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/Rat/Floor.lean | Rat.cast_fract | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nx : ℚ\n⊢ ↑(fract x) = fract ↑x",
"tactic": "simp only [fract, cast_sub, cast_coe_int, floor_cast]"
}
] | [
92,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.one_bits | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ bits 1 = [true]",
"tactic": "convert bit1_bits 0"
}
] | [
235,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.insert | [] | [
465,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
11
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_nonneg | [
{
"state_after": "X : 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\nfA : f ∈ candidates X Y\nthis : 0 ≤ 2 * f (x, y)\n⊢ 0 ≤ f (x, y)",
"stat... | [
139,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
9
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | NormedSpace.toLocallyConvexSpace' | [] | [
697,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Icc_eq_nhdsWithin_Ici | [] | [
544,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_non_unit | [] | [
103,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_mono_ae_real | [] | [
404,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.naturality | [
{
"state_after": "case h_nil\nn : ℕ\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα✝ β✝ γ : Type u\nη : ApplicativeTransformation F G\nα β : Type u\nf : α → F β\n⊢ (fun {α} => ApplicativeTransformation.app η α) (Vector.traverse... | [
702,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_biUnion_of_mem | [] | [
3621,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3619,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_finsupp_sum_index | [] | [
382,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.HasLift.iff_op | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nA B X Y : C\nf : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\ng : B ⟶ Y\nsq : CommSq f i p g\n⊢ Nonempty (LiftStruct sq) ↔ Nonempty (LiftStruct (_ : CommSq g.op p.op i.op f.op))",
"state_before": "C : Type u_1\ninst✝ : Category C\nA B X Y : C\nf : A ⟶ X\ni : A ⟶ B\np : X ... | [
211,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_inv | [] | [
500,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.coe_toNNReal | [] | [
126,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.sep_of_ncard_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.70582\ns t : Set α\na b x y : α\nf : α → β\nP : α → Prop\nh : ncard {x | x ∈ s ∧ P x} = ncard s\nha : a ∈ s\nhs : autoParam (Set.Finite s) _auto✝\n⊢ {x | x ∈ s ∧ P x} ⊆ s",
"tactic": "simp"
}
] | [
339,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_mul' | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.656983\nh : leadingCoeff p * leadingCoeff q ≠ 0\n⊢ p = 0 → leadingCoeff p * leadingCoeff q = 0",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type... | [
936,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInter_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nf g : Filter α\ns✝ t : Set α\nβ : Type v\ns : β → Set α\ninst✝ : Finite β\n⊢ (⋂ (i : β), s i) ∈ f ↔ ∀ (i : β), s i ∈ f",
"tactic": "simpa using biInter_mem finite_univ"
}
] | [
208,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map_map₂_antidistrib_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type u_5\nγ : Type u_3\nf : α → β → γ\na : Option α\nb : Option β\nc : Option γ\nδ : Type u_1\nβ' : Type u_2\ng : γ → δ\nf' : β' → α → δ\ng' : β → β'\nh_antidistrib : ∀ (a : α) (b : β), g (f a b) = f' (g' b) a\n⊢ Option.map g (map₂ f a b) = map... | [
191,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_nonneg_iff_right_nonneg_of_pos | [] | [
931,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ici' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.82412\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\nx : α\n⊢ x ∈ Ico a b ∪ Ici c ↔ x ∈ Ici (min a c)",
"state_before": "α : Type u_1\nβ : Type ?u.82412\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\n⊢ Ico a b ∪ Ici c = Ici (min... | [
1281,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1275,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.fderiv_right | [] | [
1053,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_eq_real_cos_iff_eq_or_eq_neg | [
{
"state_after": "case h\nψ x✝ : ℝ\n⊢ cos ↑x✝ = Real.cos ψ ↔ ↑x✝ = ↑ψ ∨ ↑x✝ = -↑ψ",
"state_before": "θ : Angle\nψ : ℝ\n⊢ cos θ = Real.cos ψ ↔ θ = ↑ψ ∨ θ = -↑ψ",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nψ x✝ : ℝ\n⊢ cos ↑x✝ ... | [
338,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.ofReal_tsum | [
{
"state_after": "case pos\nα : Type u_2\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → ℝ\nh : Summable f\n⊢ ↑(∑' (a : α), f a) = ∑' (a : α), ↑(f a)\n\ncase neg\nα : Type u_2\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → ℝ\nh : ¬Summable f\n⊢ ↑(∑' (a : α), f a) = ∑' (a : α), ↑(f a)",
"state_before": "α : Type u_2\... | [
523,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.modEq_three_digits_sum | [
