file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Multiset/Basic.lean | Multiset.zero_subset | [] | [
408,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Group/Defs.lean | zpow_eq_pow | [] | [
915,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
45
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhds_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.30563\nβ : Type ?u.30566\nγ : Type ?u.30569\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\n⊢ (⨅ (l : ℝ≥0∞) (_ : l < ⊤), 𝓟 (Ioi l)) = ⨅ (a : ℝ≥0∞) (_ : a ≠ ⊤), 𝓟 (Ioi a)",
"tactic": "simp [lt_top_iff_ne_top, Ioi]"
}
] | [
152,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensity | [
{
"state_after": "α : Type ?u.451381\nβ : Type ?u.451384\nm : MeasurableSpace α\nμ ν : Measure α\ns t : SignedMeasure α\nf : α → ℝ\nhf : Measurable f\nhfi : Integrable f\nhtμ : t ⟂ᵥ toENNRealVectorMeasure μ\nhadd : s = t + withDensityᵥ μ f\nthis : IsFiniteMeasure (withDensity μ fun x => ENNReal.ofReal (f x))\n⊢... | [
997,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_left | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nH : 0 < n\n⊢ m * n / n = m",
"tactic": "rw [Nat.mul_comm, mul_div_right _ H]"
}
] | [
574,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
573,
9
] |
Mathlib/GroupTheory/GroupAction/Support.lean | MulAction.supports_of_mem | [] | [
42,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.symm | [] | [
1144,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Algebra/Group/Basic.lean | leftInverse_mul_right_inv_mul | [] | [
868,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_sigma | [] | [
1545,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_ne_zero | [] | [
481,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_eq_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp a b = toIcoDiv hp 0 (b - a)",
"tactic": "rw [toIcoDiv_sub_eq_toIcoDiv_add, zero_add]"
}
] | [
769,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.iIsOrtho.not_isOrtho_basis_self_of_nondegenerate | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : Module R M\nR₁ : Type ?u.1495046\nM₁ : Type ?u.1495049\ninst✝¹⁴ : Ring R₁\ninst✝¹³ : AddCommGroup M₁\ninst✝¹² : Module R₁ M₁\nR₂ : Type ?u.1495658\nM₂ : Type ?u.1495661\ninst✝¹¹ : CommSemiring R₂\ninst✝¹⁰ : ... | [
1358,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.coePNat_injective | [] | [
117,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.le_iff' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.540108\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid M\ninst✝ : PartialOrder M\nu v w : VectorMeasure α M\nh : v ≤ w\ni : Set α\n⊢ ↑v i ≤ ↑w i",
"state_before": "α : Type u_1\nβ : Type ?u.540108\nm : MeasurableSpace α\nM... | [
855,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.finite_int_prime_iff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\n⊢ multiplicity.Finite (↑p) a ↔ a ≠ 0",
"tactic": "simp [finite_int_iff, hp.1.ne_one]"
}
] | [
261,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_pos_of_ne_zero_left | [] | [
312,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_union_mem_segment | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.222922\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : Measure α\ns✝ : Set E\nf : α → E\ns t : Set... | [
184,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.Set.Sized.upShadow | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\nh𝒜 : Set.Sized r ↑𝒜\nA : Finset α\nh : A ∈ ↑((∂⁺ ) 𝒜)\n⊢ card A = r + 1",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns ... | [
221,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
11
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.Types.pushforwardFamily_apply | [
{
"state_after": "C : Type u_4\ninst✝⁴ : Category C\nD : Type u_2\ninst✝³ : Category D\nE : Type ?u.57720\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.57772\ninst✝¹ : Category A\nG : C ⥤ D\nH : CoverDense K G\ninst✝ : Full G\nℱ : Dᵒᵖ ⥤ Typ... | [
222,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_apply_eq_of_inter_support_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.85531\nγ : Type ?u.85534\ninst✝ : MeasurableSpace α\np : Pmf α\ns✝ t✝ s t : Set α\nhs : MeasurableSet s\nht : MeasurableSet t\nh : s ∩ support p = t ∩ support p\n⊢ ↑↑(toMeasure p) s = ↑↑(toMeasure p) t",
"tactic": "simpa only [p.toM... | [
292,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Topology/Sequences.lean | seqClosure_eq_closure | [] | [
129,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | AEMeasurable.aestronglyMeasurable | [] | [
1441,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.representable_of_nat_iso | [] | [
281,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.mk_mul_mk | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.13310\nδ : Type ?u.13313\na : α\ns t : Multiset α\nf g : α → Multiset β\n⊢ (bind s fun a => f a + g a) = bind s f + bind s g",
