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/Sym/Basic.lean | Sym.cons_inj_right | [] | [
122,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.continuousOn | [] | [
478,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiable_sub_const_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.516215\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
586,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.sin_eq_tsum' | [] | [
91,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_add | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nre_eq✝ : ↑(xn a1 (m + n)) = (pellZd a1 m).re * (pellZd a1 n).re + ↑(Pell.d a1) * (pellZd a1 m).im * (pellZd a1 n).im\nh : ↑(yn a1 (m + n)) = (pellZd a1 m).re * (pellZd a1 n).im + (pellZd a1 m).im * (pellZd a1 n).re\n⊢ yn a1 (m + n) = xn a1 m * yn a1 n + yn a1 m * xn... | [
377,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.Indep.indepSets | [] | [
333,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_le_div_right | [] | [
366,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.lift.add' | [
{
"state_after": "case refine'_1\nα✝ : Type u\nα : Type u_1\nβ : Type u_2\ninst✝ : AddCommGroup β\na : FreeAbelianGroup α\nf g : α → β\n⊢ ↑(↑lift (f + g)) 0 = ↑(↑lift f) 0 + ↑(↑lift g) 0\n\ncase refine'_2\nα✝ : Type u\nα : Type u_1\nβ : Type u_2\ninst✝ : AddCommGroup β\na : FreeAbelianGroup α\nf g : α → β\n⊢ ∀ ... | [
176,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/UnionFind.lean | UnionFind.model' | [
{
"state_after": "α : Type u_1\nself : UnionFind α\nn : ℕ\nm : UFModel n\nhm : UFModel.Models self.arr m\n⊢ ∃ m, UFModel.Models self.arr m",
"state_before": "α : Type u_1\nself : UnionFind α\n⊢ ∃ m, UFModel.Models self.arr m",
"tactic": "let ⟨n, m, hm⟩ := self.model"
},
{
"state_after": "case re... | [
165,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderInverse.op | [] | [
128,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.eval_indicator_apply_eq_zero | [
{
"state_after": "case intro\nK : Type u_1\nσ : Type u_2\ninst✝² : Fintype K\ninst✝¹ : Fintype σ\ninst✝ : Field K\na b : σ → K\nh : a ≠ b\ni : σ\nhi : a i ≠ b i\n⊢ ↑(eval a) (indicator b) = 0",
"state_before": "K : Type u_1\nσ : Type u_2\ninst✝² : Fintype K\ninst✝¹ : Fintype σ\ninst✝ : Field K\na b : σ → K\... | [
121,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.units_smul | [
{
"state_after": "ι : Type u'\nι' : Type ?u.293271\nR : Type u_1\nK : Type ?u.293277\nM : Type u_2\nM' : Type ?u.293283\nM'' : Type ?u.293286\nV : Type u\nV' : Type ?u.293291\nv✝ : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹ :... | [
548,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasStrictFDerivAt.mul' | [] | [
287,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousWithinAt_right_of_monotoneOn_of_exists_between | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\ninst✝² : LinearOrder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\ns : Set α\na : α\nh_mono : MonotoneOn f s\nhs : s ∈ 𝓝[Ici a] a\nhfs : ∀ (b : β), b > f a → ∃ c, c... | [
79,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.mul_left_injective | [] | [
800,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
11
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | Submodule.Quotient.norm_mk_lt | [] | [
460,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
8
] |
Mathlib/Algebra/CharP/Basic.lean | exists_add_pow_prime_eq | [] | [
90,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.card_functions_sum_skolem₁ | [
{
"state_after": "L : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ : Structure L M\n⊢ ((sum fun i => lift (#Functions L i)) + sum fun i => lift (#BoundedFormula L Empty (i + 1))) =\n sum fun i => #BoundedFormula L Empty (i + 1)",
"state_before": "L : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ :... | [
65,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.restrict_apply | [] | [
407,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_pi_infinite | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type u_2\nπ : ι → Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns✝ t : Set α\ninst✝ : (i : ι) → TopologicalSpace (π i)\ns : (i : ι) → Set (π i)\n⊢ (∀ (i : ι) (f : Ultrafilter (π i)), s i ∈ ↑f → ∃ a, a ∈ s i ∧ ↑f ≤ 𝓝 a) →\n ∀ (f : Ultrafilte... | [
1035,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.insert_nonEmpty | [
{
"state_after": "no goals",
"state_before": "x : Nat\nxs : List Nat\n⊢ insert x xs ≠ []",
"tactic": "induction xs with\n| nil => simp [insert]\n| cons x xs _ => simp [insert]; split <;> simp"
},
{
"state_after": "no goals",
"state_before": "case nil\nx : Nat\n⊢ insert x [] ≠ []",
"tact... | [
163,
50
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
160,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_div | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 ≤ x\n⊢ toNNReal (x / y) = toNNReal x / toNNReal y",
"tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, ← Real.toNNReal_inv, ← Real.toNNReal_mul hx]"
}
] | [
