file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_mono | [] | [
879,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.107971\nγ : Type ?u.107974\nδ : Type ?u.107977\nι : Type ?u.107980\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ s t : Set α\n⊢ s =ᵐ[μ] t ↔ ↑↑μ (s \\ t) = 0 ∧ ↑↑μ (t \\ s) = 0",
"tactic": "simp [eventuallyLE_antisymm_... | [
484,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_right_le_iff | [
{
"state_after": "R : Type ?u.697823\nA : Type u_1\nK : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nJ : FractionalIdeal A⁰ K\nhJ : J ≠ 0\nI I' : FractionalIdeal A⁰ K\n⊢ I * J ≤ I' * J ↔ ... | [
558,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Analysis/Convex/Function.lean | concaveOn_of_convex_hypograph | [] | [
225,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.set_mul_normal_comm | [
{
"state_after": "case h\nα : Type ?u.21855\nG : Type u_1\nA : Type ?u.21861\nS : Type ?u.21864\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns✝ s : Set G\nN : Subgroup G\nhN : Normal N\nx : G\n⊢ x ∈ s * ↑N ↔ x ∈ ↑N * s",
"state_before": "α : Type ?u.21855\nG : Type u_1\nA : Type ?u.21861\nS : Type ?u.21864\ninst✝... | [
165,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.left_comp_retraction | [] | [
99,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_addMonoidHom_id | [] | [
681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Data/Set/Pairwise/Lattice.lean | Set.biUnion_diff_biUnion_eq | [
{
"state_after": "α : Type u_2\nβ : Type ?u.3238\nγ : Type ?u.3241\nι : Type u_1\nι' : Type ?u.3247\nr p q : α → α → Prop\ns t : Set ι\nf : ι → Set α\nh : PairwiseDisjoint (s ∪ t) f\ni : ι\nhi : i ∈ s \\ t\na : α\nha : a ∈ f i\n⊢ ¬a ∈ ⋃ (x : ι) (_ : x ∈ t), f x",
"state_before": "α : Type u_2\nβ : Type ?u.3... | [
100,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Nat/Choose/Cast.lean | Nat.cast_choose_eq_pochhammer_div | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝¹ : DivisionRing K\ninst✝ : CharZero K\na b : ℕ\n⊢ ↑(choose a b) = Polynomial.eval (↑(a - (b - 1))) (pochhammer K b) / ↑b !",
"tactic": "rw [eq_div_iff_mul_eq (cast_ne_zero.2 b.factorial_ne_zero : (b ! : K) ≠ 0), ← cast_mul,\n mul_comm, ←... | [
41,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.snd_div | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_adjugate | [] | [
230,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_mul_nonneg | [
{
"state_after": "case inl\nr : ℝ\nhn : r < 0\n⊢ 0 ≤ sign r * r\n\ncase inr.inl\n\n⊢ 0 ≤ sign 0 * 0\n\ncase inr.inr\nr : ℝ\nhp : 0 < r\n⊢ 0 ≤ sign r * r",
"state_before": "r : ℝ\n⊢ 0 ≤ sign r * r",
"tactic": "obtain hn | rfl | hp := lt_trichotomy r (0 : ℝ)"
},
{
"state_after": "case inl\nr : ℝ\n... | [
98,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | DirectSum.IsInternal.collectedBasis_orthonormal | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3801506\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_3\ndec_ι : DecidableEq ι\nG : ι... | [
2180,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2175,
1
] |
Mathlib/Algebra/CharP/Basic.lean | MonoidHom.iterate_map_frobenius | [] | [
387,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.transpose | [] | [
120,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_add_add_self | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1804599\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ inner x x + inner y x + (inner x y + inner y y) = inner x x + in... | [
666,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.pos_iff_one_le | [] | [
50,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.stronglyMeasurable | [] | [
211,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
11
] |
Std/Logic.lean | Decidable.peirce | [] | [
572,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
571,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | AddMonoidHom.coe_toIntLinearMap | [] | [
774,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Reaches₀.tail' | [] | [
819,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_le_sq | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.260389\nA : Type ?u.260392\nG : Type ?u.260395\nM : Type ?u.260398\nR : Type u_1\ninst✝ : LinearOrderedRing R\nx y : R\n⊢ x ^ 2 ≤ y ^ 2 ↔ abs x ≤ abs y",
