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_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.169521\nγ : Type ?u.169524\ninst✝ : DecidableEq α\ns t u : Multiset α\na b : α\n⊢ 0 ∪ s = s",
"tactic": "simp [union_def]"
}
] | [
1733,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1732,
9
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.map_div_left_ae | [] | [
495,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.Lp_add_le_tsum' | [] | [
528,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_mul | [
{
"state_after": "no goals",
"state_before": "b : Int\n⊢ sign (0 * b) = sign 0 * sign b",
"tactic": "simp [Int.mul_zero, Int.zero_mul]"
}
] | [
540,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
538,
9
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.univ_pi_Ioi_ae_eq_Ici | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.3710571\nα : ι → Type u_1\ninst✝⁴ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝³ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝² : ∀ (i : ι), SigmaFinite (μ i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : ∀ (i : ι), NoAtoms (μ i)\nf :... | [
506,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.min_le_multiplicity_add | [
{
"state_after": "α : Type u_1\ninst✝¹ : Semiring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p a ≤ multiplicity p b\n⊢ ∀ (n : ℕ), p ^ n ∣ a → p ^ n ∣ a + b",
"state_before": "α : Type u_1\ninst✝¹ : Semiring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplic... | [
412,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Models.rank_eq | [
{
"state_after": "α : Type u_1\narr : Array (UFNode α)\nn : ℕ\nm : UFModel n\nH : Models arr m\ni : ℕ\nh : i < Array.size arr\n⊢ i < Array.size arr",
"state_before": "α : Type u_1\narr : Array (UFNode α)\nn : ℕ\nm : UFModel n\nH : Models arr m\ni : ℕ\nh : i < Array.size arr\n⊢ i < n",
"tactic": "rw [H.s... | [
134,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.continuous_coe | [] | [
108,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.embDomain_eq_mapDomain | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.226928\nι : Type ?u.226931\nM : Type u_3\nM' : Type ?u.226937\nN : Type ?u.226940\nP : Type ?u.226943\nG : Type ?u.226946\nH : Type ?u.226949\nR : Type ?u.226952\nS : Type ?u.226955\ninst✝ : AddCommMonoid M\nv✝ v₁ v₂ : α →₀ M\nf : α ↪ β\nv : α →₀... | [
604,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.prod_X_sub_C_eq | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.180963\nS : Type u_1\nF : Type ?u.180969\nK : Type ?u.180972\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝¹ : Semiring R\ninst✝ : CommRing S\nx y z : S\n⊢ (X - ↑C x) * (X - ↑C y) * (X - ↑C z) =\n toPoly { a := 1, b := -(x + y + z), c := x * y + x... | [
81,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.coe_toContinuousMap | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.OfNatIso.cone_fac | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cone F\nX : C\nh : yoneda.obj X ⋙ uliftFunctor ≅ Functor.cones F\ns : Cone F\n⊢ Cone.extend (limitCone h) (homOfCone h (coneOfHom h (homOfCone h s))) = coneOfHom h (homOfCone h s... | [
524,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.toList_nil | [] | [
542,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.ne_natDegree_of_mem_eraseLead_support | [] | [
105,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.differentiableOn_tsum_of_summable_norm | [
{
"state_after": "no goals",
"state_before": "E : Type u_2\nι : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nU K : Set ℂ\nz : ℂ\nM r δ : ℝ\nφ : Filter ι\nF : ι → ℂ → E\nf g : ℂ → E\nu : ι → ℝ\nhu : Summable u\nhf : ∀ (i : ι), DifferentiableOn ℂ (F i) U\nhU : Is... | [
192,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.102017\nβ₂ : Type ?u.102020\nγ : Type ?u.102023\nι : Sort u_1\nι' : Sort ?u.102029\nκ : ι → Sort ?u.102034\nκ' : ι' → Sort ?u.102039\ninst✝¹ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b : α\ninst✝ : Nonempty ι\nf : ι → α\na : α\n⊢ (⨅ (x ... | [
1254,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_mono_left | [
{
"state_after": "k : Type u_2\nE : Type u_1\nPE : Type ?u.2241\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup E\ninst✝¹ : Module k E\ninst✝ : OrderedSMul k E\na a' b b' : E\nr r' : k\nha : a ≤ a'\nhr : r ≤ 1\n⊢ (1 - r) • a + r • b ≤ (1 - r) • a' + r • b",
