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/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.div_comp | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Order/CompleteLattice.lean | biInf_inf | [] | [
1280,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na : α\nhs : Set.Finite s\nht : Set.Finite t\nh : Set.Finite s\n⊢ Finset.Nonempty (Finite.toFinset h) ↔ Set.Nonempty s",
"tactic": "rw [← Finset.coe_nonempty, Finite.coe_toFinset]"
}
] | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
11
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.re_im_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1131588\nγ : Type ?u.1131591\nδ : Type ?u.1131594\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝³ : MeasurableSpace δ\ninst✝² : NormedAddCommGroup β\ninst✝¹ : NormedAddCommGroup γ\n𝕜 : Type u_2\ninst✝ : IsROrC 𝕜\nf : α → 𝕜\n⊢ Memℒp (fun x => ↑IsROrC.re (f x)) 1 ∧ M... | [
1142,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_univ | [] | [
108,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_inv | [
{
"state_after": "x : ℂ\n⊢ arg (↑(↑normSq x)⁻¹ * ↑(starRingEnd ℂ) x) = arg (↑(starRingEnd ℂ) x)",
"state_before": "x : ℂ\n⊢ arg x⁻¹ = if arg x = π then π else -arg x",
"tactic": "rw [← arg_conj, inv_def, mul_comm]"
},
{
"state_after": "case pos\nx : ℂ\nhx : x = 0\n⊢ arg (↑(↑normSq x)⁻¹ * ↑(starR... | [
326,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp_smul_const_of_mem_ball' | [] | [
364,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_pred_of_reflexive | [] | [
154,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.norm_le_pow_iff_norm_lt_pow_add_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nn : ℤ\naux : ∀ (n : ℤ), 0 < ↑p ^ n\n⊢ ‖x‖ ≤ ↑p ^ n ↔ ‖x‖ < ↑p ^ (n + 1)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nn : ℤ\n⊢ ‖x‖ ≤ ↑p ^ n ↔ ‖x‖ < ↑p ^ (n + 1)",
"tactic": "have aux : ∀ n : ℤ, 0 < ((p : ℝ) ^ n) := by\n apply ... | [
1174,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Data/PFun.lean | PFun.Part.bind_comp | [
{
"state_after": "case H\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.57854\nε : Type ?u.57857\nι : Type ?u.57860\nf✝ : α →. β\nf : β →. γ\ng : α →. β\na : Part α\nc : γ\n⊢ c ∈ Part.bind a (comp f g) ↔ c ∈ Part.bind (Part.bind a g) f",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ :... | [
619,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | LaurentSeries.coe_algebraMap | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.measurable_rnDeriv | [
{
"state_after": "α : Type u_1\nβ : Type ?u.303346\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t s : SignedMeasure α\nμ : Measure α\n⊢ Measurable fun x =>\n ENNReal.toReal (Measure.rnDeriv (toJordanDecomposition s).posPart μ x) -\n ENNReal.toReal (Measure.rnDeriv (toJordanDecomposition s).negPart μ x)"... | [
916,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_rpow_neg_div | [
{
"state_after": "case h.e'_3.h.h.e'_6.h.e'_6\nx✝ : ℝ\n⊢ x✝ = 1 * x✝ + 0",
"state_before": "⊢ Tendsto (fun x => x ^ (-1 / x)) atTop (𝓝 1)",
"tactic": "convert tendsto_rpow_div_mul_add (-(1 : ℝ)) _ (0 : ℝ) zero_ne_one"
},
{
"state_after": "case h.e'_3.h.h.e'_6.h.e'_6\nx✝ : ℝ\n⊢ x✝ = 1 * x✝ + 0",... | [
89,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.bddBelow | [] | [
1618,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1617,
11
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_rat | [
{
"state_after": "R✝ : Type u\nS : Type ?u.101390\nA✝ : Type v\ninst✝⁹ : CommRing R✝\ninst✝⁸ : CommRing S\ninst✝⁷ : Ring A✝\ninst✝⁶ : Algebra R✝ A✝\ninst✝⁵ : Algebra R✝ S\ninst✝⁴ : Algebra S A✝\ninst✝³ : IsScalarTower R✝ S A✝\nR : Type u\nA : Type v\ninst✝² : DivisionRing A\ninst✝¹ : Field R\ninst✝ : Algebra R ... | [
132,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_neg_of_neg_of_nonpos | [] | [
838,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
837,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | Monotone.ciSup_mem_Inter_Icc_of_antitone | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.61525\nι : Sort ?u.61528\ninst✝¹ : ConditionallyCompleteLattice α\ns t : Set α\na b : α\ninst✝ : SemilatticeSup β\nf g : β → α\nhf : Monotone f\nhg : Antitone g\nh : f ≤ g\nn : β\n⊢ (⨆ (n : β), f n) ∈ Icc (f n) (g n)",