"tactic": "simpa only [sq_abs] using\n (@strictMonoOn_pow R _ _ two_pos).le_iff_le (abs_non... | [
702,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_neg_iff_of_neg | [
{
"state_after": "k : Type u_1\nM : Type u_2\nN : Type ?u.32115\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhc : c < 0\n⊢ 0 < -c • a ↔ 0 < a",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.32115\ninst✝³ : OrderedRing k\nin... | [
83,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/MeasureTheory/Covering/LiminfLimsup.lean | blimsup_cthickening_mul_ae_eq | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : MeasureTheory.Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nM : ℝ\nhM : 0 < M\nr : ℕ → ℝ\nhr : Tends... | [
230,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.tendsto_abv_aeval_atTop | [] | [
131,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_lt | [
{
"state_after": "case inl\nn m l : ℕ\nhml : m ≤ l\n⊢ filter (fun x => decide (x < l)) (Ico n m) = Ico n (min m l)\n\ncase inr\nn m l : ℕ\nhlm : l ≤ m\n⊢ filter (fun x => decide (x < l)) (Ico n m) = Ico n (min m l)",
"state_before": "n m l : ℕ\n⊢ filter (fun x => decide (x < l)) (Ico n m) = Ico n (min m l)"... | [
184,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.toSubring_injective | [
{
"state_after": "no goals",
"state_before": "R' : Type u'\nR✝ : Type u\nA✝ : Type v\nB : Type w\nC : Type w'\ninst✝⁹ : CommSemiring R✝\ninst✝⁸ : Semiring A✝\ninst✝⁷ : Algebra R✝ A✝\ninst✝⁶ : Semiring B\ninst✝⁵ : Algebra R✝ B\ninst✝⁴ : Semiring C\ninst✝³ : Algebra R✝ C\nS✝ : Subalgebra R✝ A✝\nR : Type u\nA ... | [
242,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.add_nat_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\n⊢ LiouvilleWith p (x + ↑n) ↔ LiouvilleWith p x",
"tactic": "rw [← Rat.cast_coe_nat n, add_rat_iff]"
}
] | [
225,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.mul_right | [
{
"state_after": "α : Type u_1\nf g h : Perm α\nH1 : Disjoint f g\nH2 : Disjoint f h\n⊢ Disjoint (g * h) f",
"state_before": "α : Type u_1\nf g h : Perm α\nH1 : Disjoint f g\nH2 : Disjoint f h\n⊢ Disjoint f (g * h)",
"tactic": "rw [disjoint_comm]"
},
{
"state_after": "no goals",
"state_befor... | [
117,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_one | [] | [
1049,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_empty | [] | [
964,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_nat_ceil_mul_div_atTop | [
{
"state_after": "α : Type ?u.516691\nβ : Type ?u.516694\nι : Type ?u.516697\nR : Type u_1\ninst✝³ : TopologicalSpace R\ninst✝² : LinearOrderedField R\ninst✝¹ : OrderTopology R\ninst✝ : FloorRing R\na : R\nha : 0 ≤ a\nA : Tendsto (fun x => a + x⁻¹) atTop (𝓝 (a + 0))\n⊢ Tendsto (fun x => ↑⌈a * x⌉₊ / x) atTop (�... | [
610,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/BigOperators/Pi.lean | Finset.univ_prod_mulSingle | [
{
"state_after": "case h\nI : Type u_1\ninst✝² : DecidableEq I\nZ : I → Type u_2\ninst✝¹ : (i : I) → CommMonoid (Z i)\ninst✝ : Fintype I\nf : (i : I) → Z i\na : I\n⊢ Finset.prod univ (fun i => Pi.mulSingle i (f i)) a = f a",
"state_before": "I : Type u_1\ninst✝² : DecidableEq I\nZ : I → Type u_2\ninst✝¹ : (... | [
84,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.not_tendsto | [] | [
3083,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3081,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_lt_of_lt_sub_left | [
{
"state_after": "a b c : Int\nh✝ : b < c - a\nh : a + b < a + (c - a)\n⊢ a + b < c",
"state_before": "a b c : Int\nh : b < c - a\n⊢ a + b < c",
"tactic": "have h := Int.add_lt_add_left h a"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : b < c - a\nh : a + b < a + (c - a)... | [
1049,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1047,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.isIso_π_of_isTerminal | [
{
"state_after": "case w\nC : Type u₁\ninst✝³ : Category C\nJ : Type u\ninst✝² : Category J\nj : J\nI : IsTerminal j\nF : J ⥤ C\ninst✝¹ : HasLimit F\ninst✝ : ∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)\nj✝ : J\n⊢ (limit.π F j ≫ limit.lift F (coneOfDiagramTerminal I F)) ≫ limit.π F j✝ = 𝟙 (limit F) ≫ limit.π F j✝"... | [
721,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.or_eq_true_eq_eq_true_or_eq_true | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ ((a || b) = true) = (a = true ∨ b = true)",
