file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Ioc b c = Ioc (b - a) (c - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
401,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tan_mul_I | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ tan (x * I) = tanh x * I",
"tactic": "rw [tan, sin_mul_I, cos_mul_I, mul_div_right_comm, tanh_eq_sinh_div_cosh]"
}
] | [
843,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.map_exp_nhds | [] | [
354,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α Mul.mul LE.le\na : α\n⊢ a⁻ = 1 ↔ 1 ≤ a",
"tactic": "rw [le_antisymm_iff, neg_le_one_iff, inv_le_one', and_iff_left (one_le_neg _)]"
}
] | [
239,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Field/Power.lean | Odd.neg_one_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DivisionRing α\nn : ℤ\nh : Odd n\n⊢ (-1) ^ n = -1",
"tactic": "rw [h.neg_zpow, one_zpow]"
}
] | [
41,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.map_constants | [] | [
627,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Std/Data/Option/Lemmas.lean | Option.liftOrGet_none_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α → α\nb : Option α\n⊢ liftOrGet f none b = b",
"tactic": "cases b <;> rfl"
}
] | [
185,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
184,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mex_monotone | [
{
"state_after": "α✝ : Type ?u.377983\nβ✝ : Type ?u.377986\nγ : Type ?u.377989\nr : α✝ → α✝ → Prop\ns : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u\nf : α → Ordinal\ng : β → Ordinal\nh : range f ⊆ range g\ni : α\nhi : f i = mex g\n⊢ False",
"state_before": "α✝ : Type ?u.377983\nβ✝ : Type ?u.377986\nγ : T... | [
2043,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2038,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_coe | [] | [
38,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_zero | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_gt_univ | [] | [
165,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Units.mapEquiv_symm | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.hom_eval₂ | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝² : Semiring R\np q r : R[X]\ninst✝¹ : Semiring S\ninst✝ : Semiring T\nf : R →+* S\ng : S →+* T\nx : S\n⊢ ↑g (eval₂ f x p) = eval₂ (RingHom.comp g f) (↑g x) p",
"tactic": "rw [← eval₂_map... | [
1008,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | cauchySeq_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nu : ℕ → α\n⊢ CauchySeq u ↔ ∀ (V : Set (α × α)), V ∈ 𝓤 α → ∃ N, ∀ (k : ℕ), k ≥ N → ∀ (l : ℕ), l ≥ N → (u k, u l) ∈ V",
"tactic": "simp only [cauchySeq_iff', Filter.eventually_atTop_prod_self', mem_preimage, Pro... | [
234,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.fuzzy_of_equiv_of_fuzzy | [] | [
981,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.algebra_map_surjective_of_is_integral' | [] | [
164,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.subset_set_smul_iff | [] | [
925,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.inv_mul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ_[p]\nhz : ‖z‖ = 1\n⊢ inv z * z = 1",
"tactic": "rw [mul_comm, mul_inv hz]"
}
] | [
443,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_diff | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_le_apply | [
{
"state_after": "ι : Type u\nf : ι → Ordinal → Ordinal\ninst✝ : Nonempty ι\nH : ∀ (i : ι), IsNormal (f i)\na b : Ordinal\n⊢ (¬∃ i, nfpFamily f a ≤ f i b) ↔ ¬nfpFamily f a ≤ b",
"state_before": "ι : Type u\nf : ι → Ordinal → Ordinal\ninst✝ : Nonempty ι\nH : ∀ (i : ι), IsNormal (f i)\na b : Ordinal\n⊢ (∃ i, ... | [
109,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Finset/Image.lean | Function.Semiconj.finset_map | [] | [
148,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_le_iff_le_sin' | [
{
"state_after": "case inl\nx y : ℝ\nhy : y ∈ Ico (-(π / 2)) (π / 2)\nhx₁ : x ≤ -1\n⊢ arcsin x ≤ y ↔ x ≤ sin y\n\ncase inr\nx y : ℝ\nhy : y ∈ Ico (-(π / 2)) (π / 2)\nhx₁ : -1 ≤ x\n⊢ arcsin x ≤ y ↔ x ≤ sin y",
"state_before": "x y : ℝ\nhy : y ∈ Ico (-(π / 2)) (π / 2)\n⊢ arcsin x ≤ y ↔ x ≤ sin y",
"tactic... | [
159,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hasBasis_nhdsSet_cthickening | [] | [
1294,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1291,
1
] |
Mathlib/Algebra/Category/Mon/FilteredColimits.lean | MonCat.FilteredColimits.colimitMulAux_eq_of_rel_right | [
{
"state_after": "case mk\nJ : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ MonCat\ninst✝ : IsFiltered J\nx y' : (j : J) × ↑(F.obj j)\nj₁ : J\ny : ↑(F.obj j₁)\nhyy' : Types.FilteredColimit.Rel (F ⋙ forget MonCat) { fst := j₁, snd := y } y'\n⊢ colimitMulAux F x { fst := j₁, snd := y } = colimitMulAux F x y'",
"... | [
180,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Basic.lean | tendsto_const_nhds | [] | [
1037,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_erase | [] | [
1947,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1945,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.greatest_iff | [] | [
