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/Algebra/Algebra/Basic.lean | algebraMap.coe_prod | [] | [
195,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_to_linearMap_comp | [] | [
303,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/List/Zip.lean | List.zip_map' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.62030\nε : Type ?u.62033\nf : α → β\ng : α → γ\na : α\nl : List α\n⊢ zip (map f (a :: l)) (map g (a :: l)) = map (fun a => (f a, g a)) (a :: l)",
"tactic": "simp only [map, zip_cons_cons, zip_map']"
}
] | [
161,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Std/Data/List/Lemmas.lean | List.getLast?_concat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\n⊢ getLast? (l ++ [a]) = some a",
"tactic": "simp [getLast?_eq_get?]"
}
] | [
640,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
639,
9
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_of_forall_set_integral_eq_of_sigmaFinite | [
{
"state_after": "α : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\np : ℝ≥0∞\ninst✝ : SigmaFinite μ\nf : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → IntegrableOn f s\nhf_zer... | [
422,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_id_obj' | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_le_count_of_le | [] | [
1543,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1541,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_closure_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring T\ns : Set R\n⊢ ↑(closure s) = ↑(AddSubmonoid.closure ↑(Subsemigroup.closure s))",
"tactic":... | [
657,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.succ_eq_succ | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Algebra/Order/Kleene.lean | one_le_kstar | [] | [
203,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/Heyting/Basic.lean | Disjoint.sdiff_eq_right | [] | [
698,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.toOuterMeasure_pure_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4210\nγ : Type ?u.4213\na a' : α\ns : Set α\n⊢ (∑' (x : α), Set.indicator s (↑(pure a)) x) = if a ∈ s then 1 else 0",
"state_before": "α : Type u_1\nβ : Type ?u.4210\nγ : Type ?u.4213\na a' : α\ns : Set α\n⊢ ↑(toOuterMeasure (pure a)) s = if a ∈ s then 1 else 0",
... | [
82,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_zero_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1553426\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ inner x 0 = 0",
"tactic": "rw ... | [
570,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_sup | [] | [
1763,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1762,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_iSup | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nf : α → β\nhf : LeftOrdContinuous f\ng : ι → α\n⊢ sSup (range (f ∘ fun i => g i)) = sSup (range fun i => f (g i))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹... | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.coeff_expand | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nhp : 0 < p\nf : R[X]\nn : ℕ\n⊢ coeff (sum f fun e a => ↑C a * (X ^ p) ^ e) n = if p ∣ n then coeff f (n / p) else 0",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring ... | [
118,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.exists_mem | [] | [
370,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.continuous_coordChange | [
{
"state_after": "case refine'_1\nι : Type ?u.56874\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.56885\nZ : Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\nproj : Z → B\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace (TotalSpace E)\ne : Trivialization F proj\nx : Z\ne' : Trivializatio... | [
705,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Analysis/MeanInequalities.lean | ENNReal.Lp_add_le | [
{
"state_after": "case pos\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0∞\np q : ℝ\nhp : 1 ≤ p\nH' : (∑ i in s, f i ^ p) ^ (1 / p) = ⊤ ∨ (∑ i in s, g i ^ p) ^ (1 / p) = ⊤\n⊢ (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤ (∑ i in s, f i ^ p) ^ (1 / p) + (∑ i in s, g i ^ p) ^ (1 / p)\n\ncase neg\nι : Type u\ns : Finset ι\nf ... | [
