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/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.subgraphOfAdj_symm | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.218062\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nv w : V\nhvw : Adj G v w\n⊢ subgraphOfAdj G (_ : Adj G w v) = subgraphOfAdj G hvw",
"tactic": "ext <;> simp [or_comm, and_comm]"
}
] | [
910,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Order/Directed.lean | DirectedOn.mono | [] | [
91,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Parity.lean | Odd.pow_nonpos | [
{
"state_after": "case intro\nF : Type ?u.107719\nα : Type ?u.107722\nβ : Type ?u.107725\nR : Type u_1\ninst✝ : LinearOrderedRing R\na : R\nn : ℕ\nha : a ≤ 0\nk : ℕ\nhk : n = 2 * k + 1\n⊢ a ^ n ≤ 0",
"state_before": "F : Type ?u.107719\nα : Type ?u.107722\nβ : Type ?u.107725\nR : Type u_1\ninst✝ : LinearOrd... | [
479,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.image_mem_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.221422\nι : Sort x\nf : Filter α\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nhf : Injective m\nh : m '' s ∈ map m f\n⊢ s ∈ f",
"tactic": "rwa [← preimage_image_eq s hf]"
}
] | [
1842,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1841,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.mul' | [] | [
139,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_one_unitClosedBall | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.measure_Ioo_pos | [] | [
144,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.Wallis.W_eq_factorial_ratio | [
{
"state_after": "case zero\n\n⊢ W Nat.zero = ↑(2 ^ (4 * Nat.zero)) * ↑(Nat.zero ! ^ 4) / (↑((2 * Nat.zero)! ^ 2) * (2 * ↑Nat.zero + 1))\n\ncase succ\nn : ℕ\nIH : W n = ↑(2 ^ (4 * n)) * ↑(n ! ^ 4) / (↑((2 * n)! ^ 2) * (2 * ↑n + 1))\n⊢ W (Nat.succ n) = ↑(2 ^ (4 * Nat.succ n)) * ↑((Nat.succ n)! ^ 4) / (↑((2 * Nat... | [
80,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioo_eq_Ioo | [] | [
1565,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1562,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_injective | [] | [
804,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.lt_fold_max | [] | [
263,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.convergents_eq_convergents' | [
{
"state_after": "case zero\nK : Type u_1\nn : ℕ\ng✝ : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : LinearOrderedField K\ns_pos✝ : ∀ {gp : Pair K} {m : ℕ}, m < n → Stream'.Seq.get? g✝.s m = some gp → 0 < gp.a ∧ 0 < gp.b\ng : GeneralizedContinuedFraction K\ns_pos : ∀ {gp : Pair K} {m : ℕ}, m... | [
395,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.173757\nι : Sort x\np : α → Prop\nfs : Set (Filter α)\n⊢ (∃ᶠ (x : α) in sSup fs, p x) ↔ ∃ f, f ∈ fs ∧ ∃ᶠ (x : α) in f, p x",
"tactic": "simp only [Filter.Frequently, not_forall, eventually_sSup, exists_prop]"
... | [
1406,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.ext' | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.3515\nm : Type u_2\nn : Type u_1\no : Type ?u.3524\nm' : o → Type ?u.3529\nn' : o → Type ?u.3534\nR : Type ?u.3537\nS : Type ?u.3540\nα : Type v\nβ : Type w\nγ : Type ?u.3547\nM N : Matrix m n α\nh : ∀ (i : m), M i = N i\ni : m\n⊢ ∀ (j : n), M i j = ... | [
99,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Order/BoundedOrder.lean | max_top_right | [] | [
863,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Topology/Basic.lean | tendsto_nhds | [] | [
1027,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.normalize_content | [] | [
177,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_union_right | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.40835\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns✝ t s₁ s₂ t₁✝ t₂✝ u : Set E\nx y : E\ns t₁ t₂ : Set E\n⊢ convexJoin 𝕜 s (t₁ ∪ t₂) = convexJoin 𝕜 s t₁ ∪ convexJoin 𝕜 s t₂",
"tacti... | [