241,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.zero_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁶ : CommSemiring R\nR' : Type ?u.210413\ninst✝¹⁵ : Monoid R'\nR'' : Type u_4\ninst✝¹⁴ : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.210431\nQ : Type ?u.210434\nS : Type ?u.210437\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid N... | [
256,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
11
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.isLocallyFraction_pred | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.compl_mem_ae_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.98230\nγ : Type ?u.98233\nδ : Type ?u.98236\nι : Type ?u.98239\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t s : Set α\n⊢ sᶜ ∈ Measure.ae μ ↔ ↑↑μ s = 0",
"tactic": "simp only [mem_ae_iff, compl_compl]"
}
] | [
382,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodalWeight_eq_eval_nodal_erase_inv | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\n⊢ nodalWeight s v i = (eval (v i) (nodal (Finset.erase s i) v))⁻¹",
"tactic": "rw [eval_nodal, nodalWeight, prod_inv_distrib]"
}
] | [
565,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_mul_cos_add_sin_mul_I_sub | [
{
"state_after": "r : ℝ\nhr : 0 < r\nθ : ℝ\n⊢ ↑(- -⌊(-π + 2 * π - θ) / (2 * π)⌋) * (2 * π) = 2 * π * ↑⌊(π - θ) / (2 * π)⌋",
"state_before": "r : ℝ\nhr : 0 < r\nθ : ℝ\n⊢ arg (↑r * (cos ↑θ + sin ↑θ * I)) - θ = 2 * π * ↑⌊(π - θ) / (2 * π)⌋",
"tactic": "rw [arg_mul_cos_add_sin_mul_I_eq_toIocMod hr, toIocMod... | [
450,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | zero_zpow_eq | [
{
"state_after": "case inl\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\nn : ℤ\nh : n = 0\n⊢ 0 ^ n = 1\n\ncase inr\nG₀ : Type u_1\ninst✝ : GroupWithZero G₀\nn : ℤ\nh : ¬n = 0\n⊢ 0 ^ n = 0",
"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\nn : ℤ\n⊢ 0 ^ n = if n = 0 then 1 else 0",
"tactic": "split_i... | [
74,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Basic.lean | subrelation_iff_le | [] | [
1402,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.orthogonal_gc | [] | [
151,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : AddMonoidWithOne R\ninst✝ : CharZero R\nn : ℕ\n⊢ ↑n = 1 ↔ n = 1",
"tactic": "rw [← cast_one, cast_inj]"
}
] | [
92,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/BigOperators/Pi.lean | MonoidHom.functions_ext' | [] | [
105,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.quot_mk_to_coe | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.eraseNone_empty | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.12714\na✝ : α\n⊢ a✝ ∈ ↑eraseNone ∅ ↔ a✝ ∈ ∅",
"state_before": "α : Type u_1\nβ : Type ?u.12714\n⊢ ↑eraseNone ∅ = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nα : Type u_1\nβ : Type ?u.12714\na✝ : α\n⊢ a✝ ∈ ↑e... | [
136,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.hadamard_smul | [] | [
95,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/CategoryTheory/SingleObj.lean | Units.toAut_inv | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.map_add | [] | [
101,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/PathConnected.lean | Joined.symm | [] | [
784,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.tendsto_nhds' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type ?u.232913\n𝕝 : Type ?u.232916\n𝕝₂ : Type ?u.232919\nE : Type u_2\nF : Type u_4\nG : Type ?u.232928\nι : Type u_3\nι' : Type ?u.232934\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ ... | [
386,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.one_fin_two | [
{
"state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : Zero α\ninst✝ : One α\ni j : Fin 2\n⊢ OfNat.ofNat 1 i j = ↑of ![![1, 0], ![0, 1]] i j",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : Zero α\ni... | [
413,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factors_count_eq | [
{
"state_after": "case inl\np : ℕ\n⊢ count p (factors 0) = ↑(factorization 0) p\n\ncase inr\nn p : ℕ\nhn0 : n > 0\n⊢ count p (factors n) = ↑(factorization n) p",
"state_before": "n p : ℕ\n⊢ count p (factors n) = ↑(factorization n) p",
"tactic": "rcases n.eq_zero_or_pos with (rfl | hn0)"
},
{
"st... | [
86,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.induction₂_symm_neg | [] | [
1023,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.mem_nhds_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type ?u.207750\n𝕝 : Type ?u.207753\n𝕝₂ : Type ?u.207756\nE : Type u_2\nF : Type ?u.207762\nG : Type ?u.207765\nι : Type u_3\nι' : Type ?u.207771\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\n... | [
326,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_mul_of_invertible | [] | [
351,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.map_smulₛₗ | [] | [
966,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_radical | [
{