"tactic": "simp"
}
] | [
91,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_compact_closed | [
{
"state_after": "case inl\n𝕜 : Type ?u.82757\nE : Type u_1\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalAddGroup E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\nt : Set E\nx y : E\ninst✝ : LocallyConvexSpace ℝ E\nht₁ : Convex ℝ t\nht₂ : IsClosed t\nhs₁ : Convex ℝ ∅\nhs₂ : Is... | [
169,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.add_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ m = 1 ∧ n = 0",
"tactic": "cases n <;> simp [succ_eq_add_one, ← add_assoc, succ_inj']"
}
] | [
196,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.int_cast_re | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ (↑n).re = ↑n",
"tactic": "rw [← ofReal_int_cast, ofReal_re]"
}
] | [
852,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | pthRoot_pow_p' | [] | [
82,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_mem_subspace_eq_self | [] | [
704,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.neg_one_mul | [
{
"state_after": "u : Lean.Level\nR✝ : Type ?u.203351\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\na : R\n⊢ -a = Int.rawCast (Int.negOfNat 1) * a",
"state_before": "u : Lean.Level\nR✝ : Type ?u.203351\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : C... | [
527,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.mem_smul_pointwise_iff_exists | [] | [
296,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concat_append | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w x : V\np : Walk G u v\nh : Adj G v w\nq : Walk G w x\n⊢ append (concat p h) q = append p (cons h q)",
"tactic": "rw [concat_eq_append, ← append_assoc,... | [
298,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.inf_iff_and | [] | [
146,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le_eq | [] | [
88,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
88,
9
] |
Std/Data/List/Lemmas.lean | List.filter_sublist | [
{
"state_after": "α : Type u_1\np : α → Bool\na : α\nl : List α\n⊢ (match p a with\n | true => a :: filter p l\n | false => filter p l) <+\n a :: l",
"state_before": "α : Type u_1\np : α → Bool\na : α\nl : List α\n⊢ filter p (a :: l) <+ a :: l",
"tactic": "rw [filter]"
},
{
"state_after... | [
1121,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1119,
9
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.isCompact_Icc | [] | [
220,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
11
] |
Mathlib/Data/Int/ModEq.lean | Int.modEq_add_fac_self | [] | [
293,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.19335522\n𝕜 : Type ?u.19335525\nE : Type ?u.19335528\nF : Type ?u.19335531\nA : Type ?u.19335534\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → ℝ\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhab : a ≤ b\nhf : ... | [
1264,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/Order/Atoms.lean | isCoatomic_iff_forall_isCoatomic_Ici | [] | [
310,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.iInf_empty | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nf✝ : ι → ℝ≥0\ninst✝ : IsEmpty ι\nf : ι → ℝ≥0\n⊢ (⨅ (i : ι), f i) = 0",
"tactic": "rw [iInf_of_empty', sInf_empty]"
}
] | [
944,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.factorization | [
{
"state_after": "case h\np : ℕ\nhp : Prime p\nq : ℕ\n⊢ ↑(Nat.factorization p) q = ↑(single p 1) q",
"state_before": "p : ℕ\nhp : Prime p\n⊢ Nat.factorization p = single p 1",
"tactic": "ext q"
},
{
"state_after": "no goals",
"state_before": "case h\np : ℕ\nhp : Prime p\nq : ℕ\n⊢ ↑(Nat.facto... | [
276,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_add_int | [] | [
234,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_le_coe_iff | [] | [
663,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_zpow | [] | [
305,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul_param_zpow | [] | [
269,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.ret_orElse | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nc₂ : Computation α\n⊢ destruct ({ hOrElse := fun a b => OrElse.orElse a b }.1 (pure a) fun x => c₂) = Sum.inl a",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nc₂ : Computation α\n⊢ destruct (HOrElse.hOrElse (pure a) fun x => c₂) = S... | [
