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/RingTheory/Derivation/Basic.lean | Derivation.map_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁵ : CommSemiring R\nA : Type u_2\ninst✝⁴ : CommSemiring A\ninst✝³ : Algebra R A\nM : Type u_1\ninst✝² : AddCommMonoid M\ninst✝¹ : Module A M\ninst✝ : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\n⊢ ↑D (↑(algebraMap R A) r) = 0",
... | [
150,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/Cover.lean | not_covby_of_lt_of_lt | [] | [
297,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_neg | [
{
"state_after": "case a.h\nl : Type ?u.928988\nm : Type u_1\nn : Type u_2\no : Type ?u.928997\nm' : o → Type ?u.929002\nn' : o → Type ?u.929007\nR : Type ?u.929010\nS : Type ?u.929013\nα : Type v\nβ : Type w\nγ : Type ?u.929020\ninst✝ : Neg α\nM : Matrix m n α\ni✝ : n\nx✝ : m\n⊢ (-M)ᵀ i✝ x✝ = (-Mᵀ) i✝ x✝",
... | [
2015,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2013,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_norm | [] | [
2033,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2032,
1
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Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.translate_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.716463\nα : Type ?u.716466\nβ : Type u_3\nι : Type ?u.716472\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCancelCommMonoid E\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : Module 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nhf... | [
953,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow_left_iff | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 1 < x\n⊢ x ^ y < x ^ z ↔ y < z",
"tactic": "rw [lt_iff_not_le, rpow_le_rpow_left_iff hx, lt_iff_not_le]"
}
] | [
489,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Logic/Basic.lean | eq_iff_eq_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b : α\nh : ∀ {c : α}, a = c ↔ b = c\n⊢ a = b",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na✝ b : α\nh : a✝ = b\na : α\n⊢ a✝ = a ↔ b = a",
"tactic": "rw [h]"
}
] | [
92,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
9
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.ofNat_bit0 | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.mem_of_mem_of_le | [] | [
106,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_id | [] | [
427,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_list_eq_max_mk_aleph0 | [
{
"state_after": "case inl\nα : Type u\ninst✝ : Nonempty α\nh✝ : Finite α\n⊢ (#List α) = max (#α) ℵ₀\n\ncase inr\nα : Type u\ninst✝ : Nonempty α\nh✝ : Infinite α\n⊢ (#List α) = max (#α) ℵ₀",
"state_before": "α : Type u\ninst✝ : Nonempty α\n⊢ (#List α) = max (#α) ℵ₀",
"tactic": "cases finite_or_infinite ... | [
1012,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_apply_ite | [] | [
978,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_colon' | [] | [
371,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwiseDisjoint_union | [] | [
313,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_le_im | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | a ≤ z.im} = {z | z.im = a}",
"tactic": "simpa only [frontier_Ici] using frontier_preimage_im (Ici a)"
}
] | [
153,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mem_mul_span_singleton | [] | [
539,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.PosDef.prod | [] | [
119,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_zero | [] | [
52,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.copy_eq | [] | [
292,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_bound_aux1 | [
{
"state_after": "case intro\nX : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf✝ : GromovHausdorff.ProdSpaceFun X Y\nx y z t : X ⊕ Y\nf : GromovHausdorff.Cb X Y\nC Cf : ℝ\nhCf : Cf ∈ upperBounds (r... | [
308,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
9
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_of_mem_filter | [] | [
1987,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1986,
1
] |
Mathlib/Order/Bounds/Basic.lean | OrderBot.bddBelow | [] | [
991,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
11
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.Commute.zpow_zpow | [] | [
229,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ici a = Ici ↑a",
"tactic": "rw [← preimage_coe_Ici, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Ici_subset_Ioi.2 <| bot_lt_coe a)]"
}
] | [
213,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.uniformContinuous | [] | [
140,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.isLimit_iff_omega_dvd | [
{
"state_after": "case refine'_1\na : Ordinal\nl : IsLimit a\n⊢ a ≤ ω * (a / ω)\n\ncase refine'_2\na : Ordinal\nh : a ≠ 0 ∧ ω ∣ a\n⊢ IsLimit a",
"state_before": "a : Ordinal\n⊢ IsLimit a ↔ a ≠ 0 ∧ ω ∣ a",
"tactic": "refine' ⟨fun l => ⟨l.1, ⟨a / ω, le_antisymm _ (mul_div_le _ _)⟩⟩, fun h => _⟩"
},
{
... | [
