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/Order/Hom/CompleteLattice.lean | sSupHom.copy_eq | [] | [
285,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.UnderMorphism.ext | [
{
"state_after": "T : Type u₁\ninst✝ : Category T\nX✝ X : T\nU V : Under X\nf g : U ⟶ V\nleft✝ : U.left ⟶ V.left\nb : U.right ⟶ V.right\nw✝ : (Functor.fromPUnit X).map left✝ ≫ V.hom = U.hom ≫ (𝟭 T).map b\nh : (CommaMorphism.mk left✝ b).right = g.right\n⊢ CommaMorphism.mk left✝ b = g",
"state_before": "T : ... | [
332,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Sum.elim_natCast_natCast | [] | [
335,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.31727\nα : Type u_1\nβ : Type ?u.31733\nf g : Perm α\np : α → Prop\nx y z : α\n⊢ SameCycle 1 x y ↔ x = y",
"tactic": "simp [SameCycle]"
}
] | [
107,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.232451\nβ : Type ?u.232454\nγ : Type ?u.232457\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\nh : c ≠ 0\n⊢ a < b / c ↔ c * succ a ≤ b",
"tactic": "rw [← not_le, div_le h, not_lt]"
}
] | [
902,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_pow_div_pow_le' | [
{
"state_after": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA B✝ C : Finset α\nhA : Finset.Nonempty A\nB : Finset α\nm n : ℕ\n⊢ ↑(card (B⁻¹ ^ m / B⁻¹ ^ n)) ≤ (↑(card (A * B⁻¹)) / ↑(card A)) ^ (m + n) * ↑(card A)",
"state_before": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA... | [
244,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Std/Data/List/Basic.lean | List.eraseIdx_eq_eraseIdxTR | [
{
"state_after": "case h.h.h\nα : Type u_1\nl : List α\nn : Nat\n⊢ eraseIdx l n = eraseIdxTR l n",
"state_before": "⊢ @eraseIdx = @eraseIdxTR",
"tactic": "funext α l n"
},
{
"state_after": "case h.h.h\nα : Type u_1\nl : List α\nn : Nat\n⊢ eraseIdx l n = eraseIdxTR.go l l n #[]",
"state_befor... | [
72,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
61,
10
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_spec'_mk | [] | [
279,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullback_of_preservesPullback | [] | [
109,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.incl_coe | [] | [
1121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.image_mem_of_mem_comap | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.259120\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : Filter α\nc : β → α\nh : range c ∈ f\nW : Set β\nW_in : W ∈ comap c f\n⊢ c '' W ∈ map c (comap c f)",
"state_before": "α : Type u\nβ... | [
2289,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2286,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.id_c_app | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX : SheafedSpace C\nU : (Opens ↑↑X.toPresheafedSpace)ᵒᵖ\n⊢ X.presheaf.obj U = ((𝟙 X).base _* X.presheaf).obj U",
"tactic": "aesop_cat"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category ... | [
133,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_bit0 | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (↑(starRingEnd ℂ) (bit0 z)).re = (bit0 (↑(starRingEnd ℂ) z)).re ∧\n (↑(starRingEnd ℂ) (bit0 z)).im = (bit0 (↑(starRingEnd ℂ) z)).im",
"tactic": "simp [bit0]"
}
] | [
530,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_eq_one_iff_inv_eq | [] | [
362,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
11
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.ext | [] | [
521,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.left_mem_affineSpan_of_right_ne | [] | [
749,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.coe_replicate | [] | [
285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ContinuousAt.norm' | [] | [
1218,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lt_lim | [] | [
458,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | continuousOn_clm_apply | [
{
"state_after": "𝕜 : Type u\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁷ : AddCommGroup F'\ninst✝⁶ : Module 𝕜 F'\ninst✝⁵ : TopologicalSpace F'\ninst✝⁴ : ... | [
585,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/GroupTheory/PresentedGroup.lean | PresentedGroup.toGroup.of | [] | [
84,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.map_csInf_of_continuousAt | [] | [
2813,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2811,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.not_mem_erase | [] | [
187,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.inv | [
{
"state_after": "x : ℝ*\nhi : ¬Infinitesimal x\nhr : IsSt x 0\n⊢ False",
"state_before": "x : ℝ*\nr : ℝ\nhi : ¬Infinitesimal x\nhr : IsSt x r\n⊢ r ≠ 0",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_before": "x : ℝ*\nhi : ¬Infinitesimal x\nhr : IsSt x 0\n⊢ False",
"tacti... | [
789,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_det_of_invertible | [] | [
