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/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.tensor_eq_tensor | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type u_2\nγ : Type u_3\nf✝ : α ↪ β\ns : Finset α\nβ' : Type u_1\nf : β ↪ γ\ng : α ↪ β\nf' : α ↪ β'\ng' : β' ↪ γ\nh_comm : ∀ (a : α), ↑f (↑g a) = ↑g' (↑f' a)\n⊢ map f (map g s) = map g' (map f' s)",
"tactic": "simp_rw [map_map, Embedding.tra... | [
143,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.separating_iff_T1 | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.228889\n𝕝 : Type ?u.228892\n𝕝₂ : Type ?u.228895\nE : Type u_2\nF : Type ?u.228901\nG : Type ?u.228904\nι : Type u_3\nι' : Type ?u.228910\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ : TopologicalSpace E\np : ... | [
370,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.submatrix_updateRow_succAbove | [] | [
393,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_and | [] | [
772,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_ncard_of_injOn | [
{
"state_after": "case inl\nα : Type u_2\nβ : Type u_1\ns t✝ : Set α\na b x y : α\nf✝ : α → β\nt : Set β\nf : α → β\nhf : ∀ (a : α), a ∈ s → f a ∈ t\nf_inj : InjOn f s\nht : autoParam (Set.Finite t) _auto✝\nh : Set.Finite s\n⊢ ncard s ≤ ncard t\n\ncase inr\nα : Type u_2\nβ : Type u_1\ns t✝ : Set α\na b x y : α\... | [
393,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Topology/Instances/RatLemmas.lean | Rat.not_secondCountableTopology_opc | [
{
"state_after": "p q : ℚ\ns t : Set ℚ\na✝ : SecondCountableTopology ℚ∞\n⊢ False",
"state_before": "p q : ℚ\ns t : Set ℚ\n⊢ ¬SecondCountableTopology ℚ∞",
"tactic": "intro"
},
{
"state_after": "no goals",
"state_before": "p q : ℚ\ns t : Set ℚ\na✝ : SecondCountableTopology ℚ∞\n⊢ False",
"t... | [
82,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.sup_eq_map₂ | [] | [
570,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_add | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Even (m + n) ↔ (Even m ↔ Even n)",
"tactic": "cases' emod_two_eq_zero_or_one m with h₁ h₁ <;>\ncases' emod_two_eq_zero_or_one n with h₂ h₂ <;>\nsimp [even_iff, h₁, h₂, Int.add_emod]"
}
] | [
108,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.symm_eq_on_of_inter_eq_of_eqOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.30876\nδ : Type ?u.30879\ne : LocalEquiv α β\ne'✝ : LocalEquiv β γ\ns : Set α\nt : Set β\nx : α\ny : β\ne' : LocalEquiv α β\nh : IsImage e s t\nhs : e.source ∩ s = e'.source ∩ s\nheq : EqOn (↑e) (↑e') (e.source ∩ s)\n⊢ EqOn (↑(LocalEquiv.symm e)) (↑(Loca... | [
472,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofNat_im | [] | [
649,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingEquiv.coe_prod_comm_symm | [] | [
291,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_three_mul | [
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ sin (3 * x) = 3 * sin x - 4 * sin x ^ 3",
"state_before": "x y : ℂ\n⊢ sin (3 * x) = 3 * sin x - 4 * sin x ^ 3",
"tactic": "have h1 : x + 2 * x = 3 * x := by ring"
},
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ sin x * cos (2 * x) + co... | [
1077,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.All.map | [] | [
494,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
491,
11
] |
Mathlib/CategoryTheory/Sites/InducedTopology.lean | CategoryTheory.LocallyCoverDense.inducedTopology_coverLifting | [] | [
105,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toIsometryEquiv_injective | [] | [
638,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_eq_sup | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.eraseNone_eq_biUnion | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.8977\ninst✝ : DecidableEq α\ns : Finset (Option α)\na✝ : α\n⊢ a✝ ∈ ↑eraseNone s ↔ a✝ ∈ Finset.biUnion s Option.toFinset",