2463,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2450,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.integrableOn_uIcc | [] | [
296,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_eq_neg_one_iff_neg | [] | [
1291,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1290,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_add_nth_order | [
{
"state_after": "case h\nR : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : Rˣ\nn : ℕ\nhzero : Tendsto (fun x_1 => -↑x⁻¹ * x_1) (𝓝 0) (𝓝 0)\nt : R\nht : inverse (↑x + t) = inverse (1 + ↑x⁻¹ * t) * ↑x⁻¹\nht' : inverse (1 - -↑x⁻¹ * t) = ∑ i in range n, (-↑x⁻¹ * t) ^ i + (-↑x⁻¹ * t) ^ n * inverse... | [
159,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/Order/Basic.lean | isGLB_of_mem_closure | [] | [
2024,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2022,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow' | [
{
"state_after": "case intro\nβ : Type ?u.39271\nA : Type ?u.39274\nG : Type ?u.39277\nM : Type u_1\nR : Type ?u.39283\ninst✝³ : Monoid M\ninst✝² : Preorder M\ninst✝¹ : CovariantClass M M (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\nx : M\ninst✝ : CovariantClass M M (fun x x_1 => x * x_1) fun x x_1 => x < x_1\n... | [
104,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.eq | [] | [
129,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_iff' | [] | [
976,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
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] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.Integrable.const_inner | [
{
"state_after": "α : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\nE : Type u_1\n𝕜 : Type u_3\ninst✝² : IsROrC 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nf : α → E\nc : E\nhf : Memℒp f 1\n⊢ Memℒp (fun x => inner c (f x)) 1",
"state_before": "α : Type u_2\nm : Measurable... | [
89,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_toSet_mk | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.min | [] | [
448,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
11
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_mul | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ ψ : PowerSeries R\n⊢ ∑ p in Finset.Nat.antidiagonal n, ↑(coeff R p.fst) φ * ↑(coeff R p.snd) ψ = ↑(coeff R n) (φ * ψ)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ ψ : PowerSeries R\n⊢ ↑(coeff R n) (φ * ψ) = ∑ p in Finset.Nat.antid... | [
1493,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MeasureTheory.Integrable.hasSum_intervalIntegral | [
{
"state_after": "ι : Type ?u.21798231\n𝕜 : Type ?u.21798234\nE : Type u_1\nF : Type ?u.21798240\nA : Type ?u.21798243\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\nhfi : Integrable f\ny : ℝ\n⊢ HasSum (fun n => ∫ (x : ℝ) in Ioc (y + ↑... | [
1435,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_eq_span | [] | [
88,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coord_unitsSMul | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.945140\nR : Type ?u.945143\nR₂ : Type u_2\nK : Type ?u.945149\nM : Type u_3\nM' : Type ?u.945155\nM'' : Type ?u.945158\nV : Type u\nV' : Type ?u.945163\nv : ι → M\ninst✝⁸ : Ring R\ninst✝⁷ : CommRing R₂\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : AddC... | [
1263,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_hasBasis_closure | [] | [
969,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | add_one_pow_unbounded_of_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : StrictOrderedSemiring α\ninst✝ : Archimedean α\nx y : α\nhy : 0 < y\nthis : 0 ≤ 1 + y\nn : ℕ\nh : x ≤ n • y\n⊢ (1 + y) ^ n = (y + 1) ^ n",
"tactic": "rw [add_comm]"
}
] | [
138,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsClosed.lowerSemicontinuousWithinAt_indicator | [] | [
249,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sSameSide_smul_vsub_vadd_left | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.365929\nP : Type u_3\nP' : Type ?u.365935\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx p₁ p₂ : P\... | [
728,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.left_not_mem | [] | [
170,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_subset | [] | [
636,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.Nondegenerate.toMatrix | [] | [
594,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_sub_cos | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cos x - cos y) = ↑(-2 * sin ((x + y) / 2) * sin ((x - y) / 2))",
"tactic": "simp [cos_sub_cos]"
}
] | [
1218,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
8
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_mk | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.eval_apply_injective | [] | [
573,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAt_id | [] | [
641,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.comp_symm_eq | [] | [
594,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_set_mk | [] | [
223,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
9