92,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.card_support_eq' | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nn : ℕ\nk : Fin n → ℕ\nx : Fin n → R\nhk : Function.Injective k\nhx : ∀ (i : Fin n), x i ≠ 0\n⊢ support (∑ i : Fin n, ↑C (x i) * X ^ k i) = image k univ",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nn : ℕ\nk : Fin n → ℕ\nx : Fin n... | [
306,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/Constructions.lean | isOpen_set_pi | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.220683\nδ : Type ?u.220686\nε : Type ?u.220689\nζ : Type ?u.220692\nι : Type u_1\nπ : ι → Type u_2\nκ : Type ?u.220703\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf : α → (i : ι) → π i\ni : Set ι\ns : (a : ι) → Set (π a)\nhi : Set... | [
1285,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_le_domain | [] | [
1323,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableWithinAt.comp | [] | [
121,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_ofReal_im | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℂ\nx : ℝ\n⊢ (sin ↑x).im = 0",
"tactic": "rw [← ofReal_sin_ofReal_re, ofReal_im]"
}
] | [
943,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.div2_bit | [
{
"state_after": "a b✝ : ℤ\nn✝ : ℕ\nb : Bool\nn : ℤ\n⊢ (bif b then 1 else 0) / 2 = 0\n\ncase H\na b✝ : ℤ\nn✝ : ℕ\nb : Bool\nn : ℤ\n⊢ 2 ≠ 0",
"state_before": "a b✝ : ℤ\nn✝ : ℕ\nb : Bool\nn : ℤ\n⊢ div2 (bit b n) = n",
"tactic": "rw [bit_val, div2_val, add_comm, Int.add_mul_ediv_left, (_ : (_ / 2 : ℤ) = 0)... | [
131,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.adjugate | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.50563\nm : Type u_1\nn : Type ?u.50569\nA✝ : Matrix n n α\ninst✝³ : CommRing α\ninst✝² : StarRing α\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nA : Matrix m m α\nhA : IsHermitian A\n⊢ IsHermitian (Matrix.adjugate A)",
"tactic": "sim... | [
251,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.prod_map_id | [
{
"state_after": "case a.h\nn : ℕ\nα β : TypeVec n\ni : Fin2 n\nx : (α ⊗ β) i\n⊢ (id ⊗' id) i x = id i x",
"state_before": "n : ℕ\nα β : TypeVec n\n⊢ (id ⊗' id) = id",
"tactic": "ext i x : 2"
},
{
"state_after": "case a.h.fz\nn n✝ : ℕ\nα β : TypeVec (Nat.succ n✝)\nx : (α ⊗ β) Fin2.fz\n⊢ (id Fin2... | [
780,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_transpose_mul_diag | [
{
"state_after": "R : Type u_2\nα : Type u_1\nG : SimpleGraph α\ninst✝² : Fintype α\ninst✝¹ : NonAssocSemiring R\na b : α\ne : Sym2 α\ninst✝ : DecidableRel G.Adj\n⊢ ↑(card (filter (fun x => e ∈ incidenceSet G x) univ)) = if e ∈ edgeSet G then 2 else 0",
"state_before": "R : Type u_2\nα : Type u_1\nG : Simpl... | [
170,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_inf_principal_univ_pi_eq_bot | [
{
"state_after": "case mp\nι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\n⊢ pi f ⊓ 𝓟 (Set.pi univ s) = ⊥ → ∃ i, f i ⊓ 𝓟 (s i) = ⊥\n\ncase mpr\nι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\n⊢ (∃ i, f i ⊓ 𝓟 (s i) = ⊥) → pi... | [
128,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOf.ext_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁶ : Ring R\nQ : TypeMax\ninst✝⁵ : AddCommGroup Q\ninst✝⁴ : Module R Q\nM N : Type (max u v)\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\na b : ExtensionOf i f\nr : a = ... | [
134,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.out_no_max_of_succ_lt | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.103999\nβ : Type ?u.104002\nγ : Type ?u.104005\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nho : ∀ (a : Ordinal), a < o → succ a < o\n⊢ ∀ (a : Ordinal), (a < type fun a b => a < b) → succ a < type fun a b => a < b",
"tactic... | [
365,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/Holor.lean | Holor.slice_zero | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.erange_coe | [] | [
