cos_pi_div_six | [
{
"state_after": "x : ℝ\nh1 : cos (π / 6) ^ 2 = 1 / 2 + 1 / 2 / 2\n⊢ cos (π / 6) ^ 2 = 3 / 4",
"state_before": "x : ℝ\n⊢ cos (π / 6) ^ 2 = 3 / 4",
"tactic": "have h1 : cos (π / 6) ^ 2 = 1 / 2 + 1 / 2 / 2 := by\n convert cos_sq (π / 6) using 3\n have h2 : 2 * (π / 6) = π / 3 := by linarith\n rw [h2, c... | [
869,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app | [
{
"state_after": "no goals",
"state_before": "C✝³ : Type u\n𝒞 : Category C✝³\ninst✝⁸ : MonoidalCategory C✝³\nC✝² : Type u\ninst✝⁷ : Category C✝²\ninst✝⁶ : MonoidalCategory C✝²\nC✝¹ : Type u\ninst✝⁵ : Category C✝¹\ninst✝⁴ : MonoidalCategory C✝¹\nC✝ : Type u\ninst✝³ : Category C✝\ninst✝² : MonoidalCategory C... | [
597,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Hom/Aut.lean | MulAut.coe_one | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | RelIso.cof_le_lift | [
{
"state_after": "α✝ : Type ?u.1813\nr✝ : α✝ → α✝ → Prop\nα : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝ : IsRefl β s\nf : r ≃r s\n⊢ ∀ (b : Cardinal),\n b ∈ Cardinal.lift '' {c | ∃ S, (∀ (a : β), ∃ b, b ∈ S ∧ s a b) ∧ (#↑S) = c} →\n sInf (Cardinal.lift '' {c | ∃ S, (∀ (a : α), ∃ b, b ... | [
104,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Order/Atoms.lean | covby_iff_atom_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8567\ninst✝ : PartialOrder α\na b : α\nh : a ≤ b\n⊢ a ⋖ b ↔ IsAtom { val := b, property := h }",
"tactic": "simp"
}
] | [
199,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.aeval_rename | [] | [
199,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddMonoidWithOne α\nn : Num\n⊢ ↑(succ' n) = ↑n + 1",
"tactic": "rw [← PosNum.cast_to_nat, succ'_to_nat, Nat.cast_add_one, cast_to_nat]"
}
] | [
722,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff | [
{
"state_after": "case refine'_1\nι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : LinearOrderedRing α\ninst✝² : LinearOrderedAddCommGroup β\ninst✝¹ : Module α β\ninst✝ : OrderedSMul α β\ns : Finset ι\nσ : Perm ι\nf : ι → α\ng : ι → β\nhfg : MonovaryOn f g ↑s\nhσ : {x | ↑σ x ≠ x} ⊆ ↑s\nh : ¬MonovaryOn f (g ∘ ... | [
139,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.comp_base | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.pow_mem | [
{
"state_after": "M : Type u_1\ninst✝¹ : Monoid M\ns : Set M\nA : Type ?u.30867\ninst✝ : AddMonoid A\nt : Set A\na : M\nhs : IsSubmonoid s\nh : a ∈ s\n⊢ 1 ∈ s",
"state_before": "M : Type u_1\ninst✝¹ : Monoid M\ns : Set M\nA : Type ?u.30867\ninst✝ : AddMonoid A\nt : Set A\na : M\nhs : IsSubmonoid s\nh : a ∈ ... | [
217,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_set | [
{
"state_after": "α : Type u_1\nn : Nat\na' : α\nl : List α\nh : n < length l\n⊢ ∃ l₁ a l₂, l = l₁ ++ a :: l₂ ∧ length l₁ = n ∧ modifyNth (fun x => a') n l = l₁ ++ a' :: l₂",
"state_before": "α : Type u_1\nn : Nat\na' : α\nl : List α\nh : n < length l\n⊢ ∃ l₁ a l₂, l = l₁ ++ a :: l₂ ∧ length l₁ = n ∧ set l ... | [
790,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
788,
1
] |
Mathlib/Data/List/Forall2.lean | List.Sublist.sublistForall₂ | [] | [
376,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.HasPoints.existsUnique_point | [] | [
116,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_self_ne_zero | [] | [
282,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_dvd_right | [] | [
34,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.equivQuotientZPowOfEquiv_trans | [
{
"state_after": "case h\nG : Type u\ninst✝⁴ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝³ : Group H\nφ : G →* H\nA B C : Type u\ninst✝² : CommGroup A\ninst✝¹ : CommGroup B\ninst✝ : CommGroup C\nf : A →* B\ng : B →* A\ne : A ≃* B\nd : B ≃* C\nn : ℤ\nx : A ⧸ range (zpowGroupHom n)\n⊢ ↑(Mu... | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.mem_iff' | [
{
"state_after": "no goals",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\n⊢ A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R",
"tactic": "rw [← transpose_mem_iff, mem_iff, transpose_transpose]"
}
] | [
182,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Logic/Relation.lean | Reflexive.comap | [] | [
106,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.neg_dotProduct | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.173129\nm : Type u_1\nn : Type ?u.173135\no : Type ?u.173138\nm' : o → Type ?u.173143\nn' : o → Type ?u.173148\nR : Type ?u.173151\nS : Type ?u.173154\nα : Type v\nβ : Type w\nγ : Type ?u.173161\ninst✝² : Fintype m\ninst✝¹ : Fintype n\ninst✝ : NonUni... | [
862,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_eq_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.276780\nβ : Type ?u.276783\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a / b = ⊤ ↔ a ≠ 0 ∧ b = 0 ∨ a = ⊤ ∧ b ≠ ⊤",
"tactic": "simp [div_eq_mul_inv, ENNReal.mul_eq_top]"
}
] | [
1558,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1557,
1
] |
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