"state_before": "α : Type u_2\n... | [
894,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | ConformalAt.differentiableAt | [] | [
95,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | zero_memℓp | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ Memℓp 0 0\n\ncase inr.inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ Memℓp 0 ⊤\n\ncase inr.inr\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i... | [
143,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_biUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.491823\nι : Type ?u.491826\ninst✝ : PseudoMetricSpace α\nx : α\ns✝ t : Set α\nr : ℝ\nI : Set β\ns : β → Set α\nH : Set.Finite I\n⊢ Bounded (⋃ (i : β) (_ : i ∈ I), s i) ↔ ∀ (i : β), i ∈ I → Bounded (s i)",
"tactic": "simp o... | [
2383,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2381,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_one | [] | [
670,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.dist_le_mul | [] | [
273,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.bot_prod_bot | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.302242\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.302251\ninst✝² : AddGroup A\nH K : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.302278\ninst✝ : Group P\n⊢ ↑(prod ⊥ ⊥) = ↑⊥",
"tactic": "simp [coe_prod,... | [
1759,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1758,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuous_of_continuousAt_one | [] | [
872,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.summable_toReal | [] | [
1091,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.dual_ordSeparatingSet | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ ordSeparatingSet (↑ofDual ⁻¹' s) (↑ofDual ⁻¹' t) = ↑ofDual ⁻¹' ordSeparatingSet s t",
"tactic": "simp only [ordSeparatingSet, mem_preimage, ← toDual.surjective.iUnion_comp, ofDual_toDual,\n dual... | [
191,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_zero_of_not_measurable | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.592052\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\nv w : VectorMeasure α M\ni j : Set α\nhi : ¬MeasurableSet i\n⊢ restrict v i ≤ restrict 0 i",
"tactic": "rw [restrict_zero, res... | [
1014,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.union_vsub_inter_subset_union | [] | [
705,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mul_def | [] | [
1257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
src/lean/Init/SizeOfLemmas.lean | USize.sizeOf | [
{
"state_after": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝ } = toNat { val := val✝ } + 2",
"state_before": "a : USize\n⊢ SizeOf.sizeOf a = toNat a + 2",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_before": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝... | [
27,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
26,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_blsub | [] | [
1816,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1815,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | symm_trans_mem_contDiffGroupoid | [] | [
604,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isFractional | [] | [
137,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
11
] |
Mathlib/Data/Set/Function.lean | Set.restrict_eq | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin_symm_apply_succ | [
{
"state_after": "case refine'_1\nn : ℕ\ne : Perm (Fin n)\np : Fin (n + 1)\nx : Fin n\n⊢ ↑(↑decomposeFin.symm (0, e)) (Fin.succ x) = ↑(swap 0 0) (Fin.succ (↑e x))\n\ncase refine'_2\nn : ℕ\ne : Perm (Fin n)\np : Fin (n + 1)\nx : Fin n\n⊢ ∀ (i : Fin n), ↑(↑decomposeFin.symm (Fin.succ i, e)) (Fin.succ x) = ↑(swap ... | [
57,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/DisjointCoproduct.lean | CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts | [] | [
135,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup'_mem | [] | [
