module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 141,
"column": 6
} | {
"line": 141,
"column": 36
} | [
{
"pp": "case cons.cons\nexp : ℝ\nexps : List ℝ\nih✝ :\n ∀ {basis : Basis},\n WellFormedBasis basis →\n (fun a ↦ (List.zipWith (fun exp b ↦ b a ^ exp) (List.map (fun x ↦ -x) exps) basis).prod) =ᶠ[atTop] fun a ↦\n (List.zipWith (fun exp b ↦ b a ^ exp) exps basis).prod⁻¹\nbasis_hd : ℝ → ℝ\nbasis_t... | grind [Real.rpow_neg h_pos.le] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 265,
"column": 10
} | {
"line": 265,
"column": 21
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\nf g : β →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.DeriveCountable | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 41
} | [
{
"pp": "p : Prop\na b b' : ℕ\nh : b = b' → p\n⊢ Nat.pair a b = Nat.pair a b' → p",
"usedConstants": [
"Eq.mpr",
"Nat.pair_eq_pair._simp_1",
"congrArg",
"id",
"Nat.pair",
"And",
"implies_congr",
"Nat",
"True",
"eq_self",
"Eq.refl",
"con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 302,
"column": 2
} | {
"line": 302,
"column": 17
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\ninst✝ : FriendlyOperationClass op\nb : β\nh : F b = none\nthis :\n match F b with\n | none => ⋯.choose b = nil\n | some (a, c, b') => ⋯.choose b = Seq.cons a (op c (⋯.choose b'))\n⊢ gcorec F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 310,
"column": 2
} | {
"line": 310,
"column": 17
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\ninst✝ : FriendlyOperationClass op\nb : β\na : α\nc : γ\nb' : β\nh : F b = some (a, c, b')\nthis :\n match F b with\n | none => ⋯.choose b = nil\n | some (a, c, b') => ⋯.choose b = Seq.cons a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 222,
"column": 2
} | {
"line": 222,
"column": 24
} | [
{
"pp": "case a\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : Multiseries basis_hd basis_tl\nh : ms.destruct = none\n⊢ Seq.destruct ms = none",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 354,
"column": 10
} | {
"line": 354,
"column": 43
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\ns t : Multiseries basis_hd basis_tl\nf g : ℝ → ℝ\nh : mk s f = mk t g\n⊢ s = t ∧ f = g",
"usedConstants": [
"Stream'.Seq",
"Real",
"congrArg",
"Prod.mk_inj",
"ComputeAsymptotics.MultiseriesExpansion.mk.eq_1",
"Eq.mp",
"Pr... | by rwa [mk, mk, Prod.mk_inj] at h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 481,
"column": 6
} | {
"line": 481,
"column": 17
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted",
"usedConstants": [
"ComputeAsymptotics.MultiseriesExpansion... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 482,
"column": 6
} | {
"line": 482,
"column": 17
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq",
"usedConstants": [
"Eq.mpr",
"St... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 486,
"column": 6
} | {
"line": 486,
"column": 17
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ ∀ x ∈ ms.seq, x.2.Sorted",
"usedConstants": [
"ComputeAsymptotics.Multiseri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 487,
"column": 6
} | {
"line": 487,
"column": 17
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq",
"usedConstants": [
"Eq.mpr"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 515,
"column": 43
} | {
"line": 515,
"column": 66
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\nh_coef : coef.Sorted\nexp✝ : ℝ\ncoef✝ : MultiseriesExpansion basis_tl\ntl✝ : Multiseries basis_hd basis_tl\nh_comp : (Multiseries.cons exp✝ coef✝ tl✝).leadingExp < ↑exp\nh_tl_coef : ∀ x ∈ (mk (Multiseries.cons exp✝ coef✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 524,
"column": 4
} | {
"line": 524,
"column": 15
} | [
{
"pp": "case seq.left\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh_coef : ∀ x ∈ (mk (Multiseries.cons exp coef tl) 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk (Multiseries.cons exp coef tl) 0).seq\n⊢ coef.S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 538,