"state_before": "α : Type u_1\nβ : Type ?u.8977\ninst✝ : DecidableEq α\ns : Finset (Option α)\n⊢ ↑eraseNone s = Finset.biUnion s Optio... | [
100,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.induction_on | [
{
"state_after": "case refine_1\nα : Type u_1\nC : Cycle α → Prop\ns : Cycle α\nH0 : C nil\nHI : ∀ (a : α) (l : List α), C ↑l → C ↑(a :: l)\nl : List α\n⊢ C nil\n\ncase refine_2\nα : Type u_1\nC : Cycle α → Prop\ns : Cycle α\nH0 : C nil\nHI : ∀ (a : α) (l : List α), C ↑l → C ↑(a :: l)\nl : List α\n⊢ ∀ (head : α... | [
519,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsUnit.isSMulRegular | [
{
"state_after": "case intro\nR : Type u_1\nS : Type ?u.36377\nM : Type u_2\nb : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\na : Rˣ\n⊢ IsSMulRegular M ↑a",
"state_before": "R : Type u_1\nS : Type ?u.36377\nM : Type u_2\na b : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\nua : IsUnit a\n⊢ IsSMu... | [
258,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_cancel' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_3\nM' : Type u_2\nM'' : Type ?u.834666\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] ... | [
957,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Std/WF.lean | Acc.ndrecOn_eq_ndrecOnC | [
{
"state_after": "case h.h.h.h.h.h\nα : Sort u_1\nr : α → α → Prop\nmotive : α → Sort u_2\nintro : α\na : Acc r intro\nt : (x : α) → (∀ (y : α), r y x → Acc r y) → ((y : α) → r y x → motive y) → motive x\n⊢ ndrecOn a t = Acc.ndrecOnC a t",
"state_before": "⊢ @ndrecOn = @Acc.ndrecOnC",
"tactic": "funext ... | [
87,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
85,
18
] |
Mathlib/Algebra/GroupPower/Basic.lean | one_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na b : α\nn : ℕ\n⊢ 1 ^ ↑n = 1",
"tactic": "rw [zpow_ofNat, one_pow]"
},
{
"state_after": "no goals",
"state_b... | [
328,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.dual_def | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | isComplete_iff_ultrafilter | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\nH : ∀ (l : Ultrafilter α), Cauchy ↑l → ↑l ≤ 𝓟 s → ∃ x, x ∈ s ∧ ↑l ≤ 𝓝 x\nl : Filter α\nhl : Cauchy l\nhls : l ≤ 𝓟 s\n⊢ ∃ x, x ∈ s ∧ ClusterPt x l",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\n⊢ Is... | [
330,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictAntiOn_univ | [] | [
408,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
9
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.induction_on_adjoin_fg | [
{
"state_after": "case intro\nF : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nP : IntermediateField F E → Prop\nbase : P ⊥\nih : ∀ (K : IntermediateField F E) (x : E), P K → P (restrictScalars F { x // x ∈ K }⟮x⟯)\nS : Finset E\n⊢ P (adjoin F ↑S)",
"state_before": "F : T... | [
958,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.coe_smul | [] | [
272,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Tactic/Group.lean | Mathlib.Tactic.Group.zpow_trick_one' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na b : G\nn : ℤ\n⊢ a * b ^ n * b = a * b ^ (n + 1)",
"tactic": "rw [mul_assoc, mul_zpow_self]"
}
] | [
53,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLenAux_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ powersetLenAux 0 l = [0]",
"tactic": "simp [powersetLenAux_eq_map_coe]"
}
] | [
196,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.noZeroSMulDivisors_iff_torsion_eq_bot | [
{
"state_after": "case mp\nR : Type u_1\nM : Type u_2\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : NoZeroDivisors R\ninst✝ : Nontrivial R\nh : NoZeroSMulDivisors R M\n⊢ torsion R M = ⊥\n\ncase mpr\nR : Type u_1\nM : Type u_2\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M... | [
722,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.succ_le_succ_sqrt' | [] | [