872,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toSimpleFunc_toLp | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1579645\nι : Type ?u.1579648\nE : Type u_2\nF : Type ?u.1579654\n𝕜 : Type ?u.1579657\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\nf : α →ₛ E\nhfi : Memℒp (↑f) p\n⊢ AEEqFun.mk ↑(toSimpleFunc (toLp f... | [
639,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpowersHom_apply | [] | [
859,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_eq_top_iff | [] | [
490,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | summable_of_nnnorm_bounded | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.23601\nE : Type u_2\nF : Type ?u.23607\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : CompleteSpace E\nf : ι → E\ng : ι → ℝ≥0\nhg : Summable g\nh : ∀ (i : ι), ‖f i‖₊ ≤ g i\ni : ι\n⊢ ‖f i‖ ≤ (fun i => ↑(g ... | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_inf_of_inter | [] | [
440,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Algebra/Group/Commutator.lean | commutatorElement_def | [] | [
25,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableOn.add | [] | [
158,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.compRightContinuousMap_apply | [] | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.classification | [
{
"state_after": "case mp\nx y z : ℤ\nh : PythagoreanTriple x y z\n⊢ PythagoreanTriple x y z →\n ∃ k m n,\n (x = k * (m ^ 2 - n ^ 2) ∧ y = k * (2 * m * n) ∨ x = k * (2 * m * n) ∧ y = k * (m ^ 2 - n ^ 2)) ∧\n (z = k * (m ^ 2 + n ^ 2) ∨ z = -k * (m ^ 2 + n ^ 2))\n\ncase mpr\nx y z : ℤ\nh : Pythagor... | [
700,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | Convex.interior_nonempty_iff_affineSpan_eq_top | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type ?u.126361\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : FiniteDimensional ℝ V\ns : Set V\nhs : Convex ℝ s\n⊢ Set.Nonempty (interior s) ↔ affineSpan ℝ s = ⊤",
"ta... | [
164,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_C_right | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type u_1\nR : Type u_2\nS : Type ?u.79903\nT : Type ?u.79906\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ f : σ → MvPolynomial τ R\nx : R\n⊢ ↑(bind₁ f) (↑C x) = ↑C x",
"tactic": "simp [bind₁, algebraMap_eq]"... | [
176,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | subset_generatePiSystem_self | [] | [
236,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.dualDual_symm_apply | [] | [
973,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Data/Polynomial/Degree/CardPowDegree.lean | Polynomial.cardPowDegree_zero | [] | [
86,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioc_ae_eq_Icc' | [] | [
2980,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2979,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.interior_preimage_subset_preimage_interior | [] | [
410,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.one_div_zpow | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℤ\n⊢ (1 / A) ^ n = 1 / A ^ n",
"tactic": "simp only [one_div, inv_zpow]"
}
] | [
334,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.ae_eq_set_pi | [] | [
482,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.paste_vert | [] | [
511,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_subgroup_dvd_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Group α\ns✝ t : Subgroup α\ninst✝¹ : Fintype α\ns : Subgroup α\ninst✝ : Fintype { x // x ∈ s }\n⊢ Fintype.card { x // x ∈ s } ∣ Fintype.card α",
"tactic": "classical simp [card_eq_card_quotient_mul_card_subgroup s, @dvd_mul_left ℕ]"
... | [
794,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_three | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.12765\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\n⊢ a ^ 3 = a * (a * a)",
"tactic": "rw [pow_succ, pow_two]"
}
] | [
115,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.trailingCoeff_isUnit | [] | [
175,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_right₀ | [] | [
569,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_image_right | [
{
"state_after": "α : Type u_2\nα' : Type ?u.61166\nβ : Type u_4\nβ' : Type ?u.61172\nγ : Type u_3\nγ' : Type ?u.61178\nδ : Type u_1\nδ' : Type ?u.61184\nε : Type ?u.61187\nε' : Type ?u.61190\nζ : Type ?u.61193\nζ' : Type ?u.61196\nν : Type ?u.61199\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : De... | [