592,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.trans_apply | [] | [
913,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Computability/Partrec.lean | Computable.vector_ofFn' | [] | [
395,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.int_cast_ofNat | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : AddGroupWithOne R\nn : ℕ\ninst✝ : AtLeastTwo n\n⊢ ↑(OfNat.ofNat n) = OfNat.ofNat n",
"tactic": "simpa only [OfNat.ofNat] using AddGroupWithOne.intCast_ofNat (R := R) n"
}
] | [
76,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_le_of_right_le | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred ((fun x x_1 => x ≤ x_1) b)\n⊢ ∅.val = ∅",
"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred ((fun x x_1 => x ≤ x_1) b)\n⊢ fil... | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/List/Func.lean | List.Func.length_sub | [] | [
380,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_atBot_iff | [] | [
330,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.functorPullback_pushforward_covering | [
{
"state_after": "C : Type u_3\ninst✝⁴ : Category C\nD : Type u_4\ninst✝³ : Category D\nE : Type ?u.8038\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.8090\ninst✝¹ : Category A\nG : C ⥤ D\nH✝ : CoverDense K G\ninst✝ : Full G\nH : CoverDense... | [
126,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_antiperiodic | [
{
"state_after": "θ : Angle\n⊢ sin (θ + ↑π) = -sin θ",
"state_before": "⊢ Function.Antiperiodic sin ↑π",
"tactic": "intro θ"
},
{
"state_after": "case h\nx✝ : ℝ\n⊢ sin (↑x✝ + ↑π) = -sin ↑x✝",
"state_before": "θ : Angle\n⊢ sin (θ + ↑π) = -sin θ",
"tactic": "induction θ using Real.Angle.in... | [
384,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.ext | [] | [
211,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_default_eq_getI | [] | [
4484,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4483,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_union_right | [] | [
168,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_inv_of_blockTriangular | [
{
"state_after": "α : Type u_1\nβ : Type ?u.170494\nm : Type u_2\nn : Type ?u.170500\no : Type ?u.170503\nm' : α → Type ?u.170508\nn' : α → Type ?u.170513\nR : Type v\ninst✝⁶ : CommRing R\nM : Matrix m m R\nb : m → α\ninst✝⁵ : DecidableEq m\ninst✝⁴ : Fintype m\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\ninst✝¹... | [
330,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.congr | [] | [
909,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddAbove.image2_bddBelow | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Antitone (swap f b)\nh₁ : ∀ (a : α), Antitone (f a)\na : α\nha : a ∈ upperBounds s\nb : β\nhb : b... | [
1486,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1484,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular | [
{
"state_after": "α : Type u_1\nβ : Type ?u.449524\nm : MeasurableSpace α\nμ ν : Measure α\ns t : SignedMeasure α\nf : α → ℝ\nhf : Measurable f\nhtμ :\n (toJordanDecomposition t).posPart ⟂ₘ VectorMeasure.ennrealToMeasure (toENNRealVectorMeasure μ) ∧\n (toJordanDecomposition t).negPart ⟂ₘ VectorMeasure.ennre... | [
971,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image_image₂_distrib | [
{
"state_after": "α : Type u_3\nα' : Type u_5\nβ : Type u_4\nβ' : Type u_6\nγ : Type u_2\nγ' : Type ?u.79278\nδ : Type u_1\nδ' : Type ?u.79284\nε : Type ?u.79287\nε' : Type ?u.79290\nζ : Type ?u.79293\nζ' : Type ?u.79296\nν : Type ?u.79299\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : DecidableEq ... | [
414,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_simpleFunc_larger_space | [
{
"state_after": "α : Type ?u.1700816\nE : Type ?u.1700819\nF : Type u_2\n𝕜 : Type ?u.1700825\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² ... | [
1747,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
1
] |