894,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.isIso_π_of_isInitial | [
{
"state_after": "case w\nC : Type u₁\ninst✝² : Category C\nJ : Type u\ninst✝¹ : Category J\nj : J\nI : IsInitial j\nF : J ⥤ C\ninst✝ : HasLimit F\nj✝ : J\n⊢ (limit.π F j ≫ limit.lift F (coneOfDiagramInitial I F)) ≫ limit.π F j✝ = 𝟙 (limit F) ≫ limit.π F j✝",
"state_before": "C : Type u₁\ninst✝² : Category... | [
712,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.trunc_add | [
{
"state_after": "R : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\nφ ψ : PowerSeries R\nm : ℕ\n⊢ (if m < n then ↑(coeff R m) (φ + ψ) else 0) =\n (if m < n then ↑(coeff R m) φ else 0) + if m < n then ↑(coeff R m) ψ else 0",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\nφ ψ : PowerSeries R\nm :... | [
1851,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1846,
1
] |
Mathlib/Order/Lattice.lean | Pi.sup_def | [] | [
1013,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_zero | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_add_left | [] | [
222,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ofLeftInverse_apply | [] | [
2718,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2716,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.285372\nE : Type u_2\nF : Type u_3\nG : Type ?u.285381\nE' : Type ?u.285384\nF' : Type ?u.285387\nG' : Type ?u.285390\nE'' : Type ?u.285393\nF'' : Type ?u.285396\nG'' : Type ?u.285399\nR : Type ?u.285402\nR' : Type ?u.285405\n𝕜 : Type ?u.285408\n𝕜' : Type ?u.285411\... | [
1278,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.transpose_empty_cols | [] | [
201,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_neg | [
{
"state_after": "x y : ℂ\n⊢ exp (x + -x) = exp x * (exp x)⁻¹",
"state_before": "x y : ℂ\n⊢ exp (-x) = (exp x)⁻¹",
"tactic": "rw [← mul_right_inj' (exp_ne_zero x), ← exp_add]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ exp (x + -x) = exp x * (exp x)⁻¹",
"tactic": "simp [... | [
550,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.eqOn_of_fderivWithin_eq | [
{
"state_after": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nF : Type ?u.256230\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\n𝕜 : Type u_2\nG : Type u_3\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → G\n... | [
613,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.of_eq_of_ne | [] | [
130,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit1_lt | [] | [
182,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.rev_surjective | [] | [
463,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finRotate_one | [] | [
432,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | totallyBounded_Ioo | [] | [
1432,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
] |
Mathlib/Topology/Basic.lean | closure_subset_iff_isClosed | [] | [
485,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Algebra/Homology/QuasiIso.lean | HomologicalComplex.Hom.from_single₀_exact_at_succ | [] | [
201,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | map_mul_right_nhds₀ | [] | [
292,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Topology/Order/Basic.lean | induced_topology_eq_preorder | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : ∀ {x y : α}, f x < f y ↔ x < y\nH₁ : ∀ {a : α} {b : β} {x : α}, b < f a → ¬b < f x → ∃ y, y < a ∧ b ≤ f y\nH₂ : ∀ {a : α} {b : β} {x : α}, f a < b... | [
1039,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_surjective | [] | [
97,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.one_eq_range | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_cons | [] | [
390,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | contractRight_apply | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.sub_im | [] | [
283,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
9
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.mk_left | [] | [
279,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.equiv_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nι' : Type u_5\nR : Type u_3\nR₂ : Type ?u.546971\nK : Type ?u.546974\nM : Type u_4\nM' : Type u_1\nM'' : Type ?u.546983\nV : Type u\nV' : Type ?u.546988\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\... | [
677,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_union_inter | [] | [
406,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.smul_sup' | [] | [
242,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_inr | [] | [
1866,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1866,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_inf_principal_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.318879\nι : Sort x\nf : α → β\ns : Set β\nl : Filter α\nt : Set β\n⊢ t ∈ map f (l ⊓ 𝓟 (f ⁻¹' s)) ↔ t ∈ map f l ⊓ 𝓟 s",
"tactic": "simp only [mem_map', mem_inf_principal, mem_setOf_eq, mem_preimage]"
}
] | [
3076,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3074,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.extend_zero | [] | [