331,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_map_right | [
{
"state_after": "case h.e'_2.h.e'_5\nα : Type u\nβ : Type u_3\nγ : Type u_2\nδ : Type u_1\nε : Type ?u.50129\nf : α → β → γ\nl : List α\ng : δ → β\nl' : List δ\n⊢ l = map id l",
"state_before": "α : Type u\nβ : Type u_3\nγ : Type u_2\nδ : Type u_1\nε : Type ?u.50129\nf : α → β → γ\nl : List α\ng : δ → β\nl... | [
155,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.polynomial_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nl : Filter α\nk f g g' : α → β\ninst✝³ : TopologicalSpace β\ninst✝² : CommSemiring β\ninst✝¹ : ContinuousAdd β\ninst✝ : ContinuousMul β\nhf : SuperpolynomialDecay l k f\np✝ p q : β[X]\nhp : SuperpolynomialDecay l k fun x => eval (k x)... | [
135,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_injective | [] | [
965,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_sup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.16048\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ y ⊓ (x ⊔ z) ⊔ y \\ x ⊓ y \\ z = (y ⊓ (x ⊔ z) ⊔ y \\ x) ⊓ (y ⊓ (x ⊔ z) ⊔ y \\ z)",
"tactic": "rw [sup_inf_left]"
},
{
"state_after": "no goals",
"state_before": "α ... | [
301,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_div_cancel' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.63416\nG : Type ?u.63419\nα : Type u_1\nM : Type ?u.63425\nN : Type ?u.63428\ninst✝ : DivisionCommMonoid α\na b✝ c d : α\nh : IsUnit a\nb : α\n⊢ a * (b / a) = b",
"tactic": "rw [mul_comm, h.div_mul_cancel]"
}
] | [
478,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
11
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_embDomain | [] | [
845,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.ofNatCode_eq | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.ae_le_pi | [] | [
471,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.coe_mul | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_univ | [] | [
949,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_infs_subset_left | [] | [
402,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.isClosed | [
{
"state_after": "𝕜 : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing 𝕜\ninst✝⁹ : NoZeroDivisors 𝕜\ninst✝⁸ : TopologicalSpace 𝕜\ninst✝⁷ : ContinuousAdd 𝕜\ninst✝⁶ : ContinuousConstSMul 𝕜 𝕜\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ : Semiring A\ninst✝³ : Algebra 𝕜 A\ninst✝² : Nontrivial 𝕜\ninst✝¹ : T2Space 𝕜\nins... | [
185,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.uniformContinuous | [] | [
217,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
11
] |
Mathlib/Algebra/Category/ModuleCat/Kernels.lean | ModuleCat.kernelIsoKer_inv_kernel_ι | [] | [
107,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasStrictDerivAt.const_add | [] | [
123,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.dist_pointReflection_self_real | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.2147195\nV : Type u_2\nV₁ : Type ?u.2147201\nV₂ : Type ?u.2147204\nV₃ : Type ?u.2147207\nV₄ : Type ?u.2147210\nP₁ : Type ?u.2147213\nP : Type u_1\nP₂ : Type ?u.2147219\nP₃ : Type ?u.2147222\nP₄ : Type ?u.2147225\ninst✝²² : NormedField 𝕜\ninst✝²¹ : ... | [
827,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.51711\nα : Type u_1\nβ : Type ?u.51717\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢ ⌈0⌉₊ = 0",
"tactic": "rw [← Nat.cast_zero, ceil_natCast]"
}
] | [
324,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.pow_fst | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Order.cof_le | [] | [
79,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousWithinAt.add | [] | [
939,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_union_of_monotone | [] | [
601,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_union_self_eq_union | [] | [
2126,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2125,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_iff_le_one_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.18862\ninst✝³ : MulOneClass α\ninst✝² : LE α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ a * b ≤ a ↔ a * b ≤ a * 1",