{
"state_after": "no goals",
"state_before": "n✝ n : ℕ\n⊢ 10 % 3 = 1",
"tactic": "norm_num"
}
] | [
552,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_add_coeff_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r f g : R[X]\n⊢ coeff (f * g) (natDegree f + natDegree g) = coeff f (natDegree f) * coeff g (natDegree g)",
"tactic": "simp only [coeff_natDegree, coeff_mul_degree_add_degree]"
}... | [
158,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_iSup | [] | [
336,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.pure_bindOnSupport | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.112939\np : Pmf α\nf✝ : (a : α) → a ∈ support p → Pmf β\na : α\nf : (a' : α) → a' ∈ support (pure a) → Pmf β\nb : β\n⊢ ↑(bindOnSupport (pure a) f) b = ↑(f a (_ : a ∈ support (pure a))) b",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1129... | [
270,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.mul_lt_one_of_lt_of_le_of_pos | [] | [
837,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_def | [] | [
74,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_add | [] | [
611,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.induction | [
{
"state_after": "case mk.mk.mk\nC : Type u_1\ninst✝ : Category C\nr : HomRel C\nP : {a b : Quotient r} → (a ⟶ b) → Prop\nh : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)\nx y : C\nf✝ : { as := x } ⟶ { as := y }\nf : { as := x }.as ⟶ { as := y }.as\n⊢ P (Quot.mk (CompClosure r) f)",
"state_before": "C : T... | [
136,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.ge_on_segment | [] | [
661,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Topology/Instances/Int.lean | Int.dist_cast_real | [] | [
38,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonpos_of_mul_nonpos_left | [] | [
829,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.isMaximal_def | [] | [
296,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_congr_left | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1047174\nG : Type ?u.1047177\n𝕜 : Type ?u.1047180\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ℝ F'\nins... | [
1068,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.aleph_cof | [] | [
731,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_le_add | [
{
"state_after": "case zero\na c : ℕ\n⊢ choose a c ≤ choose (a + zero) c\n\ncase succ\na c b_n : ℕ\nb_ih : choose a c ≤ choose (a + b_n) c\n⊢ choose a c ≤ choose (a + succ b_n) c",
"state_before": "a b c : ℕ\n⊢ choose a c ≤ choose (a + b) c",
"tactic": "induction' b with b_n b_ih"
},
{
"state_af... | [
323,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableAt.prod | [] | [
106,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast_singleton' | [] | [
725,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.RedRed.of_false | [] | [
136,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
134,
11
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.eq_jacobson_iff_not_mem | [
{
"state_after": "case mp\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : Ideal R\n⊢ jacobson I = I → ∀ (x : R), ¬x ∈ I → ∃ M, (I ≤ M ∧ IsMaximal M) ∧ ¬x ∈ M\n\ncase mpr\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI : Ideal R\n⊢ (∀ (x : R), ¬x ∈ I → ∃ M, (I ≤ M ∧ IsMaximal M) ∧ ¬x ∈ ... | [
178,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.isGLB_of_tendsto | [] | [
2071,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2068,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivAtFilter.comp | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.16082\ninst✝¹... | [
71,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/List/Lemmas.lean | List.mem_range | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ m ∈ range n ↔ m < n",
"tactic": "simp only [range_eq_range', mem_range'_1, Nat.zero_le, true_and, Nat.zero_add]"
}
] | [
1914,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1913,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_prod_le_of_le | [] | [
1492,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1490,
1
] |
Mathlib/CategoryTheory/Category/TwoP.lean | pointedToTwoPFst_comp_swap | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.beq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.133754\nγ : Type ?u.133757\nδ : Type ?u.133760\nσ : Type ?u.133763\ninst✝⁵ : Primcodable α\ninst✝⁴ : Primcodable β\ninst✝³ : Primcodable γ\ninst✝² : Primcodable δ\ninst✝¹ : Primcodable σ\ninst✝ : DecidableEq α\na : ℕ × ℕ\n⊢ (fun x x_1 =... | [
750,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
11
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.strictMonoOn_of_deriv_pos | [
{
"state_after": "E : Type ?u.412812\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.412908\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ (x : ℝ), x ∈ interior D → 0 < deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy :... | [
898,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.cofork_π | [] | [
951,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.mod_mul_right_mod | [] | [