"column": 24
} | {
"line": 538,
"column": 35
} | [
{
"pp": "case cons\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh : (Multiseries.cons exp coef tl).Sorted\n⊢ (Multiseries.cons exp coef tl).tail.Sorted",
"usedConstants": [
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 599,
"column": 41
} | {
"line": 599,
"column": 52
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nf : ℝ → ℝ\nh : (mk (Multiseries.cons exp coef tl) f).Sorted\n⊢ (Multiseries.cons exp coef tl).Sorted",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 604,
"column": 2
} | {
"line": 604,
"column": 13
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nf : ℝ → ℝ\nh_sorted : ms.Sorted\n⊢ (ms.replaceFun f).Sorted",
"usedConstants": [
"ComputeAsymptotics.MultiseriesExpansion.replaceFun",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.Sorted",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.BigOperators | {
"line": 258,
"column": 9
} | {
"line": 258,
"column": 20
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : Fintype α\nelems : Finset α\ncomplete : ∀ (x : α), x ∈ elems\nx : α\n⊢ x ∈ Finset.univ ↔ x ∈ elems",
"usedConstants": [
"Eq.mpr",
"Finset.univ",
"congrArg",
"Finset",
"true_iff",
"Membership.mem",
"id",
"Iff",
"Fins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 24
} | [
{
"pp": "case inl\np q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nh : ∀ (m : ℕ), 0 ≠ m ^ q\n⊢ 0 ^ p ≠ m ^ q",
"usedConstants": [
"Nat.instMonoid",
"id",
"Ne",
"instOfNatNat",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instHPow",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 59,
"column": 29
} | {
"line": 59,
"column": 49
} | [
{
"pp": "n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nhf : n.factorization = q • f\n⊢ f 0 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 13
} | [
{
"pp": "case inr.h\nn p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ q ∣ n.factorization z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 65,
"column": 56
} | {
"line": 65,
"column": 67
} | [
{
"pp": "n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ p * n.factorization z = q * ?m.185",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 19
} | [
{
"pp": "case H1.H1.a\na b d : ℕ\nh_coprime : a.Coprime b\nq : ℚ\nhq : 0 ≤ q\nhb_zero : ¬b = 0\nx' : ℤ := ⋯\ny : ℕ := ⋯\nx : ℕ\nhx' : x' = ↑x\nha : a ≠ x ^ d\nh : a * y ^ d = b * x ^ d\n⊢ x.Coprime y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 71
} | [
{
"pp": "case h\nx y : ℝ\nx_num x_den y_num y_den k_den : ℕ\nhy_isNNRat : IsNNRat y y_num y_den\nhx_coprime : x_num.Coprime x_den\nhy_coprime : y_num.Coprime y_den\nhd1 : k_den ^ y_den < x_den\nhd2 : x_den < (k_den + 1) ^ y_den\nhx_inv : Invertible ↑x_den\nhx_eq : x = ↑x_num * ⅟↑x_den\n⊢ Irrational (x ^ y)⁻¹",
... | rw [← Real.inv_rpow (by simp only [hx_eq, invOf_eq_inv]; positivity)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Tactic.NormNum.LegendreSymbol | {
"line": 76,
"column": 98
} | {
"line": 82,
"column": 41
} | [
{
"pp": "b : ℕ\nhb : (b / 2).beq 0 = false\n⊢ jacobiSymNat 0 b = 0",
"usedConstants": [
"Eq.mpr",
"Trans.trans",
"instHDiv",
"HMul.hMul",
"Nat.ne_of_beq_eq_false",
"of_decide_eq_true",
"congrArg",
"Nat.succ_le_of_lt",
"_private.Mathlib.Tactic.NormNum.Leg... | by
rw [jacobiSymNat, Nat.cast_zero, jacobiSym.zero_left ?_]
calc
1 < 2 * 1 := by decide
_ ≤ 2 * (b / 2) :=
Nat.mul_le_mul_left _ (Nat.succ_le_of_lt (Nat.pos_of_ne_zero (Nat.ne_of_beq_eq_false hb)))
_ ≤ b := Nat.mul_div_le b 2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.NormNum.RealSqrt | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 89
} | [
{
