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/Topology/Algebra/InfiniteSum/Basic.lean | Equiv.hasSum_iff_of_support | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.59444\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g✝ : β → α\na b : α\ns : Finset β\ng : γ → α\ne : ↑(support f) ≃ ↑(support g)\nhe : ∀ (x : ↑(support f)), g ↑(↑e x) = f ↑x\nthis : (g ∘ Subtype.val) ∘ ↑e = f ∘ Subtype.val\n⊢ Ha... | [
239,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsInf_le_limsInf_of_le | [] | [
541,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_cyclicPermutations_iff | [
{
"state_after": "case pos\nα : Type u\nl✝ l'✝ l l' : List α\nhl : l = []\n⊢ cyclicPermutations l ~r cyclicPermutations l' ↔ l ~r l'\n\ncase neg\nα : Type u\nl✝ l'✝ l l' : List α\nhl : ¬l = []\n⊢ cyclicPermutations l ~r cyclicPermutations l' ↔ l ~r l'",
"state_before": "α : Type u\nl✝ l'✝ l l' : List α\n⊢ c... | [
701,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.not_sSameSide_bot | [] | [
230,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.exists_ne_zero_mem_isInteger | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝⁹ : CommRing R\nS : Submonoid R\nP : Type ?u.1050336\ninst✝⁸ : CommRing P\ninst✝⁷ : Algebra R P\nloc : IsLocalization S P\nK : Type u_2\nK' : Type ?u.1050800\ninst✝⁶ : Field K\ninst✝⁵ : Field K'\ninst✝⁴ : Algebra R K\ninst✝³ : IsFractionRing R K\ninst✝² : A... | [
986,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.zero_opow' | [
{
"state_after": "no goals",
"state_before": "a : Ordinal\n⊢ 0 ^ a = 1 - a",
"tactic": "simp only [opow_def, if_true]"
}
] | [
44,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_sq_mul_cos_sq | [
{
"state_after": "case h.e'_3\na b : ℝ\nn : ℕ\n⊢ (b - a) / 8 - (sin (4 * b) - sin (4 * a)) / 32 =\n ∫ (x : ℝ) in a..b, ((1 - cos (2 * x)) / 2) ^ 1 * ((1 + cos (2 * x)) / 2) ^ 1",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 2 * cos x ^ 2) = (b - a) / 8 - (sin (4 * b) - sin (4 * a)) / 32... | [
847,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_eq_bot_iff | [] | [
649,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.uniformContinuousOn_iff | [] | [
281,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_eq_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25696\nγ : Type ?u.25699\nl : List α\na : α\n⊢ ↑l = {a} ↔ l = [a]",
"tactic": "rw [← coe_singleton, coe_eq_coe, List.perm_singleton]"
}
] | [
355,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Subsemigroup.centralizer_eq_top_iff_subset | [] | [
207,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.differentiableWithinAt | [] | [
104,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Std/Data/List/Lemmas.lean | List.append_sublist_append_left | [] | [
363,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
361,
9
] |
src/lean/Init/WF.lean | WellFounded.induction | [] | [
53,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
52,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_cons_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.78062\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\nx✝ : a ≠ b\nh : a ≠ b := x✝\n⊢ indexOf a (b :: l) = succ (indexOf a l)",
"tactic": "simp only [indexOf, findIdx_cons, Bool.cond_eq_... | [
1174,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_eq_zero_of_dvd | [] | [
679,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
678,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_uIcc_right | [] | [
328,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Topology/Connected.lean | connectedComponent_subset_iInter_clopen | [] | [
998,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_max_of_aleph0_le_right | [
{
"state_after": "a b : Cardinal\nh' : a ≠ 0\nh : ℵ₀ ≤ b\n⊢ b * a = max b a",
"state_before": "a b : Cardinal\nh' : a ≠ 0\nh : ℵ₀ ≤ b\n⊢ a * b = max a b",
"tactic": "rw [mul_comm, max_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nh' : a ≠ 0\nh : ℵ₀ ≤ b\n⊢ b * a = ma... | [
630,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.insert_size | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nk : α\nv : β\nh : m.size = Bucket.size m.buckets\n⊢ (match\n AssocList.contains k\n m.buckets.val[USize.toNat (mkIdx (_ : 0 < Array.size m.buckets.val) (UInt64.toUSize (hash k))).val] with\n | tru... | [
187,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
174,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.combo_closure_interior_subset_interior | [
{
"state_after": "ι : Type ?u.64470\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\na b : 𝕜\nha : 0 ≤ a\nhb : 0 < b\nhab : a +... | [
145,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_pos | [] | [
674,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Data/Part.lean | Part.Dom.bind | [
{
"state_after": "case H\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.20498\no : Part α\nh : o.Dom\nf : α → Part β\nb : β\n⊢ b ∈ Part.bind o f ↔ b ∈ f (get o h)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.20498\no : Part α\nh : o.Dom\nf : α → Part β\n⊢ Part.bind o f = f (get o h)",