195,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/NormedSpace/Int.lean | Int.toNat_add_toNat_neg_eq_nnnorm | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ ↑(toNat n) + ↑(toNat (-n)) = ‖n‖₊",
"tactic": "rw [← Nat.cast_add, toNat_add_toNat_neg_eq_natAbs, NNReal.coe_natAbs]"
}
] | [
45,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.int_cast_apply | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/GroupTheory/Torsion.lean | IsTorsion.of_surjective | [
{
"state_after": "case intro\nG : Type u_1\nH : Type u_2\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : Group H\nf : G →* H\nhf : Function.Surjective ↑f\ntG : IsTorsion G\nh : H\ng : G\nhg : ↑f g = h\n⊢ IsOfFinOrder h",
"state_before": "G : Type u_1\nH : Type u_2\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : Group... | [
104,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_iff_lt_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a / c < b ↔ a < b * c",
"tactic": "rw [← mul_lt_mul_iff_right c, div_eq_mul_inv, inv_mul_cancel_right]"
}
] | [
924,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.one_associator | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM N P : Mon_ C\n⊢ ((λ_ (𝟙_ C)).inv ≫ (M.one ⊗ N.one) ⊗ P.one) ≫ (α_ M.X N.X P.X).hom = M.one ⊗ (λ_ (𝟙_ C)).inv ≫ (N.one ⊗ P.one)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM N P : Mon_ C\n... | [
393,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_ofSet | [] | [
758,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_sub_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.600971\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y z : F\n⊢ inner (x - y) z = inner x z - inner y z",
"tactic": "simp [sub_eq_add_neg, inner_add_left, inner_neg_left]"
}
] | [
293,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.finite_of_condCount_ne_zero | [
{
"state_after": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\ns t : Set Ω\nh : ↑↑(condCount s) t ≠ 0\nhs' : ¬Set.Finite s\n⊢ False",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\ns t : Set Ω\nh : ↑↑(condCount s) t ≠ 0\n⊢ Set.Finite s",
"tactic": "by_contra hs'"
},
{
"state_after": "no g... | [
69,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheafFor_subsieve | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nP✝ Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS✝ : Sieve X\nR✝ : Presieve X\nJ J₂ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ Type w\nS : Sieve X\nR : Presieve X\nh : S.arrows ≤ R\ntrans : ∀ ⦃Y : C⦄ (f : Y ⟶ X), IsSheafFor P (Sieve.pullback f S).arrow... | [
722,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.exists_fixedPoint' | [
{
"state_after": "α : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\ns : Set α\nhsc : IsComplete s\nhsf : MapsTo f s s\nhf : ContractingWith K (MapsTo.restrict f s s hsf)\nx : α\nhxs : x ∈ s\nhx : edist x (f x) ≠ ⊤\nthis : CompleteSpace ↑s\n⊢ ∃ y,\n y ∈ s ∧\n IsFixedPt f y ∧... | [
181,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.top_coeSubmodule | [] | [
393,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_sphere_iff_norm' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.102643\n𝕜 : Type ?u.102646\nα : Type ?u.102649\nι : Type ?u.102652\nκ : Type ?u.102655\nE : Type u_1\nF : Type ?u.102661\nG : Type ?u.102664\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁... | [
697,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Algebra/Order/Monoid/ToMulBot.lean | WithZero.toMulBot_coe | [] | [
43,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_compl_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.156422\nα : Type u_1\nβ : Type ?u.156428\ninst✝ : HeytingAlgebra α\na✝ b✝ c a b : α\n⊢ a ⇨ bᶜ = b ⇨ aᶜ",
"tactic": "simp_rw [← himp_bot, himp_left_comm]"
}
] | [