321,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.val_finset_prod | [] | [
110,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_false | [] | [
1449,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.mem_toMultiset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.57323\nι : Type ?u.57326\nf : α →₀ ℕ\ni : α\n⊢ i ∈ ↑toMultiset f ↔ i ∈ f.support",
"tactic": "rw [← Multiset.count_ne_zero, Finsupp.count_toMultiset, Finsupp.mem_support_iff]"
}
] | [
136,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Order/SMul.lean | Tactic.smul_ne_zero_of_ne_zero_of_pos | [] | [
324,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
9
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_zero | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ a * 0 = 0",
"tactic": "simp"
}
] | [
410,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
src/lean/Init/Data/Array/Mem.lean | Array.sizeOf_lt_of_mem | [
{
"state_after": "α : Type u_1\na : α\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf α\nas : Array α\nh : anyM.loop (fun b => decide (a = b)) as (size as) (_ : size as ≤ size as) 0 = true\n⊢ sizeOf a < sizeOf as",
"state_before": "α : Type u_1\na : α\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf α\nas : Array α\nh : a ∈... | [
42,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
32,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mk'_eq_coe | [
{
"state_after": "case mk\nι : Type u_1\nJ : Box ι\nx y l u lI uI : ι → ℝ\nhI : ∀ (i : ι), lI i < uI i\n⊢ mk' l u = ↑{ lower := lI, upper := uI, lower_lt_upper := hI } ↔\n l = { lower := lI, upper := uI, lower_lt_upper := hI }.lower ∧\n u = { lower := lI, upper := uI, lower_lt_upper := hI }.upper",
... | [
330,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_ennnorm | [] | [
2065,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2064,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_ne_zero | [
{
"state_after": "x y : ℂ\nh : exp x = 0\n⊢ x + -x = 0 * exp (-x)",
"state_before": "x y : ℂ\nh : exp x = 0\n⊢ 0 = 1",
"tactic": "rw [← exp_zero, ← add_neg_self x, exp_add, h]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\nh : exp x = 0\n⊢ x + -x = 0 * exp (-x)",
"tactic": "s... | [
546,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.of_image | [] | [
1321,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_pos_le_iff | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (↑f^[n]) x ≤ x + ↑n * ↑m ↔ ↑f x ≤ x + ↑m",
"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using\n (f.commute_add_int m).iterate_pos_le_iff_map_le f.monotone (strictMono_id.add_const (m : ℝ)) ... | [
591,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.pow_zero | [] | [
476,
44
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
476,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_le_left_iff_le | [] | [
146,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_pi_iff | [
{
"state_after": "case mp\nG : Type ?u.321783\nG' : Type ?u.321786\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.321795\ninst✝³ : AddGroup A\nH✝ K : Subgroup G\nk : Set G\nN : Type ?u.321816\ninst✝² : Group N\nP : Type ?u.321822\ninst✝¹ : Group P\nη : Type u_1\nf : η → Type u_2\ninst✝ : (i : η) → Group (f i... | [
1869,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1862,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.X_pow_sub_one_dvd_prod_cyclotomic | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn m : ℕ\nhpos : 0 < n\nhdiff : m ≠ n\nhm : m ∈ Nat.properDivisors n\n⊢ X ^ m - 1 ∣ ∏ i in Nat.properDivisors n, cyclotomic i R",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn m : ℕ\nhpos : 0 < n\nhm : m ∣ n\nhdiff : m ≠ n\n⊢ X ^ m - 1 ∣ ∏ i in Nat.p... | [
518,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_inf_le_add | [
{
"state_after": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\nx y : α\nh : ‖x ⊓ y - 0 ⊓ 0‖ ≤ ‖x - 0‖ + ‖y - 0‖\n⊢ ‖x ⊓ y‖ ≤ ‖x‖ + ‖y‖",
"state_before": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\nx y : α\n⊢ ‖x ⊓ y‖ ≤ ‖x‖ + ‖y‖",
"tactic": "have h : ‖x ⊓ y - 0 ⊓ 0‖ ≤ ‖x - 0‖ + ‖y - 0‖ := n... | [
151,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_eq_empty | [] | [
373,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Tactic/Congr!.lean | heq_imp_of_eq_imp | [
{
"state_after": "case refl\nα✝ : Sort u_1\nx : α✝\np : HEq x x → Prop\nh : ∀ (he : x = x), p (_ : HEq x x)\n⊢ p (_ : HEq x x)",
"state_before": "α✝ : Sort u_1\nx y : α✝\np : HEq x y → Prop\nh : ∀ (he : x = y), p (_ : HEq x y)\nhe : HEq x y\n⊢ p he",
"tactic": "cases he"
},
{
"state_after": "no ... | [
713,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
9
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.continuousWithinAt_log_of_re_neg_of_im_zero | [
{
"state_after": "case convert_1\nz : ℂ\nhre : z.re < 0\nhim : z.im = 0\n⊢ ↑abs z ≠ 0",
"state_before": "z : ℂ\nhre : z.re < 0\nhim : z.im = 0\n⊢ ContinuousWithinAt log {z | 0 ≤ z.im} z",
"tactic": "convert\n (continuous_ofReal.continuousAt.comp_continuousWithinAt\n (continuous_abs.continuousW... | [