"tactic": "simp [bind, join]"
}
] | [
127,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Control/Basic.lean | joinM_map_pure | [] | [
171,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Std/Data/List/Lemmas.lean | List.get_append_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl₁ l₂ : List α\nn : Nat\nh₁ : length l₁ ≤ n\nh₂ : n < length (l₁ ++ l₂)\n⊢ some (get (l₁ ++ l₂) { val := n, isLt := h₂ }) =\n some (get l₂ { val := n - length l₁, isLt := (_ : n - length l₁ < length l₂) })",
"tactic": "rw [← get?_eq_get, ← g... | [
607,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
605,
1
] |
Mathlib/Topology/Partial.lean | continuousWithinAt_iff_ptendsto_res | [] | [
91,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Tactic/Linarith/Lemmas.lean | Linarith.mul_nonpos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedRing α\na b : α\nha : a ≤ 0\nhb : 0 < b\nthis : -b * a ≥ 0\n⊢ b * a ≤ 0",
"tactic": "simpa"
}
] | [
48,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.lift_unique | [] | [
256,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_pi' | [] | [
1214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.exists_isMinOn' | [
{
"state_after": "case intro.intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.39941\ninst✝⁴ : ConditionallyCompleteLinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Set β\nf : β → α\nhf : ContinuousOn f s\nhsc : IsClosed s\nx₀ : β\nh... | [
278,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_def | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_bot | [] | [
718,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_tower_bot_of_isIntegral | [
{
"state_after": "case intro.intro\nR : Type u_3\nA : Type u_1\nB : Type u_2\nS : Type ?u.1449203\nT : Type ?u.1449206\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : CommRing S\ninst✝⁴ : CommRing T\ninst✝³ : Algebra A B\ninst✝² : Algebra R B\nf : R →+* S\ng : S →+* T\ninst✝¹ : Algebra ... | [
1045,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_le | [] | [
579,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.leftDistributor_assoc | [
{
"state_after": "case w.w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nf : J → C\nj✝ : J\n⊢ ((asIso (𝟙 X) ⊗ leftDistributor Y f) ≪≫ leftDistributor X fun j => Y ⊗ f... | [
177,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sinh (x - y) = sinh x * cosh y - cosh x * sinh y",
"tactic": "simp [sub_eq_add_neg, sinh_add, sinh_neg, cosh_neg]"
}
] | [
637,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_injective | [] | [
349,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_hnot_le | [] | [
70,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.eq_nil_of_length_zero | [
{
"state_after": "case nil\nU : Type u_1\ninst✝ : Quiver U\nu : U\nhzero : length nil = 0\n⊢ Path.cast (_ : u = u) (_ : u = u) nil = nil",
"state_before": "U : Type u_1\ninst✝ : Quiver U\nu v : U\np : Path u v\nhzero : length p = 0\n⊢ Path.cast (_ : u = v) (_ : v = v) p = nil",
"tactic": "cases p <;> si... | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_mk | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.inf_left | [] | [
383,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_num_denom | [] | [
1685,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1684,
1
] |
Mathlib/Order/Cover.lean | apply_covby_apply_iff | [] | [
360,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.mem_upperBounds_image_self | [] | [
1217,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_iInf_le | [] | [
234,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Logic/Basic.lean | bex_of_exists | [] | [
1069,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_le' | [] | [
1043,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_div_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.144887\nα : Type u_1\nβ : Type ?u.144893\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhc : c < 0\n⊢ a ≤ b / c ↔ b ≤ a * c",
"tactic": "rw [← neg_neg c, mul_neg, div_neg, le_neg, div_le_iff (neg_pos.2 hc), neg_mul]"
}
] | [
729,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.piecewise_compl | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.22254\nγ : Type ?u.22257\ninst✝³ : Fintype α\ns✝ t : Finset α\ninst✝² : DecidableEq α\ns : Finset α\ninst✝¹ : (i : α) → Decidable (i ∈ s)\ninst✝ : (i : α) → Decidable (i ∈ sᶜ)\nδ : α → Sort u_2\nf g : (i : α) → δ i\ni : α\n⊢ piecewise (sᶜ) f g i = piecewise s ... | [
293,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Set/Prod.lean | Set.union_prod | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.11513\nδ : Type ?u.11516\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx : α\ny : β\n⊢ (x, y) ∈ (s₁ ∪ s₂) ×ˢ t ↔ (x, y) ∈ s₁ ×ˢ t ∪ s₂ ×ˢ t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.11513\nδ : Type ?u.11516\ns s₁ s₂ : S... | [