Mathlib/Computability/Partrec.lean | Computable.option_casesOn | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.183096\nσ : Type u_3\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\no : α → Option β\nf : α → σ\ng : α → β → σ\nho : Computable o\nhf : Computable f\nhg : Computable₂ g\na :... | [
689,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_mono' | [] | [
1537,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.size_toArray | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nas : List α\n⊢ size (List.toArray as) = List.length as",
"tactic": "simp [size]"
}
] | [
24,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
9
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.stepNormal.is_ret | [
{
"state_after": "case zero'\nk : Cont\nv : List ℕ\n⊢ ∃ k' v', stepNormal Code.zero' k v = Cfg.ret k' v'\n\ncase succ\nk : Cont\nv : List ℕ\n⊢ ∃ k' v', stepNormal Code.succ k v = Cfg.ret k' v'\n\ncase tail\nk : Cont\nv : List ℕ\n⊢ ∃ k' v', stepNormal Code.tail k v = Cfg.ret k' v'\n\ncase cons\na✝¹ a✝ : Code\na_... | [
625,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_lt_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nhn : 1 ≤ n\n⊢ 2 ≤ 0 → descFactorial n 0 < n ^ 0",
"tactic": "rintro ⟨⟩"
},
{
"state_after": "n : ℕ\nhn : 1 ≤ n\na✝ : 2 ≤ 1\n⊢ descFactorial n 1 < n ^ 1",
"state_before": "n : ℕ\nhn : 1 ≤ n\n⊢ 2 ≤ 1 → descFactorial n 1 < n ^ 1",
"tactic... | [
482,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.range_projIcc | [] | [
92,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_lt_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\na : α\n⊢ Bounded (fun x x_1 => x < x_1) (Iic a)",
"tactic": "simp only [← bounded_le_iff_bounded_lt, bounded_le_Iic]"
}
] | [
191,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofAdd_neg | [] | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_le_sin_of_le_of_le_pi_div_two | [] | [
607,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/CategoryTheory/Functor/Functorial.lean | CategoryTheory.Functorial.map_comp | [] | [
60,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryFan.π_app_right | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_eq_single_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.55526\nγ : Type ?u.55529\nι : Type ?u.55532\nM : Type u_2\nM' : Type ?u.55538\nN : Type ?u.55541\nP : Type ?u.55544\nG : Type ?u.55547\nH : Type ?u.55550\nR : Type ?u.55553\nS : Type ?u.55556\ninst✝ : Zero M\na a' : α\nb : M\na₁ a₂ : α\nb₁ b₂ : M\n⊢ single a₁... | [
418,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.nat_cast_eq_iff | [
{
"state_after": "case mp\nK : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx y : ℕ\nH : ↑x = ↑y\n⊢ ↑x = ↑y\n\ncase mpr\nK : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx y : ℕ\nH : ↑x = ↑y\n⊢ ↑x = ↑y",
"state_before": "K : Type ... | [
442,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.monic_scaleRoots_iff | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.36545\nK : Type ?u.36548\nR : Type u_1\nS : Type ?u.36554\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\ns : R\n⊢ Monic (scaleRoots p s) ↔ Monic p",
"tactic": "simp... | [
94,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/Atoms.lean | IsCoatom.sup_eq_top_of_ne | [] | [
221,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.coeff_restriction' | [] | [
288,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Subtype.lean | Subtype.ext_iff | [] | [
73,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Iio_ae_eq_Iic | [] | [
3332,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3331,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.isClosed_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.64146\nδ : Type ?u.64149\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\ns : Set β\n⊢ IsClosed (↑h ⁻¹' s) ↔ IsClosed s",
"tactic": "simp o... | [