... | [
418,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_iff_coeff_lifts | [
{
"state_after": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\n⊢ (∀ (n : ℕ), coeff p n ∈ RingHom.rangeS f) ↔ ∀ (n : ℕ), coeff p n ∈ Set.range ↑f",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\n⊢ p ∈ lifts f... | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Sign.lean | SignType.nonneg_iff_ne_neg_one | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ 0 ≤ a ↔ a ≠ -1",
"tactic": "cases a <;> decide"
}
] | [
171,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/WithBot.lean | WithBot.map_bot | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.last_append1 | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_mul | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.hpath_hext | [
{
"state_after": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ x₃ : X\np₁ : Path x₀ x₁\np₂ : Path x₀ x₃\nhp : ∀ (t : ↑I), ↑p₁ t = ↑p₂ t\n⊢ HEq (Quotient.mk (Homotopic.setoid x₀ x₁) p₁) (Quotient.mk (Homotopic.setoid x₀ x₃) p₂)",
"state_before": "X : Type u\nY : Type... | [
343,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.frontier_preimage | [] | [
291,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Algebra/Order/Nonneg/Field.lean | Nonneg.inv_mk | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.totallyBounded_of_finite_discretization | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nX : Type ?u.63903\nι : Type ?u.63906\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ s : Set α\nH : ∀ (ε : ℝ), ε > 0 → ∃ β x F, ∀ (x y : ↑s), F x = F y → dist ↑x ↑y < ε\nhs : s = ∅\n⊢ TotallyBounded s\n\ncase inr\nα : Type u\nβ : Type v\nX : Type ?u... | [
880,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Topology/Order.lean | nhds_mono | [] | [
594,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/LinearAlgebra/Coevaluation.lean | contractLeft_assoc_coevaluation | [
{
"state_after": "K : Type u\ninst✝³ : Field K\nV : Type v\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nthis : DecidableEq ↑(Basis.ofVectorSpaceIndex K V) := Classical.decEq ↑(Basis.ofVectorSpaceIndex K V)\n⊢ LinearMap.comp (LinearMap.rTensor (Module.Dual K V) (contractLeft K V)... | [
80,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/Instances/Rat.lean | Nat.uniformEmbedding_coe_rat | [
{
"state_after": "no goals",
"state_before": "⊢ Pairwise fun x y => 1 ≤ dist ↑x ↑y",
"tactic": "simpa using Nat.pairwise_one_le_dist"
}
] | [
67,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "σ : Type ?u.4375066\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ : R[X]\n⊢ ↑φ = 1 ↔ φ = 1",
"tactic": "rw [← coe_one, coe_inj]"
}
] | [
2628,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2628,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isVonNBounded_of_smul_tendsto_zero | [
{
"state_after": "𝕜 : Type ?u.173131\n𝕜' : Type ?u.173134\nE : Type u_3\nE' : Type ?u.173140\nF : Type ?u.173143\nι : Type u_1\n𝕝 : Type u_2\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : NontriviallyNormedField 𝕝\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : Module 𝕝 E\ninst✝² : TopologicalSpace E\ninst✝¹ ... | [
182,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos | [
{
"state_after": "x y : ℝ*\nhx : InfinitePos x\nhy₁ : ¬Infinitesimal y\nhy₂ : 0 < y\nr : ℝ\nhy₁' : ∃ x, ¬(0 < x → -↑x < y ∧ y < ↑x)\n⊢ ↑r < x * y",
"state_before": "x y : ℝ*\nhx : InfinitePos x\nhy₁ : ¬Infinitesimal y\nhy₂ : 0 < y\nr : ℝ\n⊢ ↑r < x * y",
"tactic": "have hy₁' := not_forall.mp (mt infinite... | [
821,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.DualBases.coeffs_lc | [
{
"state_after": "case h\nR : Type u_2\nM : Type u_3\nι : Type u_1\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ne : ι → M\nε : ι → Dual R M\ninst✝ : DecidableEq ι\nh : DualBases e ε\nl : ι →₀ R\ni : ι\n⊢ ↑(coeffs h (lc e l)) i = ↑l i",
"state_before": "R : Type u_2\nM : Type u_3\nι : ... | [
714,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
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