816,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.neg_sub' | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b : X ⟶ Y\n⊢ 0 - (a - b) = 0 - a + b",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b : X ⟶ Y\n⊢ -(a - b) = -a + b",
"tactic": "rw [neg_def, neg_def]"
},
{
... | [
412,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Std/Logic.lean | and_iff_right | [] | [
206,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
206,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.42847\nδ : Type ?u.42850\nι : Sort ?u.42853\ns : Set α\nt : Set β\nf✝ : Filter α\ng : Filter β\nf : Filter α\ng₁ g₂ : Filter β\n⊢ f ×ˢ (g₁ ⊓ g₂) = f ×ˢ g₁ ⊓ f ×ˢ g₂",
"tactic": "rw [prod_inf_prod, inf_idem]"
}
] | [
397,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_eq_zero_iff | [
{
"state_after": "r : ℝ\nh : sign r = 0\n⊢ r = 0",
"state_before": "r : ℝ\n⊢ sign r = 0 ↔ r = 0",
"tactic": "refine' ⟨fun h => _, fun h => h.symm ▸ sign_zero⟩"
},
{
"state_after": "case inl\nr : ℝ\nh : sign r = 0\nhn : r < 0\n⊢ r = 0\n\ncase inr.inl\nh : sign 0 = 0\n⊢ 0 = 0\n\ncase inr.inr\nr : ... | [
74,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.dist_lt_add_of_nonempty_closedBall_inter_ball | [] | [
635,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/RingTheory/Nilpotent.lean | zero_isRadical_iff | [
{
"state_after": "R S : Type u\nx y : R\ninst✝ : MonoidWithZero R\n⊢ IsRadical 0 ↔ ∀ (x : R) (x_1 : ℕ), 0 ∣ x ^ x_1 → 0 ∣ x",
"state_before": "R S : Type u\nx y : R\ninst✝ : MonoidWithZero R\n⊢ IsRadical 0 ↔ IsReduced R",
"tactic": "simp_rw [isReduced_iff, IsNilpotent, exists_imp, ← zero_dvd_iff]"
},
... | [
118,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_sup | [] | [
498,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.isMaximal_iff_isCoatom | [] | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.dvdNotUnit_iff_lt | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.770953\nA : Type u_1\nK : Type ?u.770959\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : IsDedekindDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nI J : Ideal A\nx✝ : DvdNotUnit I J\nhI : I ≠ 0\n... | [
668,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Init/Logic.lean | or_false_iff | [] | [
185,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.unit_transferNatTrans | [
{
"state_after": "C : Type u₁\nD : Type u₂\ninst✝³ : Category C\ninst✝² : Category D\nE : Type u₃\nF : Type u₄\ninst✝¹ : Category E\ninst✝ : Category F\nG : C ⥤ E\nH : D ⥤ F\nL₁ : C ⥤ D\nR₁ : D ⥤ C\nL₂ : E ⥤ F\nR₂ : F ⥤ E\nadj₁ : L₁ ⊣ R₁\nadj₂ : L₂ ⊣ R₂\nf : G ⋙ L₂ ⟶ L₁ ⋙ H\nX : C\n⊢ G.map (adj₁.unit.app X) ≫\n... | [
132,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Finsupp/BigOperators.lean | List.support_sum_eq | [
{
"state_after": "case nil\nι : Type u_2\nM : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : AddMonoid M\nl : List (ι →₀ M)\nhl✝ : Pairwise (_root_.Disjoint on Finsupp.support) l\nhl : Pairwise (_root_.Disjoint on Finsupp.support) []\n⊢ (sum []).support = foldr ((fun x x_1 => x ⊔ x_1) ∘ Finsupp.support) ∅ []\n\ncase... | [
98,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_fst | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inv_mem_inv | [] | [
217,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/Charpoly/ToMatrix.lean | LinearMap.charpoly_toMatrix | [
{
"state_after": "R : Type u\nM : Type v\ninst✝⁶ : CommRing R\ninst✝⁵ : Nontrivial R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Module.Free R M\ninst✝¹ : Module.Finite R M\nf : M →ₗ[R] M\nι : Type w\ninst✝ : Fintype ι\nb : Basis ι R M\nA : (fun x => Matrix ι ι R) f := ↑(toMatrix b b) f\n⊢ Matrix.ch... | [
82,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofEq_symm | [] | [
2037,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2036,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_eq_sup_coe | [] | [