786,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.asAlgebraHom_of | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nG : Type u_3\nV : Type u_1\ninst✝³ : CommSemiring k\ninst✝² : Monoid G\ninst✝¹ : AddCommMonoid V\ninst✝ : Module k V\nρ : Representation k G V\ng : G\n⊢ ↑(asAlgebraHom ρ) (↑(of k G) g) = ↑ρ g",
"tactic": "simp only [MonoidAlgebra.of_apply, asAl... | [
101,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/CompleteLattice.lean | Prod.snd_iSup | [] | [
1879,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1878,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.nonneg_antisymm | [
{
"state_after": "a✝ b c a : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\nd0 : 0 < ↑d\n⊢ Rat.Nonneg (n /. ↑d) → Rat.Nonneg (-(n /. ↑d)) → n /. ↑d = 0",
"state_before": "a✝ b c a : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\n⊢ Rat.Nonneg (n /. ↑d) → Rat.Nonneg (-(n /. ↑d)) → n /. ↑d = 0",
"tactic": "have d0 : 0 < (d : ℤ) := Int.coe_nat_... | [
82,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
11
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_mul_of_le_left | [] | [
194,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter_pair | [] | [
145,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.mul_eq_bot_iff | [] | [
324,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | eventuallyEq_prod | [
{
"state_after": "case hs\nι : Type u_3\nα : Type ?u.447147\nX✝ : Type ?u.447150\nM✝ : Type ?u.447153\nN : Type ?u.447156\ninst✝⁴ : TopologicalSpace X✝\ninst✝³ : TopologicalSpace M✝\ninst✝² : CommMonoid M✝\ninst✝¹ : ContinuousMul M✝\nX : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\ns : Finset ι\nl : Filter X\n... | [
782,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_mono_left | [
{
"state_after": "p : ℕ → Prop\ninst✝¹ : DecidablePred p\nq : ℕ → Prop\ninst✝ : DecidablePred q\nn : ℕ\nhpq : ∀ (k : ℕ), p k → q k\n⊢ card (filter p (range n)) ≤ card (filter q (range n))",
"state_before": "p : ℕ → Prop\ninst✝¹ : DecidablePred p\nq : ℕ → Prop\ninst✝ : DecidablePred q\nn : ℕ\nhpq : ∀ (k : ℕ)... | [
158,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.zeta_mul_apply | [] | [
490,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.IsPure.mono | [] | [
241,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.sUnion_directed | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.4785\nπ : ι → Type ?u.4790\ninst✝ : TopologicalSpace α\ns✝ t✝ u✝ v✝ : Set α\nS : Set (Set α)\nK : DirectedOn (fun x x_1 => x ⊆ x_1) S\nH : ∀ (s : Set α), s ∈ S → IsPreconnected s\nu v : Set α\nhu : IsOpen... | [
170,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/DualNumber.lean | DualNumber.snd_eps | [] | [
74,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_le_neg | [
{
"state_after": "a b : Int\nh : a ≤ b\nthis : 0 ≤ -a + b\n⊢ -b ≤ -a",
"state_before": "a b : Int\nh : a ≤ b\n⊢ -b ≤ -a",
"tactic": "have : 0 ≤ -a + b := Int.add_left_neg a ▸ Int.add_le_add_left h (-a)"
},
{
"state_after": "a b : Int\nh : a ≤ b\nthis✝ : 0 ≤ -a + b\nthis : 0 + -b ≤ -a + b + -b\n⊢... | [
859,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
856,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_dist_dist_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.277189\nι : Type ?u.277192\ninst✝ : PseudoMetricSpace α\nx y z : α\n⊢ dist (dist x y) (dist x z) ≤ dist y z",
"tactic": "simpa only [dist_comm x] using dist_dist_dist_le_left y z x"
}
] | [
1780,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1779,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.neg_apply | [] | [
912,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_symm | [] | [
198,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.ediam_image | [] | [
369,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.neg_comp | [] | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.continuousAt_equivIoc | [
{
"state_after": "case H\n𝕜 : Type u_1\nB : Type ?u.101096\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : TopologicalSpace 𝕜\ninst✝¹ : OrderTopology 𝕜\np : 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝ : Archimedean 𝕜\nx : AddCircle p\nz✝ : 𝕜\nhx : ↑z✝ ≠ ↑a\n⊢ ContinuousAt ↑(equivIoc p a) ↑z✝",
"state_before"... | [
290,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_union_empty_singleton | [
{
"state_after": "case empty\nα : Type u_1\nβ : Type ?u.62282\nγ : Type ?u.62285\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns : Finset α\na : α\ninst✝ : DecidableEq α\n⊢ fold (fun x x_1 => x ∪ x_1) ∅ singleton ∅ = ∅\n\ncase insert\nα : Type u_1\nβ : Type ?u.62282\nγ : T... | [