152,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.smul_bot | [] | [
82,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.neg_mem | [] | [
517,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
11
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.degree_le_mul_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np✝ q p : R[X]\nhq : q ≠ 0\nhp : p = 0\n⊢ degree p ≤ degree (p * q)",
"tactic": "simp only [hp, MulZeroClass.zero_mul, le_refl]"
},
{
"state_after": "R ... | [
166,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_union | [
{
"state_after": "α : Type u_1\nβ : Type ?u.13810\nγ : Type ?u.13813\nδ : Type ?u.13816\ninst✝ : TopologicalSpace α\na : α\ns t : Set α\n⊢ 𝓝 a ⊓ 𝓟 (s ∪ t) = 𝓝 a ⊓ 𝓟 s ⊔ 𝓝 a ⊓ 𝓟 t",
"state_before": "α : Type u_1\nβ : Type ?u.13810\nγ : Type ?u.13813\nδ : Type ?u.13816\ninst✝ : TopologicalSpace α\na : α... | [
242,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.inr_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.54489\nM₆ : Type ?u.54492\nS : Type ?u.54495\ninst✝¹³ : Semiring R\ninst✝¹² : Semiring S\ninst✝¹¹ : AddCommMonoid M\nins... | [
209,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.toStructuredArrow_obj | [] | [
148,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.prod_map_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommSemiring α\ns : Multiset (Multiset α)\n⊢ prod (map sum 0) = sum (map prod (Sections 0))",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommSemiring α\ns✝ : Multiset (Multiset α)... | [
76,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.optionCongr_refl | [] | [
48,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.exists_unit_of_abs | [
{
"state_after": "case inl\na : ℤ\nh : a = ↑(natAbs a)\n⊢ ∃ u x, ↑(natAbs a) = u * a\n\ncase inr\na : ℤ\nh : a = -↑(natAbs a)\n⊢ ∃ u x, ↑(natAbs a) = u * a",
"state_before": "a : ℤ\n⊢ ∃ u x, ↑(natAbs a) = u * a",
"tactic": "cases' natAbs_eq a with h h"
},
{
"state_after": "case inl\na : ℤ\nh : a... | [
182,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop | [] | [
155,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.pure_le | [] | [
205,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean | CategoryTheory.L_faithful_of_unit_isIso | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : IsIso h.unit\nX Y : C\nf g : X ⟶ Y\nH : ↑(Adjunction.homEquiv h X (L.obj Y)) (L.map f) = ↑(Adjunction.homEquiv h X (L.obj Y)) (L.map g)\n⊢ f = g",
"state_before": "C : Type u₁\ninst... | [
132,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_add_left | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1343910\nG : Type ?u.1343913\n𝕜 : Type ?u.1343916\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ... | [
1323,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
Mathlib/Order/Bounds/Basic.lean | image2_lowerBounds_lowerBounds_subset_lowerBounds_image2 | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Antitone (f a)\na : α\nb : β\nha : a ∈ upperBoun... | [
1476,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel.desc_zero | [
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasCokernel f\nW : C\nh : f ≫ 0 = 0\n⊢ coequalizer.π f 0 ≫ desc f 0 h = coequalizer.π f 0 ≫ 0",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ ... | [
728,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.55201\ninst✝ : EDist α\nx y : α\ns : Set α\n⊢ 0 < infsep s ↔ 0 < einfsep s ∧ einfsep s < ⊤",
"tactic": "simp_rw [infsep, ENNReal.toReal_pos_iff]"
}
] | [
350,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.tropEquiv_symm_coe_fn | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.mul_atTop | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nα : Type u_2\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x => f x * g x) l atTop",
"ta... | [
75,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_lt_of_nonempty | [] | [
152,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.compl_compl | [] | [
131,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/Sigma.lean | List.kerase_of_not_mem_keys | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl : List (Sigma β)\nh : ¬a ∈ keys l\n⊢ kerase a l = l",
"tactic": "induction' l with _ _ ih <;> [rfl; (simp [not_or] at h; simp [h.1, ih h.2])]"
},
{
"state_after": ... | [
415,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.lt_addChar | [] | [
119,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
119,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.pred_inj | [
{
"state_after": "no goals",
"state_before": "a b : Nat\nx✝¹ : 0 < a + 1\nx✝ : 0 < b + 1\nh : pred (a + 1) = pred (b + 1)\n⊢ a + 1 = b + 1",
"tactic": "rw [show a = b from h]"
}
] | [