209,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.Rel.smul | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr : A → A → Prop\nk : S\na b : A\nh : Rel r a b\n⊢ Rel r (k • a) (k • b)",
"tactic": "simp only [Algebra.smul_def, Rel.mul_right h]... | [
85,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.normalizer_normalizer | [
{
"state_after": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Finite (Sylow p G)\nP : Sylow p G\nthis :\n Normal (normalizer ↑(Sylow.subtype P (_ : ↑P ≤ normalizer (normalizer ↑P)))) →\n Normal ↑(Sylow.subtype P (_ : ↑P ≤ normalizer (normalizer ↑P)))\n⊢ ... | [
738,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.30276\ninst✝ : PartialOrder α\na✝ b c a : α\n⊢ ∀ (x : α), x ∈ Icc a a ↔ x ∈ {a}",
"tactic": "simp [Icc, le_antisymm_iff, and_comm]"
}
] | [
760,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.eval₂_int_castRingHom_X | [] | [
148,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.denseRange_coe₂ | [] | [
485,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsGLB.ciInf_eq | [] | [
559,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.setSeq_mem | [] | [
657,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.translate_left | [] | [
304,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.set_walk_length_toFinset_eq | [
{
"state_after": "case a\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝¹ : DecidableEq V\ninst✝ : LocallyFinite G\nn : ℕ\nu v : V\np : Walk G u v\n⊢ p ∈ Set.toFinset {p | Walk.length p = n} ↔ p ∈ finsetWalkLength G n u v",
"state_before": "V : Ty... | [
2383,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2380,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.mul_def | [] | [
891,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Data/Pi/Algebra.lean | Function.extend_one | [
{
"state_after": "no goals",
"state_before": "I : Type u\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nf✝ : I → Type v₁\ng : I → Type v₂\nh : I → Type v₃\nx y : (i : I) → f✝ i\ni : I\ninst✝ : One γ\nf : α → β\nx✝ : β\n⊢ extend f 1 1 x✝ = OfNat.ofNat 1 x✝",
"tactic": "apply ite_self"
}
] | [
363,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.isUnit_constantCoeff | [] | [
1642,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_lt_iff_lt | [] | [
82,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_eq_iff | [
{
"state_after": "no goals",
"state_before": "ψ θ : Angle\n⊢ 2 • ψ = 2 • θ ↔ ψ = θ ∨ ψ = θ + ↑π",
"tactic": "simp_rw [← coe_nat_zsmul, Nat.cast_ofNat, two_zsmul_eq_iff]"
}
] | [
195,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_group_smul_right | [] | [
237,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_one | [] | [
146,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_top | [
{
"state_after": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nW : Submodule R M\n⊢ dualAnnihilator ⊤ ≤ ⊥",
"state_before": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nW : Submodule R M\n⊢ dualAnnihilator ⊤... | [
861,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.false | [] | [
934,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
11
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_isSqrt | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ Nat.IsSqrt 0 (sqrt 0)",
"tactic": "simp [IsSqrt]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ Nat.IsSqrt 1 (sqrt 1)",
"tactic": "simp [IsSqrt]"
},
{
"state_after": "n✝ n : ℕ\nh : ¬n + 2 ≤ 1\n⊢ Nat.IsSqrt (n + 2)... | [
65,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
9
] |
Mathlib/Topology/Separation.lean | not_preirreducible_nontrivial_t2 | [] | [
1454,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1452,
1
] |
Mathlib/Algebra/AddTorsor.lean | Equiv.coe_constVAdd | [] | [
412,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.le_tsub_of_add_le_left | [] | [
212,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.inter_indicator_mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.124894\nι : Type ?u.124897\nM : Type u_2\nN : Type ?u.124903\ninst✝ : MulZeroClass M\ns t : Set α\nf✝ g✝ : α → M\na : α\nt1 t2 : Set α\nf g : α → M\nx : α\n⊢ indicator t1 (indicator t2 fun x => f x * g x) x = indicator t1 f x * indicator t2 g x",
"state_before": "... | [
707,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | expMapCircle_two_pi | [] | [
102,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/Schreier.lean | Subgroup.closure_mul_image_eq_top' | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\nR✝ S✝ : Set G\ninst✝ : DecidableEq G\nR S : Finset G\nhR : ↑R ∈ rightTransversals ↑H\nhR1 : 1 ∈ R\nhS : closure ↑S = ⊤\n⊢ closure ((fun g => { val := g * (↑(toFun hR g))⁻¹, property := (_ : g * (↑(toFun hR g))⁻¹ ∈ H) }) '' (↑R * ↑S)) = ⊤",
"s... | [
103,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_preimage_preimage | [] | [
2127,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2125,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_toSubmodule | [] | [
