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/Analysis/Seminorm.lean | Seminorm.inf_apply | [] | [
488,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.roots_X_pow_card_sub_X | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nR : Type ?u.732401\ninst✝³ : Field K\ninst✝² : Fintype K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Algebra (ZMod p) K\n⊢ roots (X ^ q - X) = univ.val",
"tactic": "classical\n have aux : (X ^ q - X : K[X]) ≠ 0 := X_pow_card_sub_X_ne_zero K F... | [
278,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map | [] | [
1571,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1568,
1
] |
Mathlib/Algebra/Group/Ext.lean | Group.ext | [
{
"state_after": "G : Type u_1\ng₁ g₂ : Group G\nh_mul : Mul.mul = Mul.mul\nh₁ : One.one = One.one\nf : G →* G := { toOneHom := { toFun := id, map_one' := h₁ }, map_mul' := (_ : ∀ (x y : G), Mul.mul x y = Mul.mul x y) }\n⊢ g₁ = g₂",
"state_before": "G : Type u_1\ng₁ g₂ : Group G\nh_mul : Mul.mul = Mul.mul\n... | [
155,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_neg | [] | [
355,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_card_fiber_lt_of_card_lt_mul | [] | [
415,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isOrtho_zero_right | [] | [
75,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_le | [] | [
474,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.card_Icc_finset | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\n⊢ Set.InjOn ((fun x x_1 => x ∪ x_1) s) ↑(powerset (t \\ s))",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\n⊢ card (Icc s t) = 2 ^ (card t - card s)",
"tactic": "rw [← card_sdiff h, ← car... | [
104,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/Basic.lean | denseRange_id | [] | [
1803,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_sup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.173522\nι : Sort x\np : α → Prop\nf g : Filter α\n⊢ (∃ᶠ (x : α) in f ⊔ g, p x) ↔ (∃ᶠ (x : α) in f, p x) ∨ ∃ᶠ (x : α) in g, p x",
"tactic": "simp only [Filter.Frequently, eventually_sup, not_and_or]"
}
] | [
1400,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.symm_toEquiv | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.mul_def | [
{
"state_after": "a b : Rat\n⊢ Rat.mul a b = normalize (a.num * b.num) (a.den * b.den)",
"state_before": "a b : Rat\n⊢ a * b = normalize (a.num * b.num) (a.den * b.den)",
"tactic": "show Rat.mul .. = _"
},
{
"state_after": "a b : Rat\n⊢ (let g1 := Nat.gcd (Int.natAbs a.num) b.den;\n let g2 :=... | [
255,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
244,
1
] |
Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.congr_reverse_comp | [
{
"state_after": "V : Type u\ninst✝ : Quiver V\nX Y : Paths (Quiver.Symmetrify V)\np : X ⟶ Y\n⊢ Quot.mk (Quotient.CompClosure redStep) (Quiver.Path.reverse p ≫ Quiver.Path.reverse (Quiver.Path.reverse p)) =\n Quot.mk (Quotient.CompClosure redStep) (𝟙 Y)",
"state_before": "V : Type u\ninst✝ : Quiver V\nX... | [
127,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Finsupp.inner_sum | [
{
"state_after": "case h.e'_3\n𝕜 : Type u_2\nE : Type u_3\nF : Type ?u.1474372\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\nι : Type u_1\nl : ι →₀ 𝕜\nv : ι → E\nx : E\n⊢ (sum l fun i a ... | [
544,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.comp_P_eq_self_iff | [
{
"state_after": "case mp\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY : C\nn q : ℕ\nφ : Y ⟶ X.obj [n + 1].op\n⊢ φ ≫ HomologicalComplex.Hom.f (P q) (n + 1) = φ → HigherFacesVanish q φ\n\ncase mpr\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObj... | [
152,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.finite_of_linearIndependent | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Ring R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : Nontrivial R\ninst✝ : IsArtinian R M\ns : Set M\nhs : LinearIndependent R Subtype.val\nhf : ¬Set.Finite s\n⊢ (fun x x_1 => x > x_1) ↪r fun x x_1 => x < x_1",
"state_before": "R : Type u_1\nM... | [
184,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/Bounds.lean | isGLB_inv | [] | [
78,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.leftUnitor_inv_apply | [] | [
231,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Wequiv.abs' | [