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.single_smul | [] | [
103,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_eq_iInf' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\ns : Set α\n⊢ ↑(trim m) s = ⨅ (t : { t // s ⊆ t ∧ MeasurableSet t }), ↑m ↑t",
"tactic": "simp [iInf_subtype, iInf_and, trim_eq_iInf]"
}
] | [
1663,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.norm_le | [] | [
120,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_sub_inv_two | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.329111\nβ : Type ?u.329114\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 1 - 2⁻¹ = 2⁻¹",
"tactic": "simpa only [div_eq_mul_inv, one_mul] using sub_half one_ne_top"
}
] | [
1769,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticAt.continuousAt | [] | [
883,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
11
] |
Mathlib/Analysis/PSeries.lean | Finset.sum_condensed_le | [
{
"state_after": "case h.e'_3\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 1 < m → m ≤ n → f n ≤ f m\nn : ℕ\n⊢ ∑ k in range (n + 1), 2 ^ k • f (2 ^ k) = f 1 + 2 • ∑ k in range n, 2 ^ k • f (2 ^ (k + 1))",
"state_before": "M : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M... | [
91,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Sequences.lean | IsSeqCompact.exists_tendsto | [] | [
336,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | RieszExtension.step | [
{
"state_after": "case intro.intro\n𝕜 : Type ?u.190292\nE : Type u_1\nF : Type ?u.190298\nG : Type ?u.190301\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : ConvexCone ℝ E\nf : E →ₗ.[ℝ] ℝ\nnonneg : ∀ (x : { x // x ∈ f.domain }), ↑x ∈ s → 0 ≤ ↑f x\ndense : ∀ (y : E), ∃ x, ↑x + y ∈ s\nhdom : f.domain ≠ ⊤\ny : ... | [
782,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.univ_eq_zero_iff | [] | [
386,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Topology/Separation.lean | Set.Finite.t2_separation | [] | [
902,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.range_exp | [
{
"state_after": "case intro\nx : ℂ\n⊢ exp x ∈ {0}ᶜ",
"state_before": "x : ℂ\n⊢ x ∈ Set.range exp → x ∈ {0}ᶜ",
"tactic": "rintro ⟨x, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nx : ℂ\n⊢ exp x ∈ {0}ᶜ",
"tactic": "exact exp_ne_zero x"
}
] | [
60,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.fst_prod | [] | [
106,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_pos_of_ne_zero_right | [] | [
316,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.continuous_arcsin | [] | [
101,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_quotient_le | [] | [
588,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | one_eq_bit1 | [
{
"state_after": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : NoZeroDivisors R\ninst✝ : CharZero R\na : R\n⊢ bit1 a = 1 ↔ a = 0",
"state_before": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : NoZeroDivisors R\ninst✝ : CharZero R\na : R\n⊢ 1 = bit1 a ↔ a = 0",
"tactic": "rw [eq_comm]"
},
{
... | [
153,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.coprime_div_right | [] | [
331,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
330,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.rotate_darts | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v : V\nc : Walk G v v\nh : u ∈ support c\n⊢ (darts (dropUntil c u h) ++ darts (takeUntil c u h)) ~r darts c",
"state_before": "V : Type u\nV' : Type v\nV'' : Type ... | [
1219,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_zero | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Logic/Relation.lean | Relation.ReflTransGen.cases_head | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.17670\nγ : Type ?u.17673\nδ : Type ?u.17676\nr : α → α → Prop\na b c d : α\n⊢ b = b ∨ ∃ c, r b c ∧ ReflTransGen r c b\n\ncase head\nα : Type u_1\nβ : Type ?u.17670\nγ : Type ?u.17673\nδ : Type ?u.17676\nr : α → α → Prop\na b c d a✝¹ c✝ : α\nh'✝ : r a✝¹ c✝\n... | [
325,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/List/Infix.lean | List.eq_of_suffix_of_length_eq | [] | [
127,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mul_star_eq_coe | [
{
"state_after": "S : Type ?u.344129\nT : Type ?u.344132\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ star a * a = ↑(star a * a).re",
"state_before": "S : Type ?u.344129\nT : Type ?u.344132\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ a * star a ... | [
712,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.derivWithin | [] | [
462,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.ihom.ev_naturality | [] | [
122,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.toFractionRing_eq | [
{
"state_after": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nx✝¹ : RatFunc K\nx✝ : FractionRing K[X]\nx : K[X] × { x // x ∈ K[X]⁰ }\n⊢ IsLocalization.mk' (Localization K[X]⁰) x.fst x.snd =\n IsLocalization.mk' (FractionRing K[X]) (↑(RingHom.id K[X]) x.fst)\n { val := ↑(RingHom.id K[X]) ↑x.snd,... | [