940,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Analysis/Convex/Segment.lean | image_segment | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.97868\nι : Type ?u.97871\nπ : ι → Type ?u.97876\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nf : E →ᵃ[𝕜] F\... | [
239,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.mk'_coe' | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.trans_one | [] | [
137,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_sup_right | [] | [
122,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_or_distrib_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.143807\nι : Sort x\nf : Filter α\np : Prop\nq : α → Prop\nh : p\n⊢ (∀ᶠ (x : α) in f, p ∨ q x) ↔ p ∨ ∀ᶠ (x : α) in f, q x",
"tactic": "simp [h]"
},
{
"state_after": "no goals",
"state_before": "α : T... | [
1187,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.toLinearMap_injective | [] | [
376,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | deriv_zpow' | [] | [
103,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.add | [
{
"state_after": "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.127337\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.127432\... | [
133,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
8
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongr_one | [] | [
202,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | pi_norm_lt_iff' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1270061\n𝕜 : Type ?u.1270064\nα : Type ?u.1270067\nι : Type u_1\nκ : Type ?u.1270073\nE : Type ?u.1270076\nF : Type ?u.1270079\nG : Type ?u.1270082\nπ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → SeminormedGroup (π i)\ninst✝ : SeminormedG... | [
2499,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2498,
1
] |
Mathlib/CategoryTheory/Sites/CompatibleSheafification.lean | CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom | [
{
"state_after": "C : Type u\ninst✝⁸ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁷ : Category D\nE : Type w₂\ninst✝⁶ : Category E\nF : D ⥤ E\ninst✝⁵ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁴ : ∀ (α β : Type (max v u)) (fst snd : β → α),... | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_le_one_iff | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1044072\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V'\ninst✝ : Module K ... | [
1231,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.homCongr_symm | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | matPolyEquiv_smul_one | [
{
"state_after": "case a.a.h\nR : Type u_1\nA : Type ?u.620220\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\np : R[X]\nm : ℕ\ni j : n\n⊢ coeff (↑matPolyEquiv (p • 1)) m i j = coeff (Polynomial.map (algebraMap R (Matrix n n R)) p) m i ... | [
289,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.balance2_toList | [
{
"state_after": "α : Type u_1\nl : RBNode α\nv : α\nr : RBNode α\n⊢ toList\n (match l, v, r with\n | a, x, node red (node red b y c) z d => node red (node black a x b) y (node black c z d)\n | a, x, node red b y (node red c z d) => node red (node black a x b) y (node black c z d)\n | a, x, ... | [
425,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
423,
9
] |
Mathlib/Order/Height.lean | Set.one_le_chainHeight_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7989\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\n⊢ (∃ l, l ∈ subchain s ∧ length l = 1) ↔ Set.Nonempty s",
"state_before": "α : Type u_1\nβ : Type ?u.7989\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\n⊢ 1 ≤ chainHeight s ↔ Set.Non... | [
141,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.findGreatest_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nP Q : ℕ → Prop\ninst✝ : DecidablePred P\n⊢ Nat.findGreatest P k = 0 ↔ ∀ ⦃n : ℕ⦄, 0 < n → n ≤ k → ¬P n",
"tactic": "simp [findGreatest_eq_iff]"
}
] | [
628,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_add_of_nonneg_right | [
{
"state_after": "a b : Int\nh : 0 ≤ b\nthis : a + b ≥ a + 0\n⊢ a ≤ a + b",
"state_before": "a b : Int\nh : 0 ≤ b\n⊢ a ≤ a + b",
"tactic": "have : a + b ≥ a + 0 := Int.add_le_add_left h a"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : 0 ≤ b\nthis : a + b ≥ a + 0\n⊢ a ≤ a + ... | [