205,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.flatten_congr | [] | [
1173,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_nonneg_right' | [] | [
631,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_modEq_two | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ yn a1 0 ≡ 0 [MOD 2]",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ yn a1 1 ≡ 1 [MOD 2]",
"tactic": "simp"
},
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ 2 * (a * yn a1 (... | [
562,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.singleton_head | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Bounds.lean | IsGLB.inv | [] | [
72,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_neBot | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\n⊢ NeBot (pi f) ↔ ∀ (i : ι), NeBot (f i)",
"tactic": "simp [neBot_iff]"
}
] | [
161,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Fintype/CardEmbedding.lean | Fintype.card_embedding_eq_of_infinite | [] | [
62,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_pEmpty | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | RingHom.iterate_map_sub | [] | [
160,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.comp_sort_eq_comp_iff_monotone | [] | [
163,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.cancel_right | [] | [
1169,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Data/List/Sigma.lean | List.NodupKeys.nodup | [] | [
141,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
11
] |
Mathlib/Data/Int/Parity.lean | Int.even_sub' | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Even (m - n) ↔ (Odd m ↔ Odd n)",
"tactic": "rw [even_sub, even_iff_not_odd, even_iff_not_odd, not_iff_not]"
}
] | [
131,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nν : ProbabilityMeasure Ω\ns : Set Ω\n⊢ ↑((fun s => ENNReal.toNNReal (↑↑↑ν s)) s) = ↑↑↑ν s",
"tactic": "rw [← coeFn_comp_toFiniteMeasure_eq_coeFn, FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure,\n toMeasure_comp_toFin... | [
172,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.one_mul | [] | [
230,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Mathlib/Data/Real/Pointwise.lean | Real.sInf_smul_of_nonpos | [
{
"state_after": "case inl\nι : Sort ?u.7076\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : Module α ℝ\ninst✝ : OrderedSMul α ℝ\na : α\nha : a ≤ 0\n⊢ sInf (a • ∅) = a • sSup ∅\n\ncase inr\nι : Sort ?u.7076\nα : Type u_1\ninst✝² : LinearOrderedField α\ninst✝¹ : Module α ℝ\ninst✝ : OrderedSMul α ℝ\na : α\... | [
86,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum' | [] | [
255,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.zero_imJ | [] | [
855,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_def' | [] | [
2163,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2161,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Filter.TendstoNhdsWithinIoi.mul_const | [] | [
189,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/GroupTheory/Coset.lean | leftCoset_rightCoset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semigroup α\ns : Set α\na b : α\n⊢ a *l s *r b = a *l (s *r b)",
"tactic": "simp [leftCoset, rightCoset, (image_comp _ _ _).symm, Function.comp, mul_assoc]"
}
] | [
140,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mul_re | [] | [
329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_add | [] | [
511,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheafFor_singleton_iso | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP✝ Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ Type w\nx : FamilyOfElements P (singleton (𝟙 X))\na✝ : FamilyOfElements.Compatible x\n⊢ ∃! t, FamilyOfElements.IsAmalgamation x t",
"state_before": "C : T... | [
654,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Algebra/Group/Basic.lean | self_ne_mul_left | [] | [
229,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_le_iff_le_mul | [
{
"state_after": "α : Type ?u.282672\nβ : Type ?u.282675\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhb0 : b ≠ 0 ∨ c ≠ ⊤\nhbt : b ≠ ⊤ ∨ c ≠ 0\n⊢ a * b⁻¹ ≤ c ↔ a ≤ c / b⁻¹",
"state_before": "α : Type ?u.282672\nβ : Type ?u.282675\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhb0 : b ≠ 0 ∨ c ≠ ⊤\nhbt : b ≠ ⊤ ∨ c ≠ 0\n⊢ a / b ≤ c ↔ a ≤ c *... | [
1577,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
11
] |
Mathlib/Algebra/Group/Basic.lean | eq_of_div_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22837\nG : Type ?u.22840\ninst✝ : DivisionMonoid α\na b c : α\nh : a / b = 1\n⊢ a * b⁻¹ = 1",
"tactic": "rwa [← div_eq_mul_inv]"
}
] | [
391,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_mul | [] | [
196,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
195,
11
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.conjTranspose | [] | [
85,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.rank_lt_aleph0 | [] | [
52,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
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