{
"state_after": "case mk\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\ny : PFunctor.W (P F)\na✝ : (P F).A\nf✝ : PFunctor.B (P F) a✝ → WType (P F).B\nh : Qpf.abs (PFunctor.W.dest (WType.mk a✝ f✝)) = Qpf.abs (PFunctor.W.dest y)\n⊢ Wequiv (WType.mk a✝ f✝) y",
"state_before": "F : Type u → Type u\ninst✝ ... | [
209,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.add_tprodCoeff | [] | [
160,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_div_iff_of_nonzero | [
{
"state_after": "R : Type ?u.1194138\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type ?u.1194345\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝³ : CommRing R₁\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\nfrac : IsFractionRing R₁ K\ninst✝ : IsDomain R₁\nI✝ J... | [
1119,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Chain.exists_of_mem_map | [] | [
128,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_union_mul_inter_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43706\nι : Type ?u.43709\nM : Type u_2\nN : Type ?u.43715\ninst✝ : MulOneClass M\ns✝ t✝ : Set α\nf✝ g : α → M\na✝ : α\nf : α → M\ns t : Set α\na : α\n⊢ mulIndicator (s ∪ t) f a * mulIndicator (s ∩ t) f a = mulIndicator s f a * mulIndica... | [
373,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.eraseMax.valid | [
{
"state_after": "α : Type u_1\ninst✝ : Preorder α\nt : Ordnode α\nh : Valid t\n⊢ Valid (eraseMin (dual t))",
"state_before": "α : Type u_1\ninst✝ : Preorder α\nt : Ordnode α\nh : Valid t\n⊢ Valid (eraseMax t)",
"tactic": "rw [Valid.dual_iff, dual_eraseMax]"
},
{
"state_after": "no goals",
"... | [
1416,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Data/Set/Basic.lean | Set.forall_insert_of_forall | [] | [
1228,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.self_comp_symm | [] | [
367,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_nat_cast | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ x ^ ↑0 = x ^ 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nn : ℕ\nhx : x = 0\n⊢ x ^ ↑(n + 1) = x ^ (n + 1)",
"tactic": "simp only [hx, pow_succ, Complex.zero_cpow (Nat.cast_ne_zero.2 (Nat.succ_ne_zero _... | [
125,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.mul_conj | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5035191\ninst✝ : IsROrC K\nz : K\n⊢ z * ↑(starRingEnd K) z = ↑(↑normSq z)",
"tactic": "apply ext <;> simp only [normSq_apply, isROrC_simps, map_add, mul_zero] <;> ring"
}
] | [
525,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/List/Basic.lean | List.scanr_cons | [
{
"state_after": "ι : Type ?u.247779\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β → β\nb : β\na : α\nl : List α\n⊢ f a (foldr (fun a x => (f a x.fst, x.fst :: x.snd)) (b, []) l).fst = f a (foldr f b l)",
"state_before": "ι : Type ?u.247779\nα : Type u\nβ : Type v\nγ : Type w\nδ... | [
2691,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2686,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | localizationAlgebra_injective | [] | [
1392,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.universally_eq | [] | [
603,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_tendsto_indicator_closure | [
{
"state_after": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδseq : ℕ → ℝ\nδseq_pos : ∀ (n : ℕ), 0 < δseq n\nδseq_lim : Tendsto δseq atTop (𝓝 0)\nE : Set α\nkey : Tendsto (fun n => thickenedIndicatorAux (δseq n) E) atTop (𝓝 (indicator (closure E) fun x => 1))\n⊢ Tendsto (fun n => ↑(thickenedIndicator (_ : 0 ... | [
250,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
src/lean/Init/Control/Lawful.lean | Id.pure_eq | [] | [
93,
61
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
93,
9
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.composePath_id | [] | [
188,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.congr | [] | [
968,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.apply_mulSingle | [
{
"state_after": "no goals",
"state_before": "I : Type u\nα : Type ?u.14053\nβ : Type ?u.14056\nγ : Type ?u.14059\nf : I → Type v₁\ng : I → Type v₂\nh : I → Type v₃\nx✝ y : (i : I) → f i\ni✝ : I\ninst✝³ : DecidableEq I\ninst✝² : (i : I) → One (f i)\ninst✝¹ : (i : I) → One (g i)\ninst✝ : (i : I) → One (h i)\... | [