796,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
794,
11
] |
Mathlib/Topology/UniformSpace/Basic.lean | comp_open_symm_mem_uniformity_sets | [
{
"state_after": "case intro.intro\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.94197\ninst✝ : UniformSpace α\ns : Set (α × α)\nhs : s ∈ 𝓤 α\nt : Set (α × α)\nht₁ : t ∈ 𝓤 α\nht₂ : t ○ t ⊆ s\n⊢ ∃ t, t ∈ 𝓤 α ∧ IsOpen t ∧ SymmetricRel t ∧ t ○ t ⊆ s",
"state_before": "α : Type ua\nβ : Typ... | [
1060,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.map_smul | [] | [
121,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
11
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_zero | [] | [
474,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.add_strictConcaveOn | [] | [
532,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.ppow | [
{
"state_after": "case zero\nR : Type u_1\ninst✝ : CommSemiring R\nf : ArithmeticFunction R\nhf : IsMultiplicative f\n⊢ IsMultiplicative (ArithmeticFunction.ppow f Nat.zero)\n\ncase succ\nR : Type u_1\ninst✝ : CommSemiring R\nf : ArithmeticFunction R\nhf : IsMultiplicative f\nk : ℕ\nhi : IsMultiplicative (Arith... | [
832,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub_zsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIcoMod hp a (b - m • p) = toIcoMod hp a b",
"tactic": "rw [sub_eq_add_neg, ← neg_smul, toIcoMod_add_zsmul]"
}
] | [
452,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Sum.swap_map_inl | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_toDual | [] | [
3243,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3243,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.Measure.ext_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.10223\nγ : Type ?u.10226\nδ : Type ?u.10229\nι : Type ?u.10232\ninst✝ : MeasurableSpace α\nμ μ₁ : Measure α\ns✝ s₁ s₂ t s : Set α\n_hs : MeasurableSet s\n⊢ ↑↑μ₁ s = ↑↑μ₁ s",
"state_before": "α : Type u_1\nβ : Type ?u.10223\nγ : Type ?u.10226\nδ : Type ?u.10229\nι ... | [
146,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/CharP/ExpChar.lean | char_eq_expChar_iff | [
{
"state_after": "case zero\nR : Type u\ninst✝ : Semiring R\np : ℕ\nhp : CharP R p\nq : CharZero R\n⊢ p = 1 ↔ Nat.Prime p\n\ncase prime\nR : Type u\ninst✝ : Semiring R\np q : ℕ\nhp : CharP R p\nhq_prime : Nat.Prime q\nhq_hchar : CharP R q\n⊢ p = q ↔ Nat.Prime p",
"state_before": "R : Type u\ninst✝ : Semirin... | [
63,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.toFun_eq_coe | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.ker_id_sub_eq_of_proj | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.9010\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.9526\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.10489\ninst✝² : Semiring S\nM : Ty... | [
48,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.ringHom_ext | [] | [
121,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_le_add_iff_right | [] | [
778,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
11
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.liftMonoid_coe | [] | [
541,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Algebra/Order/Nonneg/Field.lean | Nonneg.coe_div | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
11
] |
Mathlib/Topology/Algebra/Group/Basic.lean | isOpenMap_mul_right | [] | [
128,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.symm_dual_comp | [] | [
902,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Topology/Order/Basic.lean | isOpen_Ioi | [] | [
302,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_zpow₀ | [] | [
440,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.preimage | [] | [
153,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
11
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitMany | [
{
"state_after": "case intro\nι : Type u_1\nM : Type ?u.49727\nn : ℕ\nI J : Box ι\ni : ι\nx : ℝ\ninst✝ : Finite ι\ns : Finset (Box ι)\nval✝ : Fintype ι\n⊢ ∀ᶠ (t : Finset (ι × ℝ)) in atTop,\n ∀ (I J : Box ι), J ∈ s → ∀ (J' : Box ι), J' ∈ splitMany I t → ¬Disjoint ↑J ↑J' → J' ≤ J",
"state_before": "ι : Typ... | [
318,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Std/Data/List/Init/Lemmas.lean | List.ne_nil_of_length_eq_succ | [] | [
47,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
47,
1
] |
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