"state_after": "case h\nR : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nrc : RingHomClass F R S\nf : F\nI J : Ideal R\nK L : Ideal S\nx✝ : R\n⊢ x✝ ∈ comap f (radical K) ↔ x✝ ∈ radical (comap f K)",
"state_before": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing R\ni... | [
1808,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1806,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.half_pos | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.325183\nβ : Type ?u.325186\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≠ 0\n⊢ 0 < a / 2",
"tactic": "simp [h]"
}
] | [
1744,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1744,
11
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ite_continuous' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type ?u.55194\nβ : Type v\nβ' : Type ?u.55199\nγ : Type ?u.55202\nφ : Type ?u.55205\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ :... | [
624,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnity_le_of_dvd | [
{
"state_after": "case intro\nM : Type u_1\nN : Type ?u.364389\nG : Type ?u.364392\nR : Type ?u.364395\nS : Type ?u.364398\nF : Type ?u.364401\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk d : ℕ+\n⊢ rootsOfUnity k M ≤ rootsOfUnity (k * d) M",
"state_before": "M : Type u_1\nN... | [
125,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_ne_top | [] | [
202,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Computability/Reduce.lean | Computable.equiv₂ | [] | [
230,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsCompl_left_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.199427\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.200390\ninst... | [
237,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3963\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard s = 0 ↔ s = ∅",
"tactic": "rw [ncard_def, @Finite.card_eq_zero_iff _ hs.to_subtype, isEmpty_subtype,\n eq_empty_iff_forall_not_mem]"
}
] | [
89,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
9
] |
Mathlib/Topology/SubsetProperties.lean | IsClopen.inter | [] | [
1558,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1557,
1
] |
Std/Logic.lean | Decidable.or_iff_not_imp_left | [] | [
544,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
543,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivWithinAt.comp_of_mem | [] | [
109,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | add_le_of_le_tsub_right_of_le | [] | [
39,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.compl_mem_cofinite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.546970\nγ : Type ?u.546973\nδ : Type ?u.546976\nι : Type ?u.546979\nR : Type ?u.546982\nR' : Type ?u.546985\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
2641,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2641,
1
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | Real.hasDerivAt_sqrt | [] | [
72,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeAddMonoid.count_apply | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/Complex/Schwarz.lean | Complex.dist_le_dist_of_mapsTo_ball_self | [
{
"state_after": "f : ℂ → ℂ\nc z : ℂ\nR R₁ R₂ : ℝ\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (ball c R)\nhc : f c = c\nhz : z ∈ ball c R\nthis : dist (f z) (f c) ≤ R / R * dist z c\n⊢ dist (f z) c ≤ dist z c",
"state_before": "f : ℂ → ℂ\nc z : ℂ\nR R₁ R₂ : ℝ\nhd : DifferentiableOn ℂ... | [
191,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S₁\np✝ q✝ : MvPolynomial σ R\ninst✝ : DecidableEq σ\np q : MvPolynomial σ R\n⊢ support (p * q) ⊆ Finset.bi... | [
597,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_iSup_nat | [] | [
848,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
11
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.IsComplement'.disjoint | [] | [
511,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.det_transvection_of_ne | [
{
"state_after": "no goals",
"state_before": "n : Type u_1\np : Type ?u.20141\nR : Type u₂\n𝕜 : Type ?u.20146\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ni j : n\ninst✝ : Fintype n\nh : i ≠ j\nc : R\n⊢ det (transvection i j c) = 1",
"tactic": "rw [← updateRo... | [
146,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_comm | [] | [
103,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_inj | [] | [
665,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquiv_refl | [
{
"state_after": "case H.a\nα : Sort u_1\np : α → Prop\nh : optParam (∀ (a : α), p a ↔ p (↑(Equiv.refl α) a)) (_ : ∀ (a : α), p a ↔ p a)\nx✝ : { a // p a }\n⊢ ↑(↑(subtypeEquiv (Equiv.refl α) h) x✝) = ↑(↑(Equiv.refl { a // p a }) x✝)",
"state_before": "α : Sort u_1\np : α → Prop\nh : optParam (∀ (a : α), p a... | [
1090,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_subset_prod | [] | [
566,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_iSup_le_lift_iSup' | [] | [
1225,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/Topology/Covering.lean | IsCoveringMap.mk | [] | [