206,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/List/Infix.lean | List.mem_inits | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.29777\nl l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\ns : List α\nthis : s = [] ↔ s <+: []\n⊢ s ∈ inits [] ↔ s <+: []",
"tactic": "simpa only [inits, mem_singleton]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\... | [
351,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.dual | [] | [
406,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : ∀ (k : ℕ), padicNorm p (↑f k) = padicNorm p (↑g k)\nhf : f ≈ 0\nhg : g ≈ 0\n⊢ norm f = norm g",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : ∀ (k : ℕ), padicNorm p (↑f k) = padicNorm p (↑g k)\nhf : f ≈ 0\n⊢ nor... | [
422,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/FieldTheory/Tower.lean | FiniteDimensional.right | [
{
"state_after": "F : Type u\nK : Type v\nA : Type w\ninst✝⁶ : Field F\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup A\ninst✝³ : Algebra F K\ninst✝² : Module K A\ninst✝¹ : Module F A\ninst✝ : IsScalarTower F K A\nhf : FiniteDimensional F A\nb : Finset A\nhb : Submodule.span F ↑b = ⊤\n⊢ ↑b ⊆ ↑(Submodule.restri... | [
121,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | WithBot.coe_nsmul | [] | [
500,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.card_Ioo_eq_card_Ioc_sub_one | [] | [
661,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Order/BoundedOrder.lean | antitone_lt | [] | [
574,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_multiset_of_infinite | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Infinite α\n⊢ (#Multiset α) = (#α)",
"tactic": "simp"
}
] | [
1076,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.MemLeftTransversals.inv_mul_toFun_mem | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nhS : S ∈ leftTransversals ↑H\ng : G\n⊢ ((↑(toFun hS g))⁻¹ * g)⁻¹ = g⁻¹ * ↑(toFun hS g)",
"tactic": "rw [mul_inv_rev, inv_inv]"
}
] | [
382,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.coe_algebraMap_ofSubsemiring | [] | [
519,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.exists_fin_succ | [] | [
1756,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1754,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.200542\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\... | [
127,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.cons_right | [] | [
894,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image_subset_image2_right | [] | [
77,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_add_negSucc | [
{
"state_after": "m n k : Nat\nh : m < n ∨ m ≥ n\n⊢ subNatNat m n + -[k+1] = subNatNat m (n + succ k)",
"state_before": "m n k : Nat\n⊢ subNatNat m n + -[k+1] = subNatNat m (n + succ k)",
"tactic": "have h := Nat.lt_or_ge m n"
},
{
"state_after": "no goals",
"state_before": "m n k : Nat\nh :... | [
259,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
245,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.divInt_nonneg | [
{
"state_after": "a✝ b✝ c : ℚ\na b : ℤ\nh : 0 < b\nx : ℚ\nha : a /. b = x\n⊢ Rat.Nonneg x ↔ 0 ≤ a",
"state_before": "a✝ b✝ c : ℚ\na b : ℤ\nh : 0 < b\n⊢ Rat.Nonneg (a /. b) ↔ 0 ≤ a",
"tactic": "generalize ha : a /. b = x"
},
{
"state_after": "case mk'\na✝ b✝ c : ℚ\na b : ℤ\nh : 0 < b\nn₁ : ℤ\nd₁ ... | [
53,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.map_univ_coe | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\nthis : map Prod.fst (toEnumFinset m).val = m\n⊢ map (fun x => x.fst) Finset.univ.val = m",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\n⊢ map (fun x => x.fst) Finset.univ.val = m",
"tactic": "have := m.... | [
239,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Logic/Basic.lean | iff_mpr_iff_true_intro | [] | [
411,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_congr_right | [] | [
810,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NormedAddCommGroup.tendsto_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ✝ : Type ?u.383130\nγ : Type ?u.383133\nι : Type ?u.383136\ninst✝² : Nonempty α\ninst✝¹ : SemilatticeSup α\nβ : Type u_2\ninst✝ : SeminormedAddCommGroup β\nf : α → β\nb : β\n⊢ (∀ (ib : ℝ), 0 < ib → ∃ ia, True ∧ ∀ (x : α), x ∈ Set.Ici ia → f x ∈ ba... | [