448,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
444,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.21918495\n𝕜 : Type ?u.21918498\nE : Type u_1\nF : Type ?u.21918504\nA : Type ?u.21918507\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\nhfi : Integrable f\n⊢ HasSum (fun n =... | [
1440,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1438,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_succ | [
{
"state_after": "no goals",
"state_before": "a b c : Ordinal\n⊢ a ♯ succ b = succ (a ♯ b)",
"tactic": "rw [← nadd_one (a ♯ b), nadd_assoc, nadd_one]"
}
] | [
309,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.range_linearIsometry | [
{
"state_after": "case refine'_1\nι : Type u_4\n𝕜 : Type u_3\ninst✝⁵ : IsROrC 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type u_1\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G i)\nV : (i : ι) → G i... | [
277,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
11
] |
Mathlib/Algebra/Algebra/RestrictScalars.lean | RestrictScalars.ringEquiv_map_smul | [] | [
216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_const_smul_right | [] | [
292,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/List/Chain.lean | List.chain_pmap_of_chain | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na✝¹ b : α\nS : β → β → Prop\np : α → Prop\nf : (a : α) → p a → β\nH : ∀ (a b : α) (ha : p a) (hb : p b), R a b → S (f a ha) (f b hb)\na✝ : α\nl : List α\nhl₁✝ : Chain R a✝ l\nha✝ : p a✝\nhl₂✝ : ∀ (a : α), a ∈ l → p a\na :... | [
105,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_subtype_le | [] | [
833,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.eventually | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Typ... | [
670,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
11
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.symm_zero | [
{
"state_after": "no goals",
"state_before": "⊢ ↑(σ 0) = ↑1",
"tactic": "simp [symm]"
}
] | [
111,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.erase_eq_filter | [] | [
174,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.swap_comp | [] | [
382,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/NormedSpace/Ray.lean | sameRay_iff_inv_norm_smul_eq_of_ne | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.229888\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nx y : F\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ SameRay ℝ x y ↔ ‖x‖⁻¹ • x = ‖y‖⁻¹ • y",
"tactic": "rw [inv_smul_eq_iff₀,... | [
87,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_singleton | [] | [
53,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.hasSum_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → ℝ\nx : ℝ\nh : HasSum (fun x => ↑(f x)) ↑x\n⊢ HasSum f x",
"tactic": "simpa only [IsROrC.reClm_apply, IsROrC.ofReal_re] using reClm.hasSum h"
}
] | [
509,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_pempty | [] | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.induction_on | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.1517\nπ : ι → Type ?u.1522\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s : Set α\nhs : IsCompact s\np : Set α → Prop\nhe : p ∅\nhmono : ∀ ⦃s t : Set α⦄, s ⊆ t → p t → p s\nhunion : ∀ ⦃s t : Set α⦄, p s → p t → p (s ∪ t)\nhnhds : ∀ (x : α),... | [
108,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_self_sub_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type ?u.40308\nN : Type u_2\nP : Type ?u.40314\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf f₁ f₂ g g₁ g₂ : α →₀ N\n⊢ neLocus (f - g) f = g.support",
"tactic": "rw [neLocus_comm, neLocus_self_sub_right]"
}
] | [
178,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.sin | [] | [
1016,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Data/Real/Basic.lean | Real.lt_sInf_add_pos | [] | [
771,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.sum_ofWithBot | [] | [
470,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_inf_iff | [] | [
394,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
11
] |
Mathlib/RingTheory/FreeRing.lean | FreeRing.of_injective | [] | [
59,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iic_top | [] | [
1216,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
8
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv_symm_toLinearMap | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/Instances/Real.lean | AddSubgroup.tendsto_zmultiples_subtype_cofinite | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\n⊢ Tendsto (↑(AddSubgroup.subtype (zmultiples 0))) cofinite (cocompact ℝ)\n\ncase inr\nα : Type u\nβ : Type v\nγ : Type w\na : ℝ\nha : a ≠ 0\n⊢ Tendsto (↑(AddSubgroup.subtype (zmultiples a))) cofinite (cocompact ℝ)",
"state_before": "α : Type u\... | [
263,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.