"pp": "num denom : ℕ\ninv : Invertible ↑denom\nh₁ : 0 ≤ ↑↑num * ⅟↑denom\n⊢ √(↑(Int.negOfNat num) * ⅟↑denom) = ↑0",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.instLE",
"Real",
"NonUnitalCommRing.toNonUnitalN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Sat.FromLRAT | {
"line": 178,
"column": 23
} | {
"line": 178,
"column": 34
} | [
{
"pp": "case cons.cons\np a : Prop\nas : List Prop\nb : Prop\nas₁ : List Prop\nih : ∀ (n n' : ℕ), n' = as₁.length + n → ∀ (bs : List Prop), mk (as₁.reverseAux bs) n' ↔ mk bs n\n⊢ ∀ (n n' : ℕ), n' = (b :: as₁).length + n → ∀ (bs : List Prop), mk ((b :: as₁).reverseAux bs) n' ↔ mk bs n",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 27,
"column": 69
} | {
"line": 27,
"column": 80
} | [
{
"pp": "m n : ℕ\nhnm : n.blt m = true\n⊢ Icc m n = ∅",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"id",
"Finset.Icc_eq_empty_iff._simp_1",
"LE.le",
"Finset.Icc"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 30,
"column": 76
} | {
"line": 30,
"column": 87
} | [
{
"pp": "m n : ℕ\ns : Finset ℕ\nhmn : m.ble n = true\nhs : Icc (m + 1) n = s\n⊢ m ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 55,
"column": 67
} | {
"line": 55,
"column": 78
} | [
{
"pp": "m n : ℤ\nhnm : n < m\n⊢ Icc m n = ∅",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Int.instLinearOrder",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"id",
"Finset.Icc_eq_empty_iff._simp_1",
"Int... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 58,
"column": 76
} | {
"line": 58,
"column": 87
} | [
{
"pp": "m n : ℤ\ns : Finset ℤ\nhmn : m ≤ n\nhs : Icc (m + 1) n = s\n⊢ m ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Testing.Plausible.Functions | {
"line": 115,
"column": 8
} | {
"line": 115,
"column": 19
} | [
{
"pp": "case mp\nα : Type u\nβ : Type v\ninst✝² : DecidableEq α\ninst✝¹ : Zero β\ninst✝ : DecidableEq β\na : α\nA : List ((_ : α) × β)\ny od : β\nhval : ⟨a, od⟩ ∈ A.dedupKeys\nhod : (decide ¬od = 0) = true\nthis : od ∈ List.dlookup a A.dedupKeys\n⊢ ¬(some od).getD 0 = 0",
"usedConstants": [
"Option.g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Algebra.Rat | {
"line": 28,
"column": 15
} | {
"line": 28,
"column": 50
} | [
{
"pp": "A : Type u_1\ninst✝³ : DivisionRing A\ninst✝² : TopologicalSpace A\ninst✝¹ : SeparatelyContinuousMul A\ninst✝ : CharZero A\nr : ℚ\n⊢ Continuous fun x ↦ r • x",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"Continuous",
"HMul.hMul",
"Algebra.algebraMap",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 63,
"column": 8
} | {
"line": 63,
"column": 44
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 80,
"column": 53
} | {
"line": 80,
"column": 64
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 59
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : UniformSpace α\nF : ι → X → α\ninst✝ : TopologicalSpace ι\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_ind : IsInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ F)\nF_cl : IsClosed[UniformOnFun.topologicalSpace X α 𝔖] (rang... | rw [← isCompact_univ_iff, this.isCompact_iff, image_univ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 490,
"column": 78
} | {
"line": 490,
"column": 89
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝³ : TopologicalSpace X\ninst✝² : UniformSpace α\nF : ι → X → α\ninst✝¹ : TopologicalSpace ι\ninst✝ : T2Space α\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_clemb : IsClosedEmbedding (⇑(UniformOnFun.ofFun 𝔖) ∘ F)\ns : Set ι\ns_eqcont : ∀ K ∈ 𝔖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 13
} | [
{
"pp": "case hU\nG : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 499,
"column": 2
} | {
"line": 501,
"column": 64
} | [
{
"pp": "X : Type u_2\nα : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : UniformSpace α\nS : Set C(X, α)\nhS1 : IsCompact (ContinuousMap.toFun '' S)\nhS2 : Equicontinuous fun x ↦ ⇑↑x\n⊢ IsCompact S",