"state_before": "k : Type u_2\nE : Type u_1\... | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.mul_map_seq | [] | [
684,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_right_left | [] | [
846,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Box.volume_face_mul | [] | [
137,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.union | [] | [
230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.ext | [] | [
268,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_pos_left | [] | [
96,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
95,
1
] |
Mathlib/Init/Logic.lean | trans_rel_left | [] | [
43,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
15
] |
Mathlib/Topology/Algebra/Monoid.lean | continuousMul_induced | [] | [
388,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_assoc' | [] | [
360,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.add_mulVec | [
{
"state_after": "case h\nl : Type ?u.856830\nm : Type u_2\nn : Type u_1\no : Type ?u.856839\nm' : o → Type ?u.856844\nn' : o → Type ?u.856849\nR : Type ?u.856852\nS : Type ?u.856855\nα : Type v\nβ : Type w\nγ : Type ?u.856862\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype n\nA B : Matrix m n α\nx : n →... | [
1757,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1754,
1
] |
src/lean/Init/Core.lean | ne_of_beq_false | [
{
"state_after": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\nh : (a == b) = false\nh' : a = b\n⊢ False",
"state_before": "α : Type u_1\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\na b : α\nh : (a == b) = false\n⊢ a ≠ b",
"tactic": "intro h'"
},
{
"state_after": "α : Type u_1\ninst✝¹ : ... | [
602,
90
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
601,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_σ_of_gt | [
{
"state_after": "case a.h.h.mk.h\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : ↑Fin.castSucc j < i\nk : ℕ\nhk : k < len [n + 1] + 1\n⊢ ↑(↑(Hom.toOrderHom (δ (Fin.succ i) ≫ σ (↑Fin.castSucc j))) { val := k, isLt := hk }) =\n ↑(↑(Hom.toOrderHom (σ j ≫ δ i)) { val := k, isLt := hk })",
"state_before": "n :... | [
323,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.exists_eq_succ_of_ne_one | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nproperty✝ : 0 < n + 2\nx✝ : { val := n + 2, property := property✝ } ≠ 1\n⊢ 0 < n + 1",
"tactic": "simp"
}
] | [
306,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/GCDMonoid/IntegrallyClosed.lean | IsLocalization.surj_of_gcd_domain | [
{
"state_after": "case intro.intro.mk\nR : Type u_1\nA : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : GCDMonoid R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nM : Submonoid R\ninst✝ : IsLocalization M A\nx y : R\nhy : y ∈ M\n⊢ ∃ a b, IsUnit (gcd a b) ∧ mk' A x { val := y, property := hy } * ↑(alg... | [
33,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_sub_bot | [] | [
861,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_two_sub | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ cos (π / 2 - x) = sin x",
"tactic": "rw [← cos_neg, neg_sub, cos_sub_pi_div_two]"
}
] | [
461,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.two_le | [] | [
76,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Order/SupIndep.lean | Finset.SupIndep.biUnion | [
{
"state_after": "α : Type u_3\nβ : Type ?u.22024\nι : Type u_1\nι' : Type u_2\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ns✝ : Finset ι\nf✝ : ι → α\ninst✝ : DecidableEq ι\ns : Finset ι'\ng : ι' → Finset ι\nf : ι → α\nhs : SupIndep s fun i => Finset.sup (g i) f\nhg : ∀ (i' : ι'), i' ∈ s → SupIndep (g i') f... | [
173,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | pow_inv_comm₀ | [] | [
41,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ioo_of_lt | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nh : a < b\n⊢ ↑(Fintype.card ↑(Set.Ioo a b)) = b - a - 1",
"tactic": "rw [card_fintype_Ioo, sub_sub, toNat_sub_of_le h]"
}
] | [
179,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.compl | [] | [
1014,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Analysis/Convex/KreinMilman.lean | IsCompact.has_extreme_point | [
{