"tactic": ... | [
507,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
11
] |
Mathlib/Analysis/Normed/Field/InfiniteSum.lean | summable_norm_sum_mul_antidiagonal_of_summable_norm | [
{
"state_after": "R : Type u_1\nι : Type ?u.5264\nι' : Type ?u.5267\ninst✝ : NormedRing R\nf g : ℕ → R\nhf : Summable fun x => ‖f x‖\nhg : Summable fun x => ‖g x‖\nthis : Summable fun n => ∑ kl in antidiagonal n, ‖f kl.fst‖ * ‖g kl.snd‖\n⊢ Summable fun n => ‖∑ kl in antidiagonal n, f kl.fst * g kl.snd‖",
"s... | [
88,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Fin/Tuple/Reflection.lean | FinVec.forall_iff | [
{
"state_after": "m n : ℕ\nα : Type u_1\nβ : Type ?u.5607\nγ : Type ?u.5610\nP : (Fin 0 → α) → Prop\n⊢ P ![] ↔ P finZeroElim",
"state_before": "m n : ℕ\nα : Type u_1\nβ : Type ?u.5607\nγ : Type ?u.5610\nP : (Fin 0 → α) → Prop\n⊢ Forall P ↔ ∀ (x : Fin 0 → α), P x",
"tactic": "simp only [Forall, Fin.foral... | [
115,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.nthRoots_two_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nr : R\n⊢ nthRoots 2 r = 0 ↔ ¬IsSquare r",
"tactic": "simp_rw [isSquare_iff_exists_sq, eq_zero_iff_forall_not_mem, mem_nthRoots (by norm_num : 0 < 2),\n ... | [
809,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Order/RelClasses.lean | IsWellFounded.induction | [] | [
307,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Set/Intervals/Infinite.lean | NoMinOrder.infinite | [] | [
34,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_add' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ c d a b : α\n⊢ abs a ≤ abs b + abs (b + a)",
"tactic": "simpa using abs_add (-b) (b + a)"
}
] | [
276,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_zero | [
{
"state_after": "case a.h\nl : Type u_2\nm : Type u_3\nn : Type u_4\no : Type u_5\np : Type ?u.36307\nq : Type ?u.36310\nm' : o → Type ?u.36315\nn' : o → Type ?u.36320\np' : o → Type ?u.36325\nR : Type ?u.36328\nS : Type ?u.36331\nα : Type u_1\nβ : Type ?u.36337\ninst✝ : Zero α\ni : n ⊕ o\nj : l ⊕ m\n⊢ fromBlo... | [
240,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Rat/Sqrt.lean | Rat.sqrt_nonneg | [] | [
45,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.fst_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.5370740\nβ : Type u_2\nβ' : Type ?u.5370746\nγ : Type ?u.5370749\nE : Type ?u.5370752\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' :... | [
820,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_inf_le | [] | [
346,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_iSup_of_directed | [
{
"state_after": "M : Type u_2\nA : Type ?u.32885\nB : Type ?u.32888\ninst✝ : MulOneClass M\nι : Sort u_1\nhι : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : M\n⊢ (x ∈ ⨆ (i : ι), S i) → ∃ i, x ∈ S i",
"state_before": "M : Type u_2\nA : Type ?u.32885\nB : Type ?u.32888\ninst✝ :... | [
210,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.prod_map | [
{
"state_after": "ι : Type ?u.47834\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type u_1\nπ : ι → Type ?u.47848\nr : α → α → Prop\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\nf : α → γ\ng : β → δ\nhf : StrictMono f\nhg : StrictMono g\na b : α × β\n⊢ a.fst < b.fst ∧ a.... | [
1173,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | SubmonoidClass.mk_pow | [] | [
571,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.snd_prod | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type u_3\nC : Type u_4\ninst✝⁹ : CommSemiring R\ninst✝⁸ : Semiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Star A\ninst✝⁵ : Semiring B\ninst✝⁴ : Algebra R B\ninst✝³ : Star B\ninst✝² : Semiring C\ninst✝¹ : Algebra R C\ninst✝ : Star C\nf : A →⋆ₐ[R] B\ng : A →⋆ₐ[... | [
636,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
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] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.sum_support_decompose | [
{
"state_after": "ι : Type u_3\nR : Type ?u.193623\nM : Type u_1\nσ : Type u_2\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : AddCommMonoid M\ninst✝³ : SetLike σ M\ninst✝² : AddSubmonoidClass σ M\nℳ : ι → σ\ninst✝¹ : Decomposition ℳ\ninst✝ : (i : ι) → (x : { x // x ∈ ℳ i }) → Decidable (x ≠ 0)\nr : M\n⊢ ∑ i in Dfinsupp.supp... | [
183,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot | [] | [
185,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/CharP/Basic.lean | list_sum_pow_char | [] | [
414,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Fin/Tuple/BubbleSortInduction.lean | Tuple.bubble_sort_induction | [] | [
58,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformEmbedding.denseEmbedding | [] | [
234,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_δ₀ | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\nn : ℕ\n⊢ Isδ₀ (SimplexCategory.δ 0)",
"tactic": "rw [Isδ₀.iff]"
}
] | [