1723,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.mul_single_zero_coeff | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nr : R\nx : HahnSeries Γ R\na : Γ\n⊢ coeff (x * ↑(single 0) r) a = coeff x a * r",
"tactic": "rw [← add_zero a, mul_single_coeff_add, add_zero]"
}
] | [
748,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/InformationTheory/Hamming.lean | hamming_zero_eq_dist | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.10710\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.10742\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y : (i : ι) → β i\n⊢ 0 = hammingDist x y ↔ x = y",
"tactic": "rw [eq_comm, hammingDist_... | [
111,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.subsingleton_closedBall | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nX : Type ?u.552898\nι : Type ?u.552901\ninst✝¹ : PseudoMetricSpace α\nγ : Type w\ninst✝ : MetricSpace γ\nx✝ : γ\ns : Set γ\nx : γ\nr : ℝ\nhr✝ : r ≤ 0\nhr : r < 0\n⊢ Set.Subsingleton (closedBall x r)\n\ncase inr\nα : Type u\nβ : Type v\nX : Type ?u.552898\nι : ... | [
2908,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2903,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.comp_apply | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\na : Pseudoelement P\nx : Over P\n⊢ Over.mk (x.hom ≫ f ≫ g) ≈ Over.mk ((Over.mk (x.hom ≫ f)).hom ≫ g)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\n... | [
199,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.getVert_of_length_le | [
{
"state_after": "no goals",
"state_before": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v u✝ : V\ni : ℕ\nhi : length nil ≤ i\n⊢ getVert nil i = u✝",
"tactic": "rfl"
},
{
"state_after": "case cons.zero\nV : Type u\nV' : Type ... | [
227,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.lt_cons_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.35311\nγ : Type ?u.35314\ns✝ t : Multiset α\na✝ : α\ns : Multiset α\na : α\nl : List α\nthis : l <+~ a :: l ∧ ¬l ~ a :: l\n⊢ Quot.mk Setoid.r l < a ::ₘ Quot.mk Setoid.r l",
"tactic": "simpa [lt_iff_le_and_ne]"
}
] | [
564,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_eq_id | [] | [
425,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.inv_le_inv | [] | [
207,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.not_finite_iff_forall | [
{
"state_after": "α : Type u_1\ninst✝ : Monoid α\na b : α\nh : ¬Finite a b\nn : ℕ\n⊢ 1 ∣ b",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b : α\nh : ¬Finite a b\nn : ℕ\n⊢ a ^ zero ∣ b",
"tactic": "rw [_root_.pow_zero]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst... | [
87,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mk_add_mk | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_one | [
{
"state_after": "no goals",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\n⊢ count p 1 = if p 0 then 1 else 0",
"tactic": "simp [count_succ]"
}
] | [
94,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.neg_left_iff | [] | [
66,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | sub_toIocDiv_zsmul_mem_Ioc | [] | [
67,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Std/Data/List/Lemmas.lean | List.range'_concat | [
{
"state_after": "step s n : Nat\n⊢ range' s (1 + n) step = range' s n step ++ [s + step * n]",
"state_before": "step s n : Nat\n⊢ range' s (n + 1) step = range' s n step ++ [s + step * n]",
"tactic": "rw [Nat.add_comm n 1]"
},
{
"state_after": "no goals",
"state_before": "step s n : Nat\n⊢ ... | [
1881,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1880,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_coe | [] | [
191,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.x_sub_y_dvd_pow | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\ny : ℕ\n⊢ 2 * ↑a * ↑y - ↑y * ↑y - 1 ∣ yz a1 0 * (↑a - ↑y) + ↑(y ^ 0) - xz a1 0",
"tactic": "simp [xz, yz, Int.ofNat_zero, Int.ofNat_one]"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\ny : ℕ\n⊢ 2 * ↑a * ↑y -... | [
587,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.eventually_mem | [] | [
929,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableOn.sub_const | [] | [
570,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_diagonal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\nx : α\n⊢ (x, x) ∈ diagonal α",
"tactic": "simp [diagonal]"
}
] | [
472,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | AlgEquiv.restrictScalars_apply | [] | [
222,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Ioc_disjoint_Ioc | [
{
"state_after": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ : α\nh :\n Disjoint (Ico (↑toDual a₂) (↑toDual a₁)) (Ico (↑toDual b₂) (↑toDual b₁)) ↔\n min (↑toDual a₁) (↑toDual b₁) ≤ max (↑toDual a₂) (↑toDual b₂)\n⊢ Disjoint (Ioc a₁ a₂) (Ioc b₁ b₂) ↔ min a₂ b₂ ≤ max a₁ b₁",
"st... | [
141,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.fg_of_surjective | [] | [
356,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comap_comp_apply | [
{
"state_after": "case h\nσ : Type u_2\nτ : Type u_3\nυ : Type u_4\nR : Type u_1\ninst✝ : CommSemiring R\nf : MvPolynomial σ R →ₐ[R] MvPolynomial τ R\ng : MvPolynomial τ R →ₐ[R] MvPolynomial υ R\nx : υ → R\ni : σ\n⊢ comap (AlgHom.comp g f) x i = comap f (comap g x) i",