"state_after": "E : Type u_1\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : T2Space E\ninst✝² : TopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhscomp : IsCompact s\nhsnemp : Set.Nonempty s\nS : Set (Set E) := {t | Set.Nonemp... | [
93,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.U_one | [] | [
109,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.le_lifts_of_splits | [
{
"state_after": "F : Type u_1\nE : Type u_2\nK : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Field K\ninst✝¹ : Algebra F E\ninst✝ : Algebra F K\nS : Set E\nx : Lifts F E K\ns : E\nh1 : IsIntegral F s\nh2 : Splits (algebraMap F K) (minpoly F s)\nt : { x_1 // x_1 ∈ x.fst }\nu : { x_1 // x_1 ∈ (liftOfS... | [
1133,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_top | [] | [
2857,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2857,
9
] |
Mathlib/Topology/PathConnected.lean | Path.coe_toContinuousMap | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_upperBounds_subset_lowerBounds_smul | [] | [
210,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Order/MinMax.lean | lt_max_of_lt_right | [] | [
96,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.inverse_range | [
{
"state_after": "R : Type u_2\ninst✝⁶ : Ring R\nE : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.710645\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nhf : LinearMap.ker f.toFun = ⊥\n⊢ Submodule.map (LinearMap.snd... | [
1042,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_strictMono | [] | [
1112,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.IsIntegral.to_finite | [
{
"state_after": "R : Type u_1\nA : Type ?u.599454\nB : Type ?u.599457\nS : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nh : IsIntegral f\nh' : FiniteType f\nthis : Algebra R S := toAlgebra f\n⊢ Finite f",
... | [
418,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Topology/FiberBundle/IsHomeomorphicTrivialBundle.lean | IsHomeomorphicTrivialFiberBundle.proj_eq | [] | [
42,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
11
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.mk'_eq_zero_iff_eq_zero | [
{
"state_after": "R : Type u_1\ninst✝¹³ : CommRing R\nM : Submonoid R\nS : Type ?u.217929\ninst✝¹² : CommRing S\ninst✝¹¹ : Algebra R S\nP : Type ?u.218166\ninst✝¹⁰ : CommRing P\nA : Type ?u.218172\ninst✝⁹ : CommRing A\ninst✝⁸ : IsDomain A\nK : Type u_2\nB : Type ?u.218349\ninst✝⁷ : CommRing B\ninst✝⁶ : IsDomain... | [
185,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.univ_pi_Iio_ae_eq_Iic | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.3602771\nα : ι → Type u_1\ninst✝⁴ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝³ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝² : ∀ (i : ι), SigmaFinite (μ i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : ∀ (i : ι), NoAtoms (μ i)\nf :... | [
501,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_lineMap_left | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.29402\nV : Type u_3\nP : Type u_1\nW : Type ?u.29411\nQ : Type ?u.29414\ninst✝⁸ : SeminormedAddCommGroup V\ninst✝⁷ : PseudoMetricSpace P\ninst✝⁶ : NormedAddTorsor V P\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : MetricSpace Q\ninst✝³ : NormedAddTorsor W ... | [
97,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_smul | [] | [
213,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.attach_eq_univ | [] | [
983,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_coe | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ tan ↑x = Real.tan x",
"tactic": "rw [tan, sin_coe, cos_coe, Real.tan_eq_sin_div_cos]"
}
] | [
785,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_fst' | [] | [
74,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAtFilter_fst | [] | [
149,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_right | [
{
"state_after": "case mp\nC : Type u_2\ninst✝ : Category C\nA✝ B✝ B' X✝ Y✝ Y'✝ : C\ni✝ : A✝ ⟶ B✝\ni' : B✝ ⟶ B'\np✝ : X✝ ⟶ Y✝\np'✝ : Y✝ ⟶ Y'✝\nA B X Y X' Y' : C\ni : A ⟶ B\np : X ⟶ Y\np' : X' ⟶ Y'\ne : Arrow.mk p ≅ Arrow.mk p'\na✝ : HasLiftingProperty i p\n⊢ HasLiftingProperty i p'\n\ncase mpr\nC : Type u_2\nin... | [
147,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.minSqFacProp_div | [
{
"state_after": "n k : ℕ\npk : Prime k\ndk : k ∣ n\ndkk : ¬k * k ∣ n\no : Option ℕ\nH : MinSqFacProp (n / k) o\nthis : ∀ (p : ℕ), Prime p → p * p ∣ n → k * (p * p) ∣ n\n⊢ MinSqFacProp n o",