1064,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_nonsing_inv_det | [] | [
408,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_le_card_fintype | [] | [
131,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.Hereditarily.empty | [
{
"state_after": "p : ZFSet → Prop\nx y : ZFSet\n⊢ ∀ (x : ZFSet), (∀ (y : ZFSet), y ∈ x → Hereditarily p y → p ∅) → Hereditarily p x → p ∅",
"state_before": "p : ZFSet → Prop\nx y : ZFSet\n⊢ Hereditarily p x → p ∅",
"tactic": "apply @ZFSet.inductionOn _ x"
},
{
"state_after": "p : ZFSet → Prop\n... | [
1439,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_sup | [] | [
665,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_deleteVerts | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.266848\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns✝ s s' : Set V\n⊢ deleteVerts (deleteVerts G' s) s' = deleteVerts G' (s ∪ s')",
"tactic": "ext <;> simp (config := { contextual := true }) [not_or, and_assoc]"
}
] | [
1224,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.mul_coeff_order_add_order | [
{
"state_after": "case pos\nΓ✝ : Type ?u.1226138\nR : Type u_2\ninst✝² : OrderedCancelAddCommMonoid Γ✝\nΓ : Type u_1\ninst✝¹ : LinearOrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y : HahnSeries Γ R\nhx : x = 0\n⊢ coeff (x * y) (order x + order y) = coeff x (order x) * coeff y (order y)\n\... | [
780,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_eq_iInter | [] | [
205,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_gt_of_unbounded_ge | [] | [
134,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexHull_insert | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.134927\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns t u : Set E\nx y : E\nhs : Set.Nonempty s\n⊢ ↑(convexHull 𝕜).toOrderHom (insert x s) = convexJoin 𝕜 {x} (↑(convexHull 𝕜).toOrderHo... | [
209,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioo_eq_nhdsWithin_Ioi | [] | [
439,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/CategoryTheory/Sites/CompatiblePlus.lean | CategoryTheory.GrothendieckTopology.plusCompIso_inv_eq_plusLift | [
{
"state_after": "case hγ\nC : Type u\ninst✝⁸ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁷ : Category D\nE : Type w₂\ninst✝⁶ : Category E\nF : D ⥤ E\ninst✝⁵ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁴ : ∀ (α β : Type (max v u)) (fst snd ... | [
227,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonnegg_neg_pos | [
{
"state_after": "no goals",
"state_before": "d✝ : ℤ\nc d b : ℕ\n⊢ Nonnegg c d (-↑0) ↑b → SqLe 0 d b c",
"tactic": "simp [SqLe, Nat.zero_le]"
},
{
"state_after": "d✝ : ℤ\nc d a b : ℕ\n⊢ Nonnegg c d (Int.negSucc a) ↑b ↔ SqLe (a + 1) d b c",
"state_before": "d✝ : ℤ\nc d a b : ℕ\n⊢ Nonnegg c d ... | [
499,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.exists_nontrivial_relation_sum_zero_of_rank_succ_lt_card | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\nt : Finset V\nh : finrank K V + 1 < card t\ncard_pos : 0 < card t\n⊢ ∃ f, ∑ e in t, f e • e = 0 ∧ ∑ e in t... | [
567,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioo_of_Ico | [] | [
208,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.is_linear_image | [] | [
215,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivAt.sin | [] | [
996,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.ext | [] | [
155,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.sub | [] | [
308,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Set/Function.lean | StrictMonoOn.congr | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9920\nι : Sort ?u.9923\nπ : α → Type ?u.9928\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na✝ : α\nb✝ : β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nh₁ : StrictMonoOn f₁ s\nh : EqOn f₁ f... | [
267,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_le_one | [
{
"state_after": "case intro\nz : ℝ\nhz : 0 ≤ z\nx : ℝ≥0\nhx : ↑x ≤ 1\n⊢ ↑x ^ z ≤ 1",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx : x ≤ 1\nhz : 0 ≤ z\n⊢ x ^ z ≤ 1",
"tactic": "lift x to ℝ≥0 using ne_of_lt (lt_of_le_of_lt hx coe_lt_top)"
},
{
"state_after": "case intro\nz : ℝ\nhz : 0 ≤ z\nx : ℝ≥0\nhx : ... | [
674,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.98205\nk : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁴ : AddCommGroup V\ninst✝³ : AffineSpace V P\ninst✝² : Ring k\ninst✝¹ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j✝ : ι\ne : ι ≃ ι'\ninst✝ : DecidableEq ι\ni j : ι\n⊢ ↑(c... | [
186,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.inv_add_inv_conj_ennreal | [
{
"state_after": "no goals",
"state_before": "p q : ℝ\nh : IsConjugateExponent p q\n⊢ 1 / ENNReal.ofReal p + 1 / ENNReal.ofReal q = 1",
"tactic": "rw [← ENNReal.ofReal_one, ← ENNReal.ofReal_div_of_pos h.pos,\n ← ENNReal.ofReal_div_of_pos h.symm.pos,\n ← ENNReal.ofReal_add h.one_div_nonneg h.symm.o... | [
117,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
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