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"isCompact_iff_compactSpace",
"... | suffices h : IsInducing (Equiv.Set.image _ S DFunLike.coe_injective) by
rw [isCompact_iff_compactSpace] at hS1 ⊢
exact (Equiv.toHomeomorphOfIsInducing _ h).symm.compactSpace | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Topology.Algebra.Group.SubmonoidClosure | {
"line": 45,
"column": 4
} | {
"line": 46,
"column": 11
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\nm : ℤ\ny : G\nhy : MapClusterPt y atTop fun x_1 ↦ x ^ x_1\nthis : ContinuousAt (fun yz ↦ x ^ m * yz.2 / yz.1) (y, y)\n⊢ MapClusterPt (x ^ m) (atTop.curry atTop) ↿fun a b ↦ x ^ (m +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.SubmonoidClosure | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt 1 atTop fun x_1 ↦ x ^ x_1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.SubmonoidClosure | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt x atTop fun x_1 ↦ x ^ x_1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 33
} | [
{
"pp": "case hf.h.h.h\nG : GrpCat\nP : ProfiniteGrp.{u}\nf g : completion G ⟶ P\nh : eta G ≫ (forget₂ ProfiniteGrp.{u} GrpCat).map f = eta G ≫ (forget₂ ProfiniteGrp.{u} GrpCat).map g\nx : ↑(completion G).toProfinite.toTop\ny : ↑G\n⊢ (⇑(Hom.hom f) ∘ etaFn G) y = (⇑(Hom.hom g) ∘ etaFn G) y",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsOpenUnits | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 81
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsOpenUnits | {
"line": 91,
"column": 27
} | {
"line": 91,
"column": 38
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 27
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Spac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 27
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Spac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 27
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 27
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Nonarchimedean.TotallyDisconnected | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 25
} | [
{
"pp": "case h\nG : Type u_1\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : NonarchimedeanGroup G\ninst✝ : T2Space G\na b : G\nh : a ≠ b\nu v : Set G\nleft✝ : IsOpen u\nopen_v : IsOpen v\nmem_u : a⁻¹ * b ∈ u\nmem_v : 1 ∈ v\ndis : Disjoint u v\nV : OpenSubgroup G\nhV : ↑V ⊆ v\nx : Set G\nmem_aV : x ⊆ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.TopCat.Sphere | {
"line": 76,
"column": 27
} | {
"line": 76,
"column": 68
} | [
{
"pp": "n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.sphere 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.sphere 0 1\nh :\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.TopCat.Sphere | {
"line": 82,
"column": 27
} | {
"line": 82,
"column": 60
} | [
{
"pp": "n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.ball 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.ball 0 1\nh :\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 75
} | [
{
"pp": "X✝ : Type u_1\ninst✝² : TopologicalSpace X✝\nC✝ D✝ : Set X✝\ninst✝¹ : RelCWComplex C✝ D✝\nX : Type u\ninst✝ : TopologicalSpace X\nC D : Set X\ncell : ℕ → Type u\nmap : (n : ℕ) → cell n → PartialEquiv (Fin n → ℝ) X\neventually_isEmpty_cell : ∀ᶠ (n : ℕ) in Filter.atTop, IsEmpty (cell n)\nfinite_cell : ∀ ... | simp_rw [Filter.eventually_atTop, ge_iff_le] at eventually_isEmpty_cell | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 327,
"column": 4
} | {
"line": 327,
"column": 30
} | [
{
"pp": "case h\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nfinite : _root_.Finite ((n : ℕ) × cell C n)\nh✝ : Nonempty ((n : ℕ) × cell C n)\nx✝ : Fintype ((n : ℕ) × cell C n)\nA : Finset ℕ := Finset.image Sigma.fst Finset.univ\nm : ℕ\na✝ : A.max' ⋯ + 1 ≤ m\nh' : Nonempty (... | linarith [A.le_max' m hmA] | Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_linarith_1 | Mathlib.Tactic.linarith |