320,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_sum_index' | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nι : Type u_2\nγ : Type ?u.618499\nA : Type u_3\nB : Type ?u.618505\nC : Type u_1\ninst✝² : AddCommMonoid A\ninst✝¹ : AddCommMonoid B\ninst✝ : AddCommMonoid C\nt : ι → A → C\nh0 : ∀ (i : ι), t i 0 = 0\nh1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x +... | [
639,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.monotone_filter_left | [] | [
1956,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1956,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.sum_apply | [] | [
950,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.478682\nγ : Type ?u.478685\ninst✝ : DecidableEq α\nl✝ l' : List α\na : α\nl : List α\n⊢ toFinset l = ∅ ↔ l = []",
"tactic": "cases l <;> simp"
}
] | [
3334,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3333,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.not_dvd_of_degree_lt | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np✝ q✝ p q : R[X]\nh0 : q ≠ 0\nhl : degree q < degree p\nhcontra : p ∣ q\n⊢ False",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivi... | [
193,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_pow_mul_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nk n : ℕ\nr : R\n⊢ X ^ k * ↑(monomial n) r = ↑(monomial (n + k)) r",
"tactic": "rw [X_pow_mul, monomial_mul_X_pow]"
}
] | [
642,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.not_le_eq | [] | [
722,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
721,
1
] |
Mathlib/Topology/PathConnected.lean | joinedIn_iff_joined | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.609371\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.609386\nF : Set X\nx_in : x ∈ F\ny_in : y ∈ F\nh : Joined { val := x, property := x_in } { val := y, property := y_in }\n⊢ ∀ (t : ↑I), ↑(Path.map (J... | [
864,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_right_cancel | [
{
"state_after": "m n a b c d : ℤ\nh₁ : c ≡ d [ZMOD n]\nh₂ : c + a ≡ d + b [ZMOD n]\n⊢ a ≡ b [ZMOD n]",
"state_before": "m n a b c d : ℤ\nh₁ : c ≡ d [ZMOD n]\nh₂ : a + c ≡ b + d [ZMOD n]\n⊢ a ≡ b [ZMOD n]",
"tactic": "rw [add_comm a, add_comm b] at h₂"
},
{
"state_after": "no goals",
"state_... | [
173,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_nil | [] | [
3262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3261,
1
] |
Mathlib/Analysis/Convex/Combination.lean | mk_mem_convexHull_prod | [
{
"state_after": "R : Type u_3\nE : Type u_2\nF : Type u_1\nι : Type ?u.246500\nι' : Type ?u.246503\nα : Type ?u.246506\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\ninst✝ : O... | [
417,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.map_of_injective | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type u_3\nG : Type ?u.2380264\nR : Type ?u.2380267\nS : Type ?u.2380270\nF : Type u_1\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ninst✝¹ : DivisionCommMonoid G\nk l : ℕ\nζ : M\nf : F\nh✝ : IsPrimitiveRoot ζ k\ninst✝ : MonoidHomClass F M N\nh... | [
515,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.orthonormal_adjustToOrientation | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nne : Nonempty ι\ne f : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\n⊢ ∀ (i : ι),\n ↑(Basis.adjustToOrientation (OrthonormalBasis.toBasis e) x) i = ↑e i ∨\n... | [
108,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.gcdB_zero_right | [
{
"state_after": "s : ℕ\nh : s ≠ 0\n⊢ (xgcdAux s 1 0 0 0 1).snd.snd = 0",
"state_before": "s : ℕ\nh : s ≠ 0\n⊢ gcdB s 0 = 0",
"tactic": "unfold gcdB xgcd"
},
{
"state_after": "case intro\ns : ℕ\nh : succ s ≠ 0\n⊢ (xgcdAux (succ s) 1 0 0 0 1).snd.snd = 0",
"state_before": "s : ℕ\nh : s ≠ 0\n⊢... | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_respects | [
{