1157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_lintegral_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.947084\nγ : Type ?u.947087\nδ : Type ?u.947090\nm : MeasurableSpace α\nμ ν✝ : Measure α\nβ : Type u_1\ninst✝ : MeasurableSpace β\nν : Measure β\nf : α → ℝ≥0∞\ng : β → ℝ≥0∞\nhf : AEMeasurable f\nhg : AEMeasurable g\n⊢ (∫⁻ (x : α), ∫⁻ (y... | [
754,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.triangle | [] | [
1167,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_of_isLUB_of_nonneg | [] | [
241,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.filter_inf | [] | [
277,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_mul_right_iff' | [] | [
1563,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
1
] |
Mathlib/Analysis/Calculus/Deriv/Prod.lean | deriv_pi | [] | [
117,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_tendsto_of_tendsto_of_monotone | [
{
"state_after": "α : Type u_1\nβ : Type ?u.483223\nγ : Type ?u.483226\nδ : Type ?u.483229\nm : MeasurableSpace α\nμ ν : Measure α\nf : ℕ → α → ℝ≥0∞\nF : α → ℝ≥0∞\nhf : ∀ (n : ℕ), AEMeasurable (f n)\nh_mono : ∀ᵐ (x : α) ∂μ, Monotone fun n => f n x\nh_tendsto : ∀ᵐ (x : α) ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (... | [
464,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Wbtw.angle₃₁₂_eq_zero_of_ne | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : p₂ ≠ p₁\n⊢ ∠ p₃ p₁ p₂ = 0",
"tactic": "rw [← h.angle₂₁₃_eq_zero_of_ne h... | [
350,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.Lp_add_le | [
{
"state_after": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nthis :\n ↑((∑ i in s,\n ((fun i => { val := abs (f i), property := (_ : 0 ≤ abs (f i)) }) i +\n (fun i => { val := abs (g i), property := (_ : 0 ≤ abs (g i)) }) i) ^\n p) ^\n (1 / p)) ≤\n ↑(... | [
590,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.widePullback_ext | [
{
"state_after": "case a\nC : Type u\ninst✝⁵ : Category C\ninst✝⁴ : ConcreteCategory C\nJ : Type w\ninst✝³ : SmallCategory J\nF : J ⥤ C\ninst✝² : PreservesLimit F (forget C)\nB : C\nι : Type w\nX : ι → C\nf : (j : ι) → X j ⟶ B\ninst✝¹ : HasWidePullback B X f\ninst✝ : PreservesLimit (wideCospan B X f) (forget C)... | [
76,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.disjoint_right_iff | [] | [
535,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.vadd_closedBall | [] | [
780,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Data/Fintype/Order.lean | Fintype.exists_le | [] | [
204,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_nat_one_mod_four | [
{
"state_after": "n : ℕ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1",
"state_before": "n : ℕ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑n = 1",
"tactic": "rw [χ₄_nat_mod_four, hn]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1",
"tactic": "rfl"
}
] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/NormedSpace/Extr.lean | IsLocalMaxOn.norm_add_self | [] | [
85,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_dist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.23278\nι : Type ?u.23281\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ nndist x y = Real.toNNReal (dist x y)",
"tactic": "rw [dist_nndist, Real.toNNReal_coe]"
}
] | [
382,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_sup | [] | [
893,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
11
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | CategoryTheory.Functor.mapPresheaf_obj_presheaf | [] | [
550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.nhds_basis_ball_pow | [] | [
996,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_apply_div_ne_zero | [
{