"state_before": "n k : ℕ\npk : Prime k\ndk : k ∣ n\ndkk : ¬k * k ∣ n\no : Option ℕ\nH : MinSqFacProp (n / k) o\n⊢ Min... | [
153,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.mk_eq_normalize | [
{
"state_after": "no goals",
"state_before": "num : Int\nden : Nat\nnz : den ≠ 0\nc : Nat.coprime (Int.natAbs num) den\n⊢ mk' num den = normalize num den",
"tactic": "simp [normalize_eq, c.gcd_eq_one]"
}
] | [
32,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
31,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.isNClique_iff | [] | [
110,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.coe_real_ereal | [] | [
1979,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1977,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_compl_iff_disjoint_left | [] | [
1739,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1738,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.span_preimage_eq | [
{
"state_after": "R : Type u_1\nM : Type u_3\nr : R\nx y : M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\np p' : Submodule R M\nR₂ : Type u_2\nM₂ : Type u_4\ninst✝³ : Ring R₂\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\ninst✝ : RingHomSurjective τ₁₂\n... | [
520,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Analysis/Complex/Circle.lean | mem_circle_iff_abs | [] | [
53,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | tsub_le_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1063\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\n⊢ a - b ≤ c ↔ a ≤ b + c",
"tactic": "rw [tsub_le_iff_right, add_comm]"
}
] | [
96,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_mono | [] | [
214,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.eq_formalMultilinearSeries | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1145337\nG : Type ?u.1145340\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ :... | [
1017,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | OrthogonalFamily.isOrtho | [] | [
434,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.Lp_toLp_restrict_add | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.319628\nE : Type u_2\nF : Type ?u.319634\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\n𝕜 : Type ?u.319643\ninst✝² : NormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : ℝ≥0∞\nμ : Measure α\nf g : { x // x ∈ Lp E p }\ns : ... | [
882,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_zero_eq_one | [
{
"state_after": "case zero\nm : ℕ\ninst✝ : NeZero zero\n⊢ succ 0 = 1\n\ncase succ\nm n✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\n⊢ succ 0 = 1",
"state_before": "n m : ℕ\ninst✝ : NeZero n\n⊢ succ 0 = 1",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zero\nm : ℕ\ninst✝ :... | [
914,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_vsub_left_image | [] | [
709,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.pow_lt_iff_lt_clog | [] | [
314,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/Filter/Interval.lean | Filter.tendstoIxxClass_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5916\ninst✝ : Preorder α\ns t : Set α\nIxx : α → α → Set α\n⊢ Tendsto (fun p => Ixx p.fst p.snd) (𝓟 s ×ˢ 𝓟 s) (smallSets (𝓟 t)) ↔ ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → Ixx x y ⊆ t",
"tactic": "simp only [smallSets_principal, prod... | [
106,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePullbackShape.hom_id | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_update | [
{
"state_after": "α : Type u_1\nβ : Type ?u.147517\nγ : Type ?u.147520\nι : Type ?u.147523\nM : Type u_2\nM' : Type ?u.147529\nN : Type ?u.147532\nP : Type ?u.147535\nG : Type ?u.147538\nH : Type ?u.147541\nR : Type ?u.147544\nS : Type ?u.147547\ninst✝¹ : Zero M\nf : α →₀ M\na : α\nb : M\ni : α\ninst✝ : Decidab... | [
566,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_lt_one_of_one_lt | [] | [
1261,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tendsto_sin_pi_div_two | [
{
"state_after": "case h.e'_5.h.e'_3\n\n⊢ 1 = sin (π / 2)",
"state_before": "⊢ Tendsto sin (𝓝[Iio (π / 2)] (π / 2)) (𝓝 1)",
"tactic": "convert continuous_sin.continuousWithinAt.tendsto"
},
{
"state_after": "no goals",
"state_before": "case h.e'_5.h.e'_3\n\n⊢ 1 = sin (π / 2)",
"tactic":... | [
1060,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.coe_lt_coe | [] | [