159,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | exists_nhds_split_inv | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : TopologicalSpace α\nf : α → G\ns✝ : Set α\nx : α\ns : Set G\nhs : s ∈ 𝓝 1\nthis : (fun p => p.fst * p.snd⁻¹) ⁻¹' s ∈ 𝓝 (1, 1)\n⊢ ∃ V, V ∈ 𝓝 1 ∧ ∀ (v : G), v ∈ ... | [
809,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_sub | [] | [
1142,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.get_eq_iff_eq_some | [] | [
205,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
8
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | edist_smul_left | [] | [
82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/RingTheory/Valuation/Integers.lean | Valuation.Integers.dvd_iff_le | [] | [
130,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.subset_set_biUnion_of_mem | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.467741\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.467750\nι : Type ?u.467753\nκ : Type ?u.467756\ns : Finset α\nf : α → Set β\nx : α\nh : x ∈ s\n⊢ f x ≤ ⨆ (_ : x ∈ s), f x",
"tactic": "simp only [h, iSup_pos, le_refl]"
}
] | [
2032,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2030,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.id | [] | [
315,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.toNat_ofNat | [
{
"state_after": "case zero\nn✝ n : ℕ\n⊢ Bitvec.toNat (Bitvec.ofNat zero n) = n % 2 ^ zero\n\ncase succ\nn✝ k : ℕ\nih : ∀ {n : ℕ}, Bitvec.toNat (Bitvec.ofNat k n) = n % 2 ^ k\nn : ℕ\n⊢ Bitvec.toNat (Bitvec.ofNat (succ k) n) = n % 2 ^ succ k",
"state_before": "k n : ℕ\n⊢ Bitvec.toNat (Bitvec.ofNat k n) = n %... | [
77,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_open_iff_eq_finite_iUnion_of_isTopologicalBasis | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Type u_1\nπ : ι → Type ?u.42425\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nb : ι → Set α\nhb : IsTopologicalBasis (range b)\nhb' : ∀ (i : ι), IsCompact (b i)\nU : Set α\n⊢ IsCompact U ∧ IsOpen U → ∃ s, Set.Finite s ∧ U = ⋃ (i : ι... | [
511,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.map_monotone | [
{
"state_after": "ι : Sort ?u.145982\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : SimpleGraph W\nf : G →g G'\nH H' : Subgraph G\nh : H ≤ H'\n⊢ Subgraph.map f H ≤ Subgraph.map f H'",
"state_before": "ι : Sort ?u.145982\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgr... | [
666,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.quotientInfEquivQuotientProd_snd | [] | [
526,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_apply_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.73203\nα : Type u_1\nβ : Type ?u.73209\nf g : Perm α\np : α → Prop\nx y z : α\n⊢ (∃ b, ↑(f ^ ↑(Equiv.addRight 1).symm b) (↑f x) = y) ↔ SameCycle f x y",
"tactic": "simp [zpow_sub, SameCycle, Int.add_neg_one, Function.comp]"
}
] | [
145,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous_extend | [] | [
249,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_eq_bot_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.277101\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\n⊢ ∅ ∈ map m f → ∅ ∈ f",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.277101\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ ... | [
2449,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2446,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_univ | [] | [
1323,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.traverse_mul | [
{
"state_after": "α β : Type u\nm : Type u → Type u\ninst✝¹ : Applicative m\nF : α → m β\ninst✝ : LawfulApplicative m\nx✝¹ y✝ : FreeSemigroup α\nx✝ : α\nL1 : List α\ny : α\nL2 : List α\nhd : α\ntl : List α\nih :\n ∀ (x : α),\n traverse F ({ head := x, tail := tl } * { head := y, tail := L2 }) =\n Seq.s... | [
666,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.IsHomogeneous.sum | [] | [
187,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.graphEquiv₂_apply | [] | [
95,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_false | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Separation.lean | regularSpace_iInf | [] | [
1622,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Finset.aestronglyMeasurable_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.330452\nγ : Type ?u.330455\nι✝ : Type ?u.330458\ninst✝⁵ : Countable ι✝\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\nf✝ g : α → β\nM : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Topologi... | [
1428,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1425,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_zero | [] | [
622,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_add | [
{
"state_after": "case h\nα : Type u_2\nβ : Type ?u.30911\nm : MeasurableSpace α\nμ ν : Measure α\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf g : α → E\nhf : Integrable f\nhg : Integrable g\ni : Set α\nhi : MeasurableSet i\n⊢ ↑(withDensityᵥ μ (f + g)) i = ↑... | [
96,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Logic/Unique.lean | unique_iff_exists_unique | [] | [
70,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.