"state_after": "case halt\nv : List ℕ\ns : Option Γ'\n⊢ ∃ b₂,\n TrCfg (stepRet Cont.halt v) b₂ ∧\n Reaches₁ (TM2.step tr)\n { l := some (Λ'.ret (trCont Cont.halt)), var := s, stk := elim (trList v) [] [] (trContStack Cont.halt) } b₂\n\ncase cons₁\na✝² : Code\na✝¹ : List ℕ\na✝ : Cont\na_ih✝ :\n ... | [
1688,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1637,
1
] |
Mathlib/Topology/MetricSpace/Polish.lean | TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist | [] | [
278,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.const_smul | [] | [
1560,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compLeft_injective | [
{
"state_after": "case h\nR : Type ?u.1793734\nM : Type ?u.1793737\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type u_1\nM₁ : Type u_2\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type ?u.1794385\nM₂ : Type ?u.1794388\ninst✝¹⁰ : CommSemiring R₂\nin... | [
1534,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/Order/Max.lean | isMin_iff_forall_not_lt | [] | [
332,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_subset_interior_cthickening | [] | [
1138,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_hyperplane | [] | [
446,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Std/Data/Option/Lemmas.lean | Option.bind_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nx : Option α\nf : α → Option β\ng : β → Option γ\n⊢ Option.bind (Option.bind x f) g = Option.bind x fun y => Option.bind (f y) g",
"tactic": "cases x <;> rfl"
}
] | [
105,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
104,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_induction_left | [
{
"state_after": "case hz\nα : Type ?u.149471\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\ng : G\nP : G → Prop\nh_one : P 1\nh_mul : ∀ (a : G), P a → P (g * a)\nh_inv : ∀ (a : G), P a → P (g⁻¹ * a)\n⊢ P (g ^ 0)\n\ncase hp\nα : Type ?u.149471... | [
285,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_mul_rat | [] | [
340,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateRow_subsingleton | [
{
"state_after": "case a.h\nl : Type ?u.1222192\nm : Type u_1\nn : Type u_2\no : Type ?u.1222201\nm' : o → Type ?u.1222206\nn' : o → Type ?u.1222211\nR : Type u_3\nS : Type ?u.1222217\nα : Type v\nβ : Type w\nγ : Type ?u.1222224\nM : Matrix m n α\ni✝ : m\nj : n\nb✝ : n → α\nc : m → α\ninst✝ : Subsingleton m\nA ... | [
2798,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2795,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_le_ord | [] | [
1413,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1412,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_def_zero | [] | [
907,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_mul_X_pow | [
{
"state_after": "case a\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nhp : p ≠ 0\nn : ℕ\n⊢ natTrailingDegree (p * X ^ n) ≤ natTrailingDegree p + n\n\ncase a\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nhp : p ≠ 0\nn : ℕ\n⊢ natTrailingDegree... | [
355,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhdsWithin_Ioi_nat_neBot | [] | [
223,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.6054\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\ninst✝ : DecidableEq β\n⊢ lcm (∅ ∪ s₂) f = GCDMonoid.lcm (lcm ∅ f) (lcm s₂ f)",
"tactic": "rw [empty_union, lcm_e... | [
100,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_eq_filter | [
{
"state_after": "case a\nα : Type u_1\ns✝ t : Finset α\nn : ℕ\ns a✝ : Finset α\n⊢ a✝ ∈ powersetLen n s ↔ a✝ ∈ filter (fun x => card x = n) (powerset s)",
"state_before": "α : Type u_1\ns✝ t : Finset α\nn : ℕ\ns : Finset α\n⊢ powersetLen n s = filter (fun x => card x = n) (powerset s)",
"tactic": "ext"
... | [
238,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_symm | [] | [
439,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
9
] |
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