Mathlib.Topology.Compactness.DeltaGeneratedSpace | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 56
} | [
{
"pp": "case a.h.a.refine_1\nX : Type u_1\ntX : TopologicalSpace X\nu : Set X\nn : ℕ\nh : ∀ (p : C(Fin n → ℝ, X)), IsOpen (⇑p ⁻¹' u)\np : C(Fin n → ℝ, X)\n⊢ Continuous[_, deltaGenerated X] ⇑p",
"usedConstants": [
"Iff.mpr",
"Real",
"Continuous",
"Pi.topologicalSpace",
"Continu... | exact continuous_euclidean_to_deltaGenerated.mpr p.2 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Compactness.DeltaGeneratedSpace | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 56
} | [
{
"pp": "case a.h.a.refine_1\nX : Type u_1\ntX : TopologicalSpace X\nu : Set X\nn : ℕ\nh : ∀ (p : C(Fin n → ℝ, X)), IsOpen (⇑p ⁻¹' u)\np : C(Fin n → ℝ, X)\n⊢ Continuous[_, deltaGenerated X] ⇑p",
"usedConstants": [
"Iff.mpr",
"Real",
"Continuous",
"Pi.topologicalSpace",
"Continu... | exact continuous_euclidean_to_deltaGenerated.mpr p.2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Compactness.DeltaGeneratedSpace | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 56
} | [
{
"pp": "case a.h.a.refine_1\nX : Type u_1\ntX : TopologicalSpace X\nu : Set X\nn : ℕ\nh : ∀ (p : C(Fin n → ℝ, X)), IsOpen (⇑p ⁻¹' u)\np : C(Fin n → ℝ, X)\n⊢ Continuous[_, deltaGenerated X] ⇑p",
"usedConstants": [
"Iff.mpr",
"Real",
"Continuous",
"Pi.topologicalSpace",
"Continu... | exact continuous_euclidean_to_deltaGenerated.mpr p.2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Compactum | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 11
} | [
{
"pp": "X Y : Compactum\nf : X ⟶ Y\nxs : Ultrafilter X.A\n⊢ (ConcreteCategory.hom (X.a ≫ f.f)) xs = Y.str (Ultrafilter.map (⇑(ConcreteCategory.hom f)) xs)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Monad.Algebra.Hom.h",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | ← f.h | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Category.Compactum | {
"line": 251,
"column": 6
} | {
"line": 251,
"column": 16
} | [
{
"pp": "X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Category.Compactum | {
"line": 256,
"column": 4
} | {
"line": 256,
"column": 14
} | [
{
"pp": "X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 161,
"column": 15
} | {
"line": 161,
"column": 45
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ (n : ℕ) (i : CWComplex.cell C n),\n ∃ I,\n MapsTo (↑(CWComplex.map n i)) (sphere 0 1)\n (∅ ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(CWComplex.map m j) '' closedBall 0 1)",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 162,
"column": 16
} | {
"line": 162,
"column": 72
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ A ⊆ C,\n (∀ (n : ℕ) (j : CWComplex.cell C n), IsClosed[inst✝¹] (A ∩ ↑(CWComplex.map n j) '' closedBall 0 1)) ∧\n IsClosed[inst✝¹] (A ∩ ∅) →\n IsClosed[inst✝¹] A",
"usedConstants": [
"Eq.mpr",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 164,
"column": 15
} | {
"line": 164,
"column": 45
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∅ ∪ ⋃ n, ⋃ j, ↑(CWComplex.map n j) '' closedBall 0 1 = C",
"usedConstants": [
"Eq.mpr",
"Real",
"pseudoMetricSpacePi",
"outParam",
"Real.instZero",
"congrArg",
"Set.empty_union",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 176,
"column": 16
} | {
"line": 176,
"column": 27
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ (n : ℕ) (i : cell C n),\n ∃ I, MapsTo (↑(map n i)) (sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(map m j) '' closedBall 0 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 32
} | [
{
"pp": "X Y : Compactum\nf : X ⟶ Y\n⊢ Continuous ⇑(ConcreteCategory.hom f)",
"usedConstants": [
"Eq.mpr",
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"PartialOrder.toPreorder",
"Cate... | continuous_iff_ultrafilter | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 177,
"column": 16