552,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.orderIsoMapComap_apply' | [] | [
2531,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2529,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.appendFun_comp_id | [] | [
281,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.toSubalgebra_injective | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.43327\nR : Type u_2\nA : Type u_1\nB : Type ?u.43336\nC : Type ?u.43339\ninst✝¹³ : CommSemiring R\ninst✝¹² : StarRing R\ninst✝¹¹ : Semiring A\ninst✝¹⁰ : StarRing A\ninst✝⁹ : Algebra R A\ninst✝⁸ : StarModule R A\ninst✝⁷ : Semiring B\ninst✝⁶ : StarRing... | [
102,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.815667\nβ : Type ?u.815670\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx : ℝ\nn : ℕ\n⊢ ENNReal.ofReal (n • x) = n • ENNReal.ofReal x",
"tactic": "simp only [nsmul_eq_mul, ← ofReal_coe_nat n, ← ofReal_mul n.cast_nonneg]"
}
] | [
2182,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2181,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.wellFounded | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\nhs : ∀ (i : ι), WellFounded (s i)\nhr : WellFounded (rᶜ ⊓ fun x x_1 => x ≠ x_1)\nx : Π₀ (i : ι), α i\n⊢ Acc (Dfi... | [
164,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
src/lean/Init/Core.lean | HEq.trans | [] | [
631,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
630,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.val_mkOfMulEqOne | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedOrderRingIso_symm | [] | [
339,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Std/Data/Option/Lemmas.lean | Option.join_eq_some | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : α✝\nx : Option (Option α✝)\n⊢ join x = some a ↔ x = some (some a)",
"tactic": "simp"
}
] | [
108,
7
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
107,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_list_prod | [] | [
300,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inl | [] | [
1395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝³ : Category C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ (pullbackZeroZeroIso X Y).hom ≫ prod.fst = pullback.fst",
"tactic": "simp [← Iso.eq_inv_comp]"
}
] | [
188,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivWithinAt.mul_const | [
{
"state_after": "case h.e'_10\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type ?u.903195\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type ?u.903290\ninst✝⁷ : NormedAddCommGroup G\ninst✝⁶ : NormedSpace 𝕜 ... | [
408,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasSum_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.229498\nγ : Type ?u.229501\na b c d : ℝ≥0∞\nr✝ p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α → ℝ≥0∞\nf : α → ℝ≥0\nr : ℝ≥0\n⊢ HasSum (fun a => ↑(f a)) ↑r ↔ HasSum f r",
"tactic": "simp only [HasSum, ← coe_finset_sum, tendst... | [
764,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
11
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.generate_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nd : DynkinSystem α\ns : Set (Set α)\nhs : IsPiSystem s\nt₁ t₂ : Set α\nht₁ : Has (generate s) t₁\nht₂ : Has (generate s) t₂\ns₁ : Set α\nhs₁ : s₁ ∈ s\nthis✝¹ : Has (generate s) s₁\nthis✝ : generate s ≤ restrictOn (generate s) this✝¹\nthis : Has (ge... | [
715,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.minSqFac_dvd | [
{
"state_after": "n d : ℕ\nh : minSqFac n = some d\nthis : MinSqFacProp n (minSqFac n)\n⊢ d * d ∣ n",
"state_before": "n d : ℕ\nh : minSqFac n = some d\n⊢ d * d ∣ n",
"tactic": "have := minSqFac_has_prop n"
},
{
"state_after": "n d : ℕ\nh : minSqFac n = some d\nthis : MinSqFacProp n (some d)\n⊢ ... | [
228,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_toMeasurable_union | [] | [
377,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_pow_mul_C | [] | [
599,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_cos | [] | [
966,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Logic/Basic.lean | not_imp_self | [] | [
269,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
9
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finrank_zero_iff_forall_zero | [] | [
1028,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.