290,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Basic.lean | Disjoint.frontier_left | [] | [
793,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_coe_submodule | [] | [
164,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.comp_eq_zero_iff | [
{
"state_after": "case mp\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\n⊢ comp p q = 0 → p = 0 ∨ eval (coeff q 0) p = 0 ∧ q = ↑C (coeff q 0)\n\ncase mpr\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q :... | [
866,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma_is_cong_sub | [
{
"state_after": "no goals",
"state_before": "N✝ : ℕ\nN : ℕ+\n⊢ Gamma ↑N ≤ Gamma ↑N",
"tactic": "simp only [le_refl]"
}
] | [
221,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_lt | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nhn : 1 < n\n⊢ 0 ∈ range n ∧ ¬coprime n 0",
"tactic": "simp [hn.ne', pos_of_gt hn]"
}
] | [
70,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_bot_bijective | [] | [
279,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.div_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.204600\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : DivisionSemiring α\ninst✝ : Neg β\nh : Antiperiodic f c\na : α\nha : a ≠ 0\n⊢ Antiperiodic (fun x => f (x / a)) (c * a)",
"tactic": "simpa only [div_eq_mul_inv] using h.mul_... | [
505,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.exists_nonneg_right | [] | [
676,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.neg | [] | [
989,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
11
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.neg_apply | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_filter_filter' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.355965\nγ : Type ?u.355968\np✝ q✝ : α → Prop\ninst✝³ : DecidablePred p✝\ninst✝² : DecidablePred q✝\ns t : Finset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : _root_.Disjoint p q\n⊢ ∀ ⦃a : α⦄, a ∈ s ∧ p a → ¬(a ∈ t ∧ q a)",
"state_befor... | [
2783,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2777,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftl_add | [] | [
325,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_le_le_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na✝ b✝ a b : α\n⊢ b = a ∨ b = pred a → pred a ≤ b ∧ b ≤ a",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na✝ b✝ a b : α\n⊢ pred a ≤ b ∧ b ≤ a ↔ b = a ∨ b = pred a",
"tactic": "refine'\n ⟨fun h =>... | [
781,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atBot_of_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.226440\nι' : Type ?u.226443\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.226452\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x => r * f x) l atBot ↔ Tendsto f l atBot",
"tactic": "simpa only [← mul_neg, ← ... | [
1079,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/Data/List/Forall2.lean | List.Forall₂.nthLe | [] | [
171,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.symm_trans_rev | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Measurable.ceil | [] | [
47,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Std/Data/List/Lemmas.lean | List.map_sub_range' | [
{
"state_after": "step a s n : Nat\nh : a ≤ s\n⊢ map (fun x => x - a) (range' (a + (s - a)) n step) = range' (s - a) n step",
"state_before": "step a s n : Nat\nh : a ≤ s\n⊢ map (fun x => x - a) (range' s n step) = range' (s - a) n step",
"tactic": "conv => lhs; rw [← Nat.add_sub_cancel' h]"
},
{
... | [
1836,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1832,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_eq_bot | [] | [
190,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.contDiffOn_arcsin | [] | [
126,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_approx_start | [
{
"state_after": "no goals",
"state_before": "x a b : ℝ\nh : abs' (exp x - expNear 0 x a) ≤ abs' x ^ 0 / ↑(Nat.factorial 0) * b\n⊢ abs' (exp x - a) ≤ b",
"tactic": "simpa using h"
}
] | [
1804,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1803,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | max_mul_of_nonneg | [] | [
977,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.continuous_exp | [] | [
124,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_apply | [] | [