122,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/MinMax.lean | le_max_of_le_left | [] | [
84,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Computability/Language.lean | Language.zero_def | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_unique_nonzero_prime | [
{
"state_after": "case intro.intro.intro.mk\nR : Type u\nS : Type v\nT : Type w\nK : Type u'\ninst✝ : CommSemiring R\nP : Ideal R\nhPunique : ∀ (y : Ideal R), (fun P => P ≠ ⊥ ∧ Ideal.IsPrime P) y → y = P\nhPnonzero : P ≠ ⊥\nhPnot_top : P ≠ ⊤\nmem_or_mem'✝ : ∀ {x y : R}, x * y ∈ P → x ∈ P ∨ y ∈ P\n⊢ ∃! I, Ideal.... | [
91,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.pow_bit1 | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\nk : ℕ\n⊢ a ^ Nat.add (Nat.mul 2 k) 1 = a ^ k * a ^ k * a",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\nk : ℕ\nb... | [
666,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.mkₐ_toRingHom | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_le_of_lt | [] | [
906,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.localTrivAt_apply_mk | [] | [
759,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.dist_le_diam_of_mem | [] | [
2678,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2677,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_trans_apply | [] | [
296,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
9
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.head_main_ok | [
{
"state_after": "q : Λ'\ns : Option Γ'\nL : List ℕ\nc d : List Γ'\no : Option Γ' := List.casesOn L none fun x x => some Γ'.cons\n⊢ Reaches₁ (TM2.step tr) { l := some (head main q), var := s, stk := elim (trList L) [] c d }\n { l := some q, var := none, stk := elim (trList [List.headI L]) [] c d }",
"sta... | [
1493,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_coe_symm_apply_coe_apply | [] | [
335,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.inl_aut_inv | [
{
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"state_before": "N : Type u_1\nG : Type u_2\nH : Type ?u.83486\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\ng : G\nn : N\n⊢ ↑inl (↑(↑φ g)⁻¹ n) = ↑inr g⁻¹ * ↑inl n * ↑inr g",
"tactic": "rw [← MonoidHom.map_inv, inl_aut, inv_inv]"
}
] | [
166,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.zero_f | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_imI | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff' | [
{
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"state_before": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
151,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.coe_of_apply | [
{
"state_after": "case inl\nι : Type v\ndec_ι : DecidableEq ι\nβ : ι → Type w\ninst✝⁵ : (i : ι) → AddCommMonoid (β i)\nγ : Type u₁\ninst✝⁴ : AddCommMonoid γ\nM : Type u_1\nS : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid M\ninst✝¹ : SetLike S M\ninst✝ : AddSubmonoidClass S M\nA : ι → S\ni : ι\nx : {... | [
376,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.degree_cyclotomic | [
{
"state_after": "n : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\n⊢ degree (map (Int.castRingHom R) (cyclotomic n ℤ)) = ↑(Nat.totient n)",
"state_before": "n : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\n⊢ degree (cyclotomic n R) = ↑(Nat.totient n)",
"tactic": "rw [← map_cyclotom... | [
347,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.tendsto_comp | [] | [
958,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.zero_le | [] | [
1087,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1086,
11
] |
Mathlib/Data/Finset/PImage.lean | Finset.pimage_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : DecidableEq β\nf g : α →. β\ninst✝¹ : (x : α) → Decidable (f x).Dom\ninst✝ : (x : α) → Decidable (g x).Dom\ns t✝ : Finset α\nb : β\nt : Finset β\n⊢ pimage f s ⊆ t ↔ ∀ (x : α), x ∈ s → ∀ (y : β), y ∈ f x → y ∈ t",
"tactic"... | [
115,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.const_apply | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_prod' | [] | [
1421,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1419,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_sigma | [] | [
806,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
11
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_add_mul_I | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ exp (x + y * I) = exp x * (cos y + sin y * I)",
"tactic": "rw [exp_add, exp_mul_I]"
}
] | [
1085,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.centralBinom_eq_two_mul_choose | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_image_left | [
{
"state_after": "α : Type u_4\nα' : Type ?u.59914\nβ : Type u_3\nβ' : Type ?u.59920\nγ : Type u_2\nγ' : Type ?u.59926\nδ : Type u_1\nδ' : Type ?u.59932\nε : Type ?u.59935\nε' : Type ?u.59938\nζ : Type ?u.59941\nζ' : Type ?u.59944\nν : Type ?u.59947\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : De... | [
324,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_one_div_cancel | [] | [