344,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/GroupTheory/Coset.lean | one_leftCoset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\ns : Set α\n⊢ ∀ (x : α), x ∈ 1 *l s ↔ x ∈ s",
"tactic": "simp [leftCoset]"
}
] | [
152,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_pow_le | [] | [
350,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.differentiableAt | [] | [
99,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderiv.snd | [] | [
321,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sup_eq_union | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPullback.iso_hom_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nh : W ⟶ X\nk : W ⟶ Y\ncomm : h ≫ f = k ≫ g\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g... | [
129,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.isZero_zero | [] | [
206,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.top_apply | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.coforkOfCokernelCofork_π | [] | [
376,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.forall_of_forall_of_flip | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.5128\nR S T : α → α → Prop\na : α\nl : List α\nh₁✝ : ∀ (x : α), x ∈ l → R x x\nh₂✝ : Pairwise R l\nh₃✝ : Pairwise (flip R) l\nh₁ : ∀ (x : α), x ∈ [] → R x x\nh₂ : Pairwise R []\nh₃ : Pairwise (flip R) []\n⊢ ∀ ⦃x : α⦄, x ∈ [] → ∀ ⦃y : α⦄, y ∈ [] → R x y\n\nca... | [
135,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.ne_bot_iff_nonempty | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.28417\nα : Type u_1\nβ : Type ?u.28423\nγ : Type ?u.28426\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nU : Opens α\n⊢ U ≠ ⊥ ↔ Set.Nonempty ↑U",
"tactic": "rw [Ne.def, ← not_nonempty_iff_eq_bot, not_not]"
... | [
275,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos | [] | [
1981,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_le_inf | [] | [
169,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_dirac_eq | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.600866\nγ : Type ?u.600869\nδ : Type ?u.600872\nι : Type ?u.600875\nR : Type ?u.600878\nR' : Type ?u.600881\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝¹ : Measurable... | [
3017,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3015,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isPath_iff_eq_nil | [
{
"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\np : Walk G u u\n⊢ IsPath p ↔ p = nil",
"tactic": "cases p <;> simp [IsPath.nil]"
}
] | [
980,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_mapRange | [] | [
794,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr_refl | [] | [
530,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
9
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_eq_zero | [] | [
1012,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.exists_of_mem_partition | [] | [
241,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.exists_mem_forall_mem_nhds_within_pos | [
{
"state_after": "α : Type u_1\nβ : Type ?u.10003\nR : Type ?u.10006\nR' : Type ?u.10009\nms : Set (OuterMeasure α)\nm✝ : OuterMeasure α\ninst✝¹ : TopologicalSpace α\ninst✝ : SecondCountableTopology α\nm : OuterMeasure α\ns : Set α\nhs : ∀ (x : α), x ∈ s → ∃ t, t ∈ 𝓝[s] x ∧ ↑m t ≤ 0\n⊢ ↑m s = 0",
"state_be... | [
176,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.le_total | [] | [
114,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_apply | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/List/Init/Lemmas.lean | List.forall_mem_cons | [] | [
116,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
113,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.support_divMonomial | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_div_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a / b ≤ c / d ↔ a * d ≤ c * b",
"tactic": "simpa only [div_eq_mul_inv] using mul_inv_le_mul_inv_iff'"
}
] | [
805,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk'_eq_mk' | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectMap_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nX Y Z : C\ninst✝³ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝² : HasKernel f\nX' Y' : C\nf' : X' ⟶ Y'\ninst✝¹ : HasKernel f'\nX'' Y'' : C\nf'' : X'' ⟶ Y''\ninst✝ : HasKernel f''\nsq : Arrow.mk f ⟶ Arrow.mk f'\nsq' : Arrow.mk f' ⟶ Arro... | [
174,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousCore_mono | [] | [
192,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.image_preimage | [] | [
94,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_smul_nnreal | [] | [
1215,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.exists_max_three | [
{