"state_after": "K : Type u\ninst✝⁴ : CommRing K\ninst✝³ : IsDomain K\nR : Type u_1\nF : Type u_2\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : MonoidHomClass F K[X] R[X]\nφ : F\nhφ : K[X]⁰ ≤ Submonoid.comap φ R[X]⁰\np q : K[X]\nhq : q ≠ 0\nhq' : ↑φ q ≠ 0\n⊢ ↑(map φ hφ) (↑(algebraMap K[X] (RatFunc K)) p /... | [
863,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.hasSum_lintegral_measure | [] | [
627,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofAdd_toAdd | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subset_right_of_subset_union | [] | [
442,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.lt_rpow_one_div_iff | [
{
"state_after": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ 1 < y ^ (1 / z) ↔ x ^ z < y",
"state_before": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x < y ^ (1 / z) ↔ x ^ z < y",
"tactic": "nth_rw 1 [← rpow_one x]"
},
{
"state_after": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ (z * z⁻¹) < y ^ (1 / z) ↔ x ^ z < y",... | [
590,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nE : Type u_3\nF : Type u_4\nG : Type ?u.70658\nE' : Type ?u.70661\nF' : Type ?u.70664\nG' : Type ?u.70667\nE'' : Type ?u.70670\nF'' : Type ?u.70673\nG'' : Type ?u.70676\nR : Type ?u.70679\nR' : Type ?u.70682\n𝕜 : Type ?u.70685\n𝕜' :... | [
439,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.ucs_eq_self_of_normalizer_eq_self | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk : ℕ\nN N₁ N₂ : LieSubmodule R L M\nh : normalizer N₁ = N₁\n⊢ ucs Nat.zero N₁ = N... | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mem_toSubalgebra | [] | [
114,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castLT_castSucc | [
{
"state_after": "case mk\nn✝ m n val✝ : ℕ\nisLt✝ : val✝ < n\nh : ↑{ val := val✝, isLt := isLt✝ } < n\n⊢ castLT (↑castSucc { val := val✝, isLt := isLt✝ }) h = { val := val✝, isLt := isLt✝ }",
"state_before": "n✝ m n : ℕ\na : Fin n\nh : ↑a < n\n⊢ castLT (↑castSucc a) h = a",
"tactic": "cases a"
},
{
... | [
1254,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/Order/Filter/Extr.lean | isExtrOn_dual_iff | [] | [
242,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_inter_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.190523\nγ : Type ?u.190526\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na✝ b a : α\ns t : Multiset α\n⊢ a ::ₘ s ∩ t = (a ::ₘ s) ∩ (a ::ₘ t)",
"tactic": "simp"
}
] | [
1880,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1879,
1
] |
Mathlib/Topology/Homotopy/Contractible.lean | Homeomorph.contractibleSpace_iff | [] | [
107,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
11
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.isSplitEpi_of_epi | [] | [
248,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_zero | [] | [
149,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | NNReal.nndist_zero_eq_val | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.239049\nι : Type ?u.239052\ninst✝ : PseudoMetricSpace α\nz : ℝ≥0\n⊢ nndist 0 z = z",
"tactic": "simp only [NNReal.nndist_eq, max_eq_right, tsub_zero, zero_tsub, zero_le']"
}
] | [
1693,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1692,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.den_zero | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheafFor_iff_yonedaSheafCondition | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP✝ Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ Type v₁\n⊢ (∀ (x : FamilyOfElements P S.arrows), FamilyOfElements.Compatible x → ∃! t, FamilyOfElements.IsAmalgamation x t) ↔\n ∀ (f : functor S ⟶ P), ∃! g,... | [
529,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_surjective | [
{
"state_after": "α : Type u_1\nM : Type u_2\nN : Type ?u.325806\nP : Type ?u.325809\nR : Type u_3\nS : Type ?u.325815\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R P\nα' : T... | [
592,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.