} | {
"line": 177,
"column": 27
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ A ⊆ C, (∀ (n : ℕ) (j : cell C n), IsClosed[inst✝¹] (A ∩ ↑(map n j) '' closedBall 0 1)) → IsClosed[inst✝¹] A",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 178,
"column": 15
} | {
"line": 178,
"column": 26
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ⋃ n, ⋃ j, ↑(map n j) '' closedBall 0 1 = C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 400,
"column": 8
} | {
"line": 400,
"column": 18
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : CompactSpace X\ninst✝ : T2Space X\nFF : Ultrafilter (Ultrafilter X)\nx : X := ⋯\nc1 : x = (Ultrafilter.map Ultrafilter.lim FF).lim\nc2 : ∀ (U : Set X) (F : Ultrafilter X), F.lim ∈ U → IsOpen[inst✝²] U → U ∈ F\nc3 : ↑(Ultrafilter.map Ultrafilter.lim FF... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Category.Compactum | {
"line": 411,
"column": 10
} | {
"line": 411,
"column": 36
} | [
{
"pp": "X Y : Compactum\nf : X.A → Y.A\ncont : Continuous f\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"usedConstants": [
"Continuous",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.ofTypeMonad",
"Compactum.inst... | continuous_iff_ultrafilter | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Category.Compactum | {
"line": 414,
"column": 6
} | {
"line": 414,
"column": 17
} | [
{
"pp": "case h.toFun.h\nX Y : Compactum\nf : X.A → Y.A\nF : Ultrafilter X.A\ncont : Tendsto f (↑F) (𝓝 (f (X.str F)))\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Monad.Algebra.a",
"congrAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 439,
"column": 4
} | {
"line": 439,
"column": 15
} | [
{
"pp": "case f.h.toFun.h\nX✝ Y✝ : Compactum\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : compactumToCompHaus.map a₁✝ = compactumToCompHaus.map a₂✝\nx✝ : X✝.A\n⊢ (ConcreteCategory.hom a₁✝.f).toFun x✝ = (ConcreteCategory.hom a₂✝.f).toFun x✝",
"usedConstants": [
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 64
} | [
{
"pp": "case h\nI : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\n⊢ e (π C fun x ↦ x ∈ s) a * c m • Products.eval (π C fun x ↦ x ∈ s) m ∈... | have hsm := (LinearMap.mulLeft ℤ (e (π C (· ∈ s)) a)).map_smul | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 62
} | [
{
"pp": "case a\nI : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\nhsm :\n ∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x ↦ x ∈ s) ℤ),\n e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 23
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 467,
"column": 2
} | {
"line": 467,
"column": 13
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ⋃ n, ⋃ j, openCell n j = C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 28
} | [
{
"pp": "case h\nI : Type u\nJ : I → Prop\ninst✝ : (i : I) → Decidable (J i)\nx : I → Bool\nh : ∀ (i : I), x i ≠ false → J i\ni : I\n⊢ false ≠ x i → J i",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 534,
"column": 2
} | {
"line": 534,
"column": 80
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝¹ : RelCWComplex C D\ninst✝ : T2Space X\nA : Set X\nhAC : A ⊆ C\nhDA : IsClosed[t] (A ∩ D)\nh : ∀ (n : ℕ), 0 < n → ∀ (j : cell C n), Disjoint A (openCell n j) ∨ IsClosed[t] (A ∩ closedCell n j)\n⊢ IsClosed[t] A",
"usedConstants": [
"Topo... | apply isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell hAC hDA | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 216,
"column": 17
} | {
"line": 216,
"column": 75
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ns : Finset I\ninst✝ : WellFoundedLT I\nx : ↑(π C fun x ↦ x ∈ s)\nl : List I := s.sort fun x1 x2 ↦ x1 ≥ x2\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nhmap :\n ∀ (g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 596,
"column": 2
} | {
"line": 596,
"column": 13