2130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2128,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mul_const'' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.945240\nγ : Type ?u.945243\nδ : Type ?u.945246\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\nhf : AEMeasurable f\n⊢ (∫⁻ (a : α), f a * r ∂μ) = (∫⁻ (a : α), f a ∂μ) * r",
"tactic": "simp_rw [mul_comm, lintegral_con... | [
738,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.last_add_one | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ last 0 + 1 = 0",
"tactic": "simp only"
},
{
"state_after": "case h\nn✝ m n : ℕ\n⊢ ↑(last (n + 1) + 1) = ↑0",
"state_before": "n✝ m n : ℕ\n⊢ last (n + 1) + 1 = 0",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_b... | [
752,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_le | [] | [
120,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_nat_num_of_pos | [
{
"state_after": "no goals",
"state_before": "a : ℕ\nha0 : 0 < a\n⊢ 0 < ↑a",
"tactic": "exact_mod_cast ha0"
}
] | [
266,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | Differentiable.diffContOnCl | [] | [
44,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.range_comp | [] | [
2159,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2157,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_eq_singleton | [] | [
469,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Ioi_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Ioi ⊥ = univ",
"tactic": "rw [← range_coe, preimage_range]"
}
] | [
185,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_max_aux₂ | [
{
"state_after": "E : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : ℂ → F\nz w : ℂ\nhd : DiffContOnCl ℂ f (ball z (dist w z))\nhz : IsMaxOn (norm ∘ f) (closedBall z (dist w z)) z\ne : F →L[ℂ] F̂ := UniformSpace.Completion... | [
154,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_mul_cancel_left | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.957542\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx : M\ny : { x // x ∈ S }\n⊢ mk' f (↑y * x) y = ↑(toMap f) x",
"tactic": "rw [mul_comm, mk'_mul_canc... | [
875,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_ciSup | [
{
"state_after": "α : Type u_3\nβ : Type ?u.1649128\nγ : Type ?u.1649131\nγ₂ : Type ?u.1649134\nδ : Type u_2\nι✝ : Sort y\ns t u : Set α\ninst✝¹³ : TopologicalSpace α\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : BorelSpace α\ninst✝¹⁰ : TopologicalSpace β\ninst✝⁹ : MeasurableSpace β\ninst✝⁸ : BorelSpace β\ninst✝⁷ : T... | [
1371,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.17585\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.17597\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ng : β →CO γ\nf₁ f₂ : α →CO β\nhg : Injective ↑g\nh : comp g f₁ = co... | [
164,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mul_div_cancel_left | [
{
"state_after": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\na0 : a ≠ 0\nh : ¬b - a * b / a = 0\nthis : ¬EuclideanDomain.r (a * (b - a * b / a)) a\n⊢ False",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\na0 : a ≠ 0\nh : ¬b - a * b / a = 0\n⊢ False",
"tactic": "have := mul_left_no... | [
44,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Std/Logic.lean | Decidable.not_imp_not | [] | [
550,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
549,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_eq_uniformity_closure | [] | [
959,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.preimage_null | [] | [
2511,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2509,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | AlgHom.map_adjoin | [] | [
420,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.Rel.sub_left | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u₁\ninst✝⁴ : Semiring R✝\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nR : Type u₁\ninst✝ : Ring R\nr : R → R → Prop\na b c : R\nh : Rel r a b\n⊢ Rel r (a - c) (b - c)",
"tactic": "simp only [sub_eq_... | [
77,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Topology/SubsetProperties.lean | irreducibleComponent_property | [] | [