"state_before": "σ : Type u_2\nτ : Typ... | [
77,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.nodup_nil | [] | [
658,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
8
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.openEmbedding_of_le | [
{
"state_after": "ι : Type ?u.27267\nα : Type u_1\nβ : Type ?u.27273\nγ : Type ?u.27276\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nU V : Opens α\ni : U ≤ V\n⊢ IsOpen {x | ↑x ∈ ↑U}",
"state_before": "ι : Type ?u.27267\nα : Type u_1\nβ : Type ?u.27273\nγ : Type ?u.2... | [
267,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.smul_tprodCoeff | [
{
"state_after": "ι : Type u_1\nι₂ : Type ?u.59540\nι₃ : Type ?u.59543\nR : Type u_3\ninst✝¹² : CommSemiring R\nR₁ : Type u_2\nR₂ : Type ?u.59555\ns : ι → Type u_4\ninst✝¹¹ : (i : ι) → AddCommMonoid (s i)\ninst✝¹⁰ : (i : ι) → Module R (s i)\nM : Type ?u.59745\ninst✝⁹ : AddCommMonoid M\ninst✝⁸ : Module R M\nE : ... | [
179,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/GroupTheory/Coset.lean | normal_iff_eq_cosets | [] | [
267,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/Monotone/Basic.lean | antitoneOn_univ | [] | [
392,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
9
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.smul_zero_mk | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.1812\nP : Type ?u.1815\nE : Type ?u.1818\nα✝ : Type ?u.1821\nβ : Type u_3\ninst✝⁶ : SMul M α✝\ninst✝⁵ : SMul M β\ninst✝⁴ : SMul N α✝\ninst✝³ : SMul N β\na✝ : M\nx : α✝ × β\nα : Type u_1\ninst✝² : Monoid M\ninst✝¹ : AddMonoid α\ninst✝ : ... | [
78,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.lift_surjective_of_surjective | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nx y✝ : R\ninst✝ : CommRing S\nI : Ideal R\nf : R →+* S\nH : ∀ (a : R), a ∈ I → ↑f a = 0\nhf : Function.Surjective ↑f\ny : S\n⊢ ∃ a, ↑(lift I f H) a = y",
"state_before": "R : Type u\ninst✝¹ : CommRing R\nI✝ : Ideal R\na b ... | [
286,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.subset_map_iff | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α ↪ β\ns : Finset β\nt : Finset α\nh : s ⊆ map f t\n⊢ s = map f (preimage s ↑f (_ : InjOn (↑f) (↑f ⁻¹' ↑s)))\n\ncase refine'_2\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α ↪ β\ns : Finset β\nt : Finset α\n⊢ (∃ u x, s... | [
120,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/Algebra/Affine.lean | AffineMap.homothety_isOpenMap | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nE : Type ?u.20960\nF : Type u_2\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : TopologicalAddGroup F\ninst✝² : Field R\ninst✝¹ : Module R F\ninst✝ : ContinuousConstSMul R F\nx :... | [
83,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.mem_finPairsLT | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\na : (_ : Fin n) × Fin n\n⊢ a ∈ finPairsLT n ↔ a.snd < a.fst",
"tactic": "simp only [finPairsLT, Fin.lt_iff_val_lt_val, true_and_iff, mem_attachFin, mem_range, mem_univ,\n mem_sigma]"
}
] | [
310,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.coe_bot | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.finite_co_support | [] | [
1427,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1425,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.add_biSup | [] | [
586,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Algebra/Regular/Basic.lean | not_isLeftRegular_zero | [] | [
260,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.mem_degrees | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.44438\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q p : MvPolynomial σ R\ni : σ\n⊢ i ∈ degrees p ↔ ∃ d, coeff d p ≠ 0 ∧ i ∈ d.support",
"tactic": "classical\nsimp only [degrees_def, Multise... | [
192,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Sign.lean | sign_one | [] | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | uniformity_basis_dist_pow_of_lt_1 | [] | [
125,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compRight_apply | [] | [
603,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_comap_map | [] | [
504,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Comp.lean | MvQPF.Comp.map_mk | [] | [
73,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_insert_subset | [] | [
1995,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1994,
1
] |
Mathlib/Data/ULift.lean | PLift.up_injective | [] | [
45,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_smul | [] | [
302,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/List/AList.lean | AList.insert_singleton_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb b' : β a\n⊢ (insert a b (singleton a b')).entries = (singleton a b).entries",
"tactic": "simp only [AList.insert_entries, List.kerase_cons_eq, and_self_iff, AList.singleton_entries,\n heq_iff_eq, e... | [
335,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
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