853,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_vsub | [] | [
717,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsRegular.aleph0_le | [] | [
955,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_ofMul | [] | [
2240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2239,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subset_normalClosure | [] | [
2464,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2463,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.zeta_mul_pow_eq_sigma | [
{
"state_after": "case h\nR : Type ?u.525734\nk x✝ : ℕ\n⊢ ↑(ζ * pow k) x✝ = ↑(σ k) x✝",
"state_before": "R : Type ?u.525734\nk : ℕ\n⊢ ζ * pow k = σ k",
"tactic": "ext"
},
{
"state_after": "case h\nR : Type ?u.525734\nk x✝ : ℕ\n⊢ ∑ i in divisors x✝, ↑(pow k) i =\n ↑{ toFun := fun n => ∑ d in d... | [
805,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt.zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\n⊢ padicValInt p 0 = 0",
"tactic": "simp [padicValInt]"
}
] | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.join₂_map | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type ?u.203301\nR : Type u_1\nS : Type u_2\nT : Type ?u.203310\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* MvPolynomial σ S\nφ : MvPolynomial σ R\n⊢ ↑join₂ (↑(map f) φ) = ↑(bin... | [
199,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.cofinite_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1147\nα : Type u_1\nβ : Type ?u.1153\nl : Filter α\n⊢ cofinite = ⊥ ↔ Finite α",
"tactic": "simp [← empty_mem_iff_bot, finite_univ_iff]"
}
] | [
64,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_irrefl | [] | [
1213,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | Filter.HasBasis.uniformEmbedding_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nι : Sort u_1\nι' : Sort u_2\np : ι → Prop\np' : ι' → Prop\ns : ι → Set (α × α)\ns' : ι' → Set (β × β)\nh : HasBasis (𝓤 α) p s\nh' : HasBasis (𝓤 β) p' ... | [
155,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Finset/Pi.lean | Finset.pi_insert | [
{
"state_after": "case a\nα : Type u_1\nβ : α → Type u\nδ : α → Sort v\ninst✝¹ : DecidableEq α\ninst✝ : (a : α) → DecidableEq (β a)\ns : Finset α\nt : (a : α) → Finset (β a)\na : α\nha : ¬a ∈ s\n⊢ (pi (insert a s) t).val = (Finset.biUnion (t a) fun b => image (Pi.cons s a b) (pi s t)).val",
"state_before": ... | [
111,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.coe_aeval_eq_evalRingHom | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Basic.lean | le_Prop_eq | [] | [
1398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | summable_of_isBigO_nat' | [] | [
693,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_pos_iff_mem_periodicPts | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21811\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nh : ¬x ∈ periodicPts f\n⊢ ¬0 < minimalPeriod f x",
"tactic": "simp only [minimalPeriod, dif_neg h, lt_irrefl 0, not_false_iff]"
}
] | [
316,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.aux_uniformity_eq | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.66094\n𝕜' : Type ?u.66097\nι : Type u_1\nα : ι → Type ?u.66105\nβ : ι → Type u_2\ninst✝³ : Fact (1 ≤ p)\ninst✝² : (i : ι) → PseudoMetricSpace (α i)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nA : UniformInducing ↑(PiLp.equiv p β)\n⊢ 𝓤 (PiLp p β) = ... | [
431,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsPrime.mem_or_mem_of_mul_eq_zero | [] | [
258,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
src/lean/Init/Control/Lawful.lean | seq_eq_bind_map | [
{
"state_after": "no goals",
"state_before": "m : Type u → Type u_1\nα β : Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : m (α → β)\nx : m α\n⊢ (Seq.seq f fun x_1 => x) = do\n let x_1 ← f\n x_1 <$> x",
"tactic": "rw [← bind_map]"
}
] | [
66,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
65,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.single_subsingleton_eq_refl | [
{
"state_after": "case h.a\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq β\ninst✝¹ : DecidableEq γ\ninst✝ : Subsingleton α\na b i j : α\n⊢ j ∈ ↑(single a b) i ↔ j ∈ ↑(PEquiv.refl α) i",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ninst✝³ : ... | [