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\nn : ℕ\ni : cell C n\n⊢ ∃ I, cellFrontier n i ⊆ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, openCell m j",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 626,
"column": 4
} | {
"line": 626,
"column": 15
} | [
{
"pp": "case e_I.hIJ\nX : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nE : Set X\nI✝¹ : (n : ℕ) → Set (cell C n)\nclosed'✝¹ : IsClosed[t] E\nhE : D ∪ ⋃ n, ⋃ j, openCell n ↑j = E\nF : Set X\nI✝ : (n : ℕ) → Set (cell C n)\nclosed'✝ : IsClosed[t] F\nhF : D ∪ ⋃ n, ⋃ j, openCell n ↑j = F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 39
} | [
{
"pp": "case h\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nx✝ : ↑(smaller C o)\na : LocallyConstant ↑C ℤ\nb : LocallyConstant ↑(π C fun x ↦ ord I x < o) ℤ\nhb : b ∈ range (π C fun x ↦ ord I x < o) ∧ (πs C o) b = a\n⊢ (fun x ↦ ⟨(πs C o) ↑x, ⋯⟩) ⟨b, ⋯⟩ = ⟨a,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 426,
"column": 2
} | {
"line": 426,
"column": 24
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\nl : Products I\nJ : I → Prop\ninst✝ : (j : I) → Decidable (J j)\nh✝ : isGood (π C J) l\ni : I\nhi : i ∈ ↑l\nh' : ¬J i\nw✝ : I → Bool\nleft✝ : w✝ ∈ C\nh : ∀ i ∈ ↑l, ↑⟨Proj J w✝, ⋯⟩ i = true\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 600,
"column": 2
} | {
"line": 600,
"column": 46
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\nl : Products I\no : Ordinal.{u}\nhlt : ∀ i ∈ ↑l, ord I i < o\n⊢ (πs C o) (eval (π C fun x ↦ ord I x < o) l) = eval C l",
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"Int.instAddCommMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 26
} | [
{
"pp": "case pos\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\ng : I → Bool\nhg : g ∈ C1 C ho\ni : I\nh : term I ho = i\n⊢ true = g i",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 56
} | [
{
"pp": "case refine_2\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nf : LocallyConstant ↑C ℤ\nhf :\n ⇑((LocallyConstant.comapₗ ℤ { toFun := CC'₁ C hsC ho, continuo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 260,
"column": 8
} | {
"line": 260,
"column": 70
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nf : LocallyConstant ↑C ℤ\nhf :\n ⇑((LocallyConstant.comapₗ ℤ { toFun := CC'₁ C hsC ho, continuous_toFun := ⋯ }... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 264,
"column": 8
} | {
"line": 264,
"column": 70
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nf : LocallyConstant ↑C ℤ\nhf :\n ⇑((LocallyConstant.comapₗ ℤ { toFun := CC'₁ C hsC ho, continuous_toFun := ⋯ }... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 35
} | [
{
"pp": "α : Type u_1\nS : Set (Set α)\nhpi : IsPiSystem S\nh : ∀ (C : ℕ → Set α), Directed (fun x1 x2 ↦ x1 ⊇ x2) C → (∀ (i : ℕ), C i ∈ S) → ⋂ i, C i = ∅ → ∃ n, C n = ∅\nC : ℕ → Set α\nh1 : ∀ (i : ℕ), C i ∈ insert ∅ S\nh2 : ⋂ n, ⋂ m, ⋂ (_ : m ≤ n), C m = ∅\nthis : (∀ (n : ℕ), dissipate C n ∈ S ∨ dissipate C n =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 25
} | [
{
"pp": "case pos\nα : Type u_1\nS : Set (Set α)\nhpi : IsPiSystem S\nh : ∀ (C : ℕ → Set α), Directed (fun x1 x2 ↦ x1 ⊇ x2) C → (∀ (i : ℕ), C i ∈ S) → ⋂ i, C i = ∅ → ∃ n, C n = ∅\nC : ℕ → Set α\nh1 : ∀ (i : ℕ), C i ∈ insert ∅ S\nh2 : ⋂ n, ⋂ m, ⋂ (_ : m ≤ n), C m = ∅\nn : ℕ\ng : (dissipate C n).Nonempty\n⊢ dissi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 170,
"column": 4
} | {
"line": 170,
"column": 15
} | [
{
"pp": "case refine_2\nα : Type u_2\ninst✝ : TopologicalSpace α\nC : ℕ → Set α\nhC_cc : ∀ (i : ℕ), C i ∈ {s | IsCompact s ∧ IsClosed s}\nh_nonempty : ∀ (n : ℕ), (dissipate C n).Nonempty\n⊢ IsCompact (dissipate C 0)",
"usedConstants": [
"Set.dissipate",
"Eq.mpr",
"congrArg",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 13
} | [
{
"pp": "case h.e'_2.h.e'_2.h.a\nα : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : T2Space α\ns : Set α\n⊢ IsCompact s ↔ IsCompact s ∧ IsClosed s",