"state_after": "case intro.intro.intro\nF : Type u_3\nE : Type u_2\nK : Type u_1\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Field K\ninst✝¹ : Algebra F E\ninst✝ : Algebra F K\nS : Set E\nc : Set (Lifts F E K)\nx y z : Lifts F E K\nhc : IsChain (fun x x_1 => x ≤ x_1) c\nhx : x ∈ insert ⊥ c\nhy : y ∈ insert ... | [
1022,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.isCompact_closedBall | [] | [
256,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/Regular/Pow.lean | IsRightRegular.pow | [
{
"state_after": "R : Type u_1\na b : R\ninst✝ : Monoid R\nn : ℕ\nrra : IsRightRegular a\n⊢ Function.Injective ((fun x => x * a)^[n])",
"state_before": "R : Type u_1\na b : R\ninst✝ : Monoid R\nn : ℕ\nrra : IsRightRegular a\n⊢ IsRightRegular (a ^ n)",
"tactic": "rw [IsRightRegular, ← mul_right_iterate]"... | [
40,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.aemeasurable | [] | [
366,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
11
] |
Mathlib/Data/List/Basic.lean | List.length_eq_two | [] | [
220,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_a_eq_zero' | [] | [
318,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.isCompact_candidatesB | [
{
"state_after": "case refine'_1\nX : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : GromovHausdorff.ProdSpaceFun X Y\nx y z t : X ⊕ Y\n⊢ ∀ (f : (X ⊕ Y) × (X ⊕ Y) →ᵇ ℝ) (x : (X ⊕ Y) × (X ⊕ Y)),\n ... | [
282,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.ι_comp_sigmaComparison | [] | [
270,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.self_trans_symm | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nβ : Sort v\nγ : Sort w\ne : α ≃ β\n⊢ ∀ (x : α), ↑(e.trans e.symm) x = ↑(Equiv.refl α) x",
"tactic": "simp"
}
] | [
353,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.zero_sub | [
{
"state_after": "α : Type ?u.131620\nβ : Type ?u.131623\nγ : Type ?u.131626\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ 0 - a ≤ 0",
"state_before": "α : Type ?u.131620\nβ : Type ?u.131623\nγ : Type ?u.131626\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ 0 -... | [
591,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_left_on_Ioo | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhdf✝ : DifferentiableOn ℝ f (Ioo a b)\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → deriv g x ≠ 0\nhfb : Tendsto f (𝓝[Iio b] b) (𝓝 0)\nhgb : Tendsto g (𝓝[Iio b] b) (𝓝 0)\nhdiv : Tendsto (fun x => deriv f x / deriv g x) (𝓝[Iio b] b) l\nhdf : ∀ (x : ... | [
245,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.equiv_of_eq | [
{
"state_after": "x : PGame\n⊢ x ≈ x",
"state_before": "x y : PGame\nh : x = y\n⊢ x ≈ y",
"tactic": "subst h"
},
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ x ≈ x",
"tactic": "rfl"
}
] | [
775,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.dotProduct_adjMatrix | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.37315\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype V\ninst✝ : NonAssocSemiring α\nv : V\nvec : V → α\n⊢ vec ⬝ᵥ adjMatrix α G v = ∑ u in neighborFinset G v, vec u",
"tactic": "simp [neighborFinset_e... | [
210,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_and_natDegree_eq_and_monic | [
{
"state_after": "case inl\nR : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\nhlifts : p ∈ lifts f\nhp : Monic p\nhR : Subsingleton S\n⊢ ∃ q, map f q = p ∧ natDegree q = natDegree p ∧ Monic q\n\ncase inr\nR : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : ... | [
242,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_tensor_id_comp_evaluation | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX Y : C\ninst✝ : HasRightDual X\nf : Y ⟶ Xᘁ\n⊢ (ρ_ Y).inv ≫ (𝟙 Y ⊗ η_ X Xᘁ) ≫ (α_ Y X Xᘁ).inv ≫ ((f ⊗ 𝟙 X) ≫ ε_ X Xᘁ ⊗ 𝟙 Xᘁ) = f ≫ (λ_ Xᘁ).inv",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\... | [
541,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_cons | [
{
"state_after": "case inl\nα : Type ?u.367165\nβ : Type ?u.367168\nγ : Type ?u.367171\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\na : α\ns : Finset α\nha : ¬a ∈ s\nh✝ : p a\n⊢ _root_.Disjoint {a} (filter p s)\n\ncase inr\nα : Type ?u.367165\nβ : Type ?u.367168\nγ : Type ?u.367171\np q :... | [
2807,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2797,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_two_add_invOf_two | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : NonAssocSemiring α\ninst✝ : Invertible 2\n⊢ ⅟2 + ⅟2 = 1",
"tactic": "rw [← two_mul, mul_invOf_self]"
}
] | [
270,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.tr_supports | [
{
"state_after": "K : Type u_2\ninst✝² : DecidableEq K\nΓ : K → Type u_3\nΛ : Type u_1\ninst✝¹ : Inhabited Λ\nσ : Type u_4\ninst✝ : Inhabited σ\nM : Λ → Stmt₂\nS : Finset Λ\nss : TM2.Supports M S\nl' : Λ'\nh : l' ∈ trSupp M S\n⊢ ∀ (q : Stmt₂),\n TM2.SupportsStmt S q →\n (∀ (x : Λ'), x ∈ trStmts₁ q → x ∈... | [
2817,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2772,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.