390,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/Convex/Integral.lean | Convex.integral_mem | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.117564\nm0 : MeasurableSpace α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nμ : MeasureTheory.Measure α\ns : Set E\nt : Set α\nf : α... | [
84,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_inf | [] | [
1181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1180,
1
] |
Mathlib/MeasureTheory/Group/GeometryOfNumbers.lean | MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd | [
{
"state_after": "E : Type u_2\nL : Type u_1\ninst✝⁶ : MeasurableSpace E\nμ : Measure E\nF s : Set E\ninst✝⁵ : AddCommGroup L\ninst✝⁴ : Countable L\ninst✝³ : AddAction L E\ninst✝² : MeasurableSpace L\ninst✝¹ : MeasurableVAdd L E\ninst✝ : VAddInvariantMeasure L E μ\nfund : IsAddFundamentalDomain L F\nhS : NullMe... | [
61,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.cancel_right | [] | [
214,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_compl | [] | [
341,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
9
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.congr | [
{
"state_after": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝¹⁵ : CommRing 𝕜\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module 𝕜 E\ninst✝¹² : TopologicalSpace E\ninst✝¹¹ : TopologicalAddGroup E\ninst✝¹⁰ : ContinuousConstSMul 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜 F\ninst✝⁷ : Top... | [
123,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/CategoryTheory/Bicategory/LocallyDiscrete.lean | CategoryTheory.LocallyDiscrete.eq_of_hom | [] | [
71,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_mul_left | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\nb c : α\n⊢ gcd (0 * b) (0 * c) = ↑normalize 0 * gcd b c",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\na b c : α\n⊢ a = 0 → gcd (a * b) (a * c) = ↑normali... | [
446,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_eq_left | [] | [
144,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_rotateR | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ dual (rotateR l x r) = rotateL (dual r) x (dual l)",
"tactic": "rw [← dual_dual (rotateL _ _ _), dual_rotateL, dual_dual, dual_dual]"
}
] | [
343,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.restrictScalars_top | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.sorted_last_eq_max' | [
{
"state_after": "α : Type ?u.20499\nβ : Type ?u.20502\ninst✝ : LinearOrder α\ns : Finset α\nh : card s - 1 < card s\n⊢ Finset.Nonempty s",
"state_before": "α : Type ?u.20499\nβ : Type ?u.20502\ninst✝ : LinearOrder α\ns : Finset α\nh : List.length (sort (fun x x_1 => x ≤ x_1) s) - 1 < List.length (sort (fun... | [
135,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | eq_inv_smul_iff₀ | [] | [
209,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.norm_exp_ofReal_mul_I | [
{
"state_after": "no goals",
"state_before": "t : ℝ\n⊢ ‖exp (↑t * I)‖ = 1",
"tactic": "simp only [norm_eq_abs, abs_exp_ofReal_mul_I]"
}
] | [
58,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_compl | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inf_subgroupOf_inf_normal_of_right | [] | [
3574,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3569,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_exists | [] | [
686,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.union | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.376032\nR : Type u_2\nK : Type ?u.376038\nM : Type u_1\nM' : Type ?u.376044\nM'' : Type ?u.376047\nV : Type u\nV' : Type ?u.376052\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''... | [
692,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eqOn_quadrant_I | [] | [
460,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_congr_norm_ae | [] | [
467,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.add_eq_left_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : LinearOrder R\nx y : Tropical R\n⊢ x + y = x ↔ x ≤ y",
"tactic": "rw [trop_add_def, trop_eq_iff_eq_untrop, ← untrop_le_iff, min_eq_left_iff]"
}
] | [
339,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.leadingCoeff_of_b_ne_zero' | [] | [
219,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
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