78,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.star_iff | [] | [
738,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nS : C ⥤ D\nT : D\nA : CostructuredArrow S T\nP Q : (CostructuredArrow S T)ᵒᵖ\nf : P ⟶ A.op\ng : Q ⟶ A.op\ninst✝¹ : Mono f.unop.left.op\ninst✝ : Mono g.unop.left.op\nh : Subobject.mk f.unop.left.op ≤ Subobject.mk g.unop.left.op... | [
206,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_neg | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.62017\nG : Type ?u.62020\nA : Type u_1\nB : Type ?u.62026\nα : Type ?u.62029\nβ : Type ?u.62032\nγ : Type ?u.62035\nδ : Type ?u.62038\ninst✝² : Monoid M\ninst✝¹ : AddGroup A\ninst✝ : DistribMulAction M A\nr : M\nx : A\n⊢ r • -x + r • x ... | [
952,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/Data/List/Infix.lean | List.mem_of_mem_tail | [] | [
199,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_inj | [] | [
120,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.zero_mul | [] | [
167,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
165,
19
] |
Mathlib/Analysis/Normed/Field/InfiniteSum.lean | Summable.mul_norm | [] | [
44,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le_mul | [] | [
386,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_of_monotone_of_subseq | [] | [
1733,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1730,
1
] |
Mathlib/Analysis/PSeries.lean | NNReal.summable_one_div_rpow | [
{
"state_after": "no goals",
"state_before": "p : ℝ\n⊢ (Summable fun n => 1 / ↑n ^ p) ↔ 1 < p",
"tactic": "simp"
}
] | [
286,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.comp_id | [] | [
1262,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/Dynamics/Ergodic/Conservative.lean | MeasureTheory.MeasurePreserving.conservative | [] | [
67,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
11
] |
Mathlib/Analysis/MeanInequalities.lean | Real.inner_le_Lp_mul_Lq_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhpq : IsConjugateExponent p q\nhf : ∀ (i : ι), i ∈ s → 0 ≤ f i\nhg : ∀ (i : ι), i ∈ s → 0 ≤ g i\n⊢ ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q)",
"tactic": "convert inner_... | [
602,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Analysis/Complex/Circle.lean | coe_inv_circle_eq_conj | [
{
"state_after": "no goals",
"state_before": "z : { x // x ∈ circle }\n⊢ ↑z⁻¹ = ↑(starRingEnd ℂ) ↑z",
"tactic": "rw [coe_inv_circle, inv_def, normSq_eq_of_mem_circle, inv_one, ofReal_one, mul_one]"
}
] | [
85,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_neBot_iff | [] | [
995,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicRel.refl | [] | [
686,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.sub_floor_div_mul_lt | [
{
"state_after": "F : Type ?u.186509\nα : Type ?u.186512\nβ : Type ?u.186515\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\nz : ℤ\na✝ : α\nk : Type u_1\ninst✝¹ : LinearOrderedField k\ninst✝ : FloorRing k\nb a : k\nhb : 0 < b\n⊢ a / b < ↑⌊a / b⌋ + 1",
"state_before": "F : Type ?u.186509\nα : Type ?u.18... | [
1033,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
src/lean/Init/Core.lean | ne_true_of_not | [] | [
586,
17
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
583,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_star | [] | [
1469,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Mathlib/Topology/Connected.lean | IsClopen.eq_univ | [] | [
848,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.ext | [] | [
215,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toEquiv_eq_coe | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | le_of_abs_le | [] | [
248,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.funext | [] | [
57,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_of_add_le_add_right | [] | [
762,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
11
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_iff_sameRay_vsub | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.601094\nP : Type u_3\nP' : Type ?u.601100\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y z : P\nh : SameRay R (y -ᵥ x) (z -ᵥ y)\n⊢ Wbtw R x y z",
"state_before": "R : Type u_1\nV : Type u_2\n... | [
906,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.surjective | [] | [
346,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
11
] |
Mathlib/Topology/Constructions.lean | continuousAt_subtype_val | [] | [
1058,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Order/Cover.lean | Prod.covby_iff | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b₂ : β\ny : α × β\nfst✝ : α\nsnd✝ : β\n⊢ (fst✝, snd✝) ⋖ y ↔\n (fst✝, snd✝).fst ⋖ y.fst ∧ (fst✝, snd✝).snd = y.snd ∨ (fst✝, snd✝).snd ⋖ y.snd ∧ (fst✝, snd✝).fst = y.fst",
"state_before... | [
565,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | isometry_subtype_coe | [] | [
176,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
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