"usedConstants": [
"Eq.mpr",
"id",
"IsClosed",
"And",
"Iff",
"iff_self_and._simp_1",
"Eq",
"IsCompact"
]
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 521,
"column": 4
} | {
"line": 521,
"column": 84
} | [
{
"pp": "case neg.h\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nq : ↑(GoodProducts (π C fun x ↦ ord I x < o))\nl : ↑(MaxProducts C ho)\nthis : Inhabited I\nh : ¬↑↑q = []\n⊢ (Ordina... | exact Products.prop_of_isGood C _ q.prop q.val.val.head! (List.head!_mem_self h) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 38
} | [
{
"pp": "case h₂.h.h.a\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nl : ↑(MaxProducts C ho)\nh₁ : ⊤ ≤ Submodule.span ℤ (Set.range (eval (π C fun x ↦ ord I x < o)))\... | rw [max_eq_o_cons_tail C hsC ho l] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 617,
"column": 2
} | {
"line": 617,
"column": 35
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nh₁ : ⊤ ≤ Submodule.span ℤ (Set.range (eval (π C fun x ↦ ord I x < o)))\nh : LinearIndependent ℤ (eval (C' C ho)... | let f := MaxToGood C hC hsC ho h₁ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli | {
"line": 62,
"column": 61
} | {
"line": 62,
"column": 72
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\ninst✝² : CompactSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : CompactSpace β\nA : Set (α →ᵇ β)\nclosed : IsClosed A\nH : ∀ (x₀ : α), ∀ ε > 0, ∃ U ∈ nhds x₀, ∀ x ∈ U, ∀ x' ∈ U, ∀ (i : ↑A), dist (↑i x) (↑i x') < ε\nε : ℝ\nε0 : ε > 0\nε₁ : ℝ\nε₁0 : 0 <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.BoundedCompactlySupported | {
"line": 78,
"column": 2
} | {
"line": 79,
"column": 9
} | [
{
"pp": "α : Type u_1\nγ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : NonUnitalNormedRing γ\ninst✝ : Nontrivial γ\nh : C_cb(α, γ) = ⊤\nx : γ\nhx : x ≠ 0\n⊢ IsCompact univ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.Interval | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\na b c : α\ninst✝² : Fact (a ≤ b)\ninst✝¹ : Fact (b ≤ c)\nE : Type u_2\ninst✝ : TopologicalSpace E\nf : C(↑(Icc a b), E)\ng : C(↑(Icc b c), E)\nι : Type u_3\np : Filter ι\nF : ι → C(↑(Icc a b), E)\nG : ι → C(↑(I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 98,
"column": 36
} | {
"line": 98,
"column": 47
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : ∀ (x : ℕ → E), (∀ᶠ (n : ℕ) in atTop, x n ∈ A) → ∃ a ∈ A, MapClusterPt a atTop x\nf : Filter E\nx✝¹ : f.NeBot\nx✝ : f.IsCountablyGenerated\nhle : f ≤ 𝓟 A\nx : ℕ → E\nhx : Tendsto x atTop f\n⊢ ∀ᶠ (n : ℕ) in atTop, x n ∈ A",
"usedConstants": [... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousMap.Interval | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\na b c : α\ninst✝² : Fact (a ≤ b)\ninst✝¹ : Fact (b ≤ c)\nE : Type u_2\ninst✝ : TopologicalSpace E\nf : C(↑(Icc a b), E)\ng : C(↑(Icc b c), E)\nι : Type u_3\np : Filter ι\nF : ι → C(↑(Icc a b), E)\nG : ι → C(↑(I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 156,
"column": 77
} | {
"line": 156,
"column": 88
} | [
{
"pp": "ι : Type u_1\nE : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nb : Set ι\nhb : b.Countable\nU : ι → Set E\nhUo : ∀ i ∈ b, IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i ∈ b, U i\nthis : Countable ↑b\n⊢ A ⊆ ⋃ i, U ↑i",
"usedConstants": [
"Eq.mpr",
"Iff.of_eq",
"c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 15
} | [
{
"pp": "ι : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝³ : TopologicalSpace E\ninst✝² : TopologicalSpace F\nA✝ B : Set E\ninst✝¹ : SequentialSpace E\ninst✝ : CountablyCompactSpace E\nx : ℕ → E\nhx : ∀ (x_1 : E) (x_2 : ℕ → ℕ), StrictMono x_2 → ¬Tendsto (x ∘ x_2) atTop (𝓝 x_1)\nA : Set E := ⋃ i, closure[inst✝³]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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