1793,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.destruct_eq_think | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns s' : Computation α\n⊢ (match ↑s 0 with\n | none => Sum.inr (tail s)\n | some a => Sum.inl a) =\n Sum.inr s' →\n s = think s'",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns s' : Computation α\n⊢ destruct s = Sum.inr s' → s = ... | [
141,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.succ_le_iff' | [
{
"state_after": "α✝ : Type ?u.168588\nβ✝ : Type ?u.168591\nγ : Type ?u.168594\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt✝ : γ → γ → Prop\na b : Ordinal\nα : Type u_1\nr : α → α → Prop\nhr : IsWellOrder α r\nβ : Type u_1\ns : β → β → Prop\nhs : IsWellOrder β s\nx✝ : type r < type s\nf : r ↪r s\nt : β\nhf : ∀ ... | [
1048,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
9
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.mul_lt_one_of_lt_of_le | [] | [
835,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_eight | [
{
"state_after": "x : ℝ\n⊢ cos (π / 8) = cos (π / 2 ^ 3)\n\nx : ℝ\n⊢ cos (π / 2 ^ 3) = sqrt (2 + sqrt 2) / 2",
"state_before": "x : ℝ\n⊢ cos (π / 8) = sqrt (2 + sqrt 2) / 2",
"tactic": "trans cos (π / 2 ^ 3)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\n⊢ 8 = 2 ^ 3\n\nx : ℝ\n⊢ cos (π / 2 ^ 3) = sqr... | [
801,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Topology/Basic.lean | interior_mono | [] | [
324,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | measurable_measure_prod_mk_left_finite | [
{
"state_after": "case refine'_1\nα : Type u_2\nα' : Type ?u.1615115\nβ : Type u_1\nβ' : Type ?u.1615121\nγ : Type ?u.1615124\nE : Type ?u.1615127\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : MeasureTheory.M... | [
178,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Maps.lean | ClosedEmbedding.closed_iff_image_closed | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.270791\nδ : Type ?u.270794\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nhf : ClosedEmbedding f\ns : Set α\nh : IsClosed (f '' s)\n⊢ IsClosed (f ⁻¹' (f '' s))",
"state_before": "α : Type u_1\nβ : Ty... | [
667,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Set/Image.lean | Function.Surjective.range_comp | [] | [
1329,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.finite_biUnion_mem_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.15563\nf g : Ultrafilter α\ns✝ t : Set α\np q : α → Prop\nis : Set β\ns : β → Set α\nhis : Set.Finite is\n⊢ (⋃ (i : β) (_ : i ∈ is), s i) ∈ f ↔ ∃ i, i ∈ is ∧ s i ∈ f",
"tactic": "simp only [← sUnion_image, finite_sUnion_me... | [
209,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rdropWhile_concat_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\nh : p x = true\n⊢ rdropWhile p (l ++ [x]) = rdropWhile p l",
"tactic": "rw [rdropWhile_concat, if_pos h]"
}
] | [
115,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_intCast | [] | [
511,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.inv | [] | [
112,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Quot.lean | Quot.induction_on | [] | [
49,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
11
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.mem_basicOpen | [] | [
394,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_inter_add_diff₀ | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.293388\nγ : Type ?u.293391\nδ : Type ?u.293394\nι : Type ?u.293397\nR : Type ?u.293400\nR' : Type ?u.293403\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t s : Set α\nht : NullMeasurabl... | [
1698,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1694,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | neg_pow | [] | [
202,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.apply_symm_apply | [] | [
151,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.to_mul_symm_eq | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.isQuadratic_χ₈' | [
{
"state_after": "a : ZMod 8\n⊢ ↑χ₈' a = 0 ∨ ↑χ₈' a = 1 ∨ ↑χ₈' a = -1",
"state_before": "⊢ MulChar.IsQuadratic χ₈'",
"tactic": "intro a"
},
{
"state_after": "case head\n\n⊢ ↑χ₈' { val := 0, isLt := (_ : 0 < 7 + 1) } = 0 ∨\n ↑χ₈' { val := 0, isLt := (_ : 0 < 7 + 1) } = 1 ∨ ↑χ₈' { val := 0, isL... | [
194,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_comp_sym | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.