module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.HahnSeries.Binomial | {
"line": 114,
"column": 33
} | {
"line": 114,
"column": 35
} | {
"line": 115,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝⁴ : LinearOrder Γ\ninst✝³ : AddCommMonoid Γ\ninst✝² : IsOrderedCancelAddMonoid Γ\ninst✝¹ : CommRing R\ninst✝ : BinomialRing R\ng : Γ\nhg : 0 < g\nr s : R\nk : ℕ\n⊢ (↑↑(toOrderTopSubOnePos ⋯ ^ s)).coeff (k • g) = Ring.choose s k • r ^ k",
"ppTerm": "?m.51",
"assi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 151,
"column": 28
} | {
"line": 151,
"column": 30
} | {
"line": 152,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nM : Type ?u.14\ninst✝ : SMulZeroClass M R\nr : M\nt : SummableFamily Γ R β\n⊢ ∀ (g : Γ), {a | ((r • ⇑t) a).coeff g ≠ 0}.Finite",
"ppTerm": "?m.46",
"assigned":... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 177,
"column": 25
} | {
"line": 177,
"column": 27
} | {
"line": 177,
"column": 28
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\na : α\n⊢ a ∈ Set.Finite.toFinset ⋯ ↔ (s a).coeff g ≠ 0",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Fun... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 187,
"column": 41
} | {
"line": 187,
"column": 43
} | {
"line": 188,
"column": 6
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\n⊢ (g ∈ Function.support fun g ↦ ∑ᶠ (i : α), (s i).coeff g) → g ∈ ⋃ a, (s a).support",
"ppTerm": "?m.31",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 199,
"column": 59
} | {
"line": 199,
"column": 61
} | {
"line": 200,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\n⊢ hsum 0 = 0",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"finsum_zero",
"HahnSeries.SummableFamily.instZero",
"congrArg",
"AddMonoid.toAddZeroClass",
"Hahn... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 204,
"column": 14
} | {
"line": 204,
"column": 16
} | {
"line": 205,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\nhg : g ∈ s.hsum.support\n⊢ g ∈ ⋃ a, (s a).support",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HahnSeries.support",
"Eq.mpr",
"Finset.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 211,
"column": 82
} | {
"line": 211,
"column": 84
} | {
"line": 212,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns t : SummableFamily Γ R α\n⊢ (s + t).hsum = s.hsum + t.hsum",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"AddMonoid.toAddZeroClass",
"HahnSeries.ext",
"AddZeroClass.to... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 138,
"column": 67
} | {
"line": 138,
"column": 69
} | {
"line": 139,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\na b : PowerSeries R\nh : 0 < x.orderTop\ng : Γ\ni : (_ : ℕ) × ℕ × ℕ\nhi : i ∈ (image (fun i ↦ i.1 + i... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 220,
"column": 55
} | {
"line": 220,
"column": 57
} | {
"line": 220,
"column": 58
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\nt : Finset α\nh : {a | (s a).coeff g ≠ 0} ⊆ ↑t\n⊢ ∀ x ∈ t, x ∉ Set.Finite.toFinset ⋯ → (s x).coeff g = 0",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 218,
"column": 85
} | {
"line": 218,
"column": 87
} | {
"line": 219,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\nt : Finset α\nh : {a | (s a).coeff g ≠ 0} ⊆ ↑t\n⊢ s.hsum.coeff g = ∑ i ∈ t, (s i).coeff g",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 223,
"column": 65
} | {
"line": 223,
"column": 67
} | {
"line": 224,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\n⊢ s.hsum.coeff g = ∑ i ∈ (s.coeff g).support, (s i).coeff g",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"finsum_... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 231,
"column": 66
} | {
"line": 231,
"column": 68
} | {
"line": 231,
"column": 69
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type ?u.21\ninst✝ : DecidableEq ι\ni : ι\nx : R⟦Γ⟧\n⊢ (Pi.single i x i).support.IsPWO",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 230,
"column": 27
} | {
"line": 230,
"column": 29
} | {
"line": 231,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type ?u.21\ninst✝ : DecidableEq ι\ni : ι\nx : R⟦Γ⟧\n⊢ (⋃ a, (Pi.single i x a).support).IsPWO",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 236,
"column": 67
} | {
"line": 236,
"column": 69
} | {
"line": 237,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type ?u.21\ninst✝ : DecidableEq ι\ni : ι\nx : R⟦Γ⟧\ng : Γ\nj : ι\n⊢ j ∈ {a | (Pi.single i x a).coeff g ≠ 0} → j ∈ {i}",
"ppTerm": "?m.78",
"assigned": true... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 240,
"column": 86
} | {
"line": 240,
"column": 88
} | {
"line": 241,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type u_7\ninst✝ : DecidableEq ι\ni : ι\nx : R⟦Γ⟧\n⊢ (single i x).hsum = x",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"eq_false",
"congrArg",
"fi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 249,
"column": 27
} | {
"line": 249,
"column": 29
} | {
"line": 250,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type ?u.20\ninst✝ : Finite ι\nx : R⟦Γ⟧\n⊢ (⋃ a, x.support).IsPWO",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"HahnSeries.support",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 168,
"column": 11
} | {
"line": 168,
"column": 13
} | {
"line": 169,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 168,
"column": 11
} | {
"line": 175,
"column": 8
} | {
"line": 177,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
... | [] | by
obtain aux₁ := HasSubst.cons_subst_zero_left (f := X₀ + X₁ + X₀ * X₁) (0 : Fin 3) 1 2 (by simp)
obtain aux₂ := HasSubst.cons_subst_zero_right (f := X₀ + X₁ + X₀ * X₁) (0 : Fin 3) 1 2 (by simp)
simp_rw [subst_add aux₁, subst_mul aux₁, subst_X aux₁, subst_add aux₂, subst_mul aux₂,
subst_X aux₂]
s... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 178,
"column": 10
} | {
"line": 178,
"column": 12
} | {
"line": 178,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ 𝔾ₘ.toPowerSeries = subst ![X₁, X₀] 𝔾ₘ.toPowerSeries",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNon... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 256,
"column": 86
} | {
"line": 256,
"column": 88
} | {
"line": 257,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : AddCommMonoid R\nι : Type u_7\ninst✝ : Unique ι\nx : SummableFamily Γ R ι\n⊢ x.hsum = x default",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"congrArg",
"AddMonoid.toAddZeroClas... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 186,
"column": 24
} | {
"line": 186,
"column": 26
} | {
"line": 186,
"column": 27
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nf : R →+* S\n⊢ constantCoeff ((MvPowerSeries.map f) F.toPowerSeries) = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomCla... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 187,
"column": 17
} | {
"line": 187,
"column": 19
} | {
"line": 187,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nf : R →+* S\n⊢ (coeff (single 0 1)) ((MvPowerSeries.map f) F.toPowerSeries) = 1",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"RingHom.instRin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 188,
"column": 17
} | {
"line": 188,
"column": 19
} | {
"line": 188,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nf : R →+* S\n⊢ (coeff (single 1 1)) ((MvPowerSeries.map f) F.toPowerSeries) = 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"RingHom.instRin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 146,
"column": 51
} | {
"line": 146,
"column": 53
} | {
"line": 146,
"column": 54
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\na b : PowerSeries R\nh : 0 < x.orderTop\ng : Γ\ni : (_ : ℕ) × ℕ × ℕ\nhis : i ∉ (fun x ↦ ⟨x.1 + x.2, x... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 191,
"column": 38
} | {
"line": 191,
"column": 40
} | {
"line": 191,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nf : R →+* S\ng₁ g₂ : MvPowerSeries (Fin 3) R\n⊢ ![(MvPowerSeries.map f) g₁, (MvPowerSeries.map f) g₂] = fun i ↦ (MvPowerSeries.map f) (![g₁, g₂] i)",
"ppTerm": "?m.57",... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 264,
"column": 27
} | {
"line": 264,
"column": 29
} | {
"line": 265,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ne : α ≃ β\ns : SummableFamily Γ R α\n⊢ (⋃ a, (s (e.symm a)).support).IsPWO",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"HahnSeries.suppo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 272,
"column": 89
} | {
"line": 272,
"column": 91
} | {
"line": 273,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ne : α ≃ β\ns : SummableFamily Γ R α\n⊢ (Equiv e s).hsum = s.hsum",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"Equiv.bije... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 282,
"column": 27
} | {
"line": 282,
"column": 29
} | {
"line": 283,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝³ : PartialOrder Γ\ninst✝² : AddCommMonoid R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : α → R\ns : SummableFamily Γ V α\n⊢ (⋃ a, (f a • s a).support).IsPWO",
"ppTerm": "?m.22",
"assigned": tr... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 119,
"column": 66
} | {
"line": 119,
"column": 68
} | {
"line": 120,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\na b : PowerSeries R\n⊢ (powerSeriesFamily x (a * b)).hsum = ((powerSeriesFamily x a).mul (powerSeries... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 13
} | {
"line": 173,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\ng : Γ\n⊢ { coeff := fun g ↦ ∑ᶠ (i : ℕ), (if i = 0 then (if 0 < x.orderTop then x else 0... | [
"Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\ng : Γ\n⊢ ∑ᶠ (i : ℕ), (if i = 0 then (if 0 < x.orderTop then x else 0) ^ i else 0).coeff g = HahnSer... | simp only | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 173,
"column": 48
} | {
"line": 173,
"column": 50
} | {
"line": 173,
"column": 51
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\ng : Γ\nn : ℕ\nhn : n ≠ 0\n⊢ (if n = 0 then (if 0 < x.orderTop then x else 0) ^ n else 0... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 287,
"column": 26
} | {
"line": 287,
"column": 28
} | {
"line": 288,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝³ : PartialOrder Γ\ninst✝² : AddCommMonoid R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : α → R\ns : SummableFamily Γ V α\ng : Γ\n⊢ {a | (f a • s a).coeff g ≠ 0}.Finite",
"ppTerm": "?m.57",
"as... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 169,
"column": 14
} | {
"line": 169,
"column": 16
} | {
"line": 170,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\n⊢ (powerSeriesFamily x 1).hsum = 1",
"ppTerm": "?m.48",
"assigned": true,
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 175,
"column": 18
} | {
"line": 175,
"column": 20
} | {
"line": 176,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\na b : R⟦X⟧\n⊢ (powerSeriesFamily x (a * b)).hsum = (powerSeriesFamily x a).hsum * (powe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 177,
"column": 15
} | {
"line": 177,
"column": 17
} | {
"line": 178,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\n⊢ (powerSeriesFamily x 0).hsum = 0",
"ppTerm": "?m.77",
"assigned": true,
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 180,
"column": 18
} | {
"line": 180,
"column": 20
} | {
"line": 181,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\na b : R⟦X⟧\n⊢ (powerSeriesFamily x (a + b)).hsum = (powerSeriesFamily x a).hsum + (powe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 186,
"column": 41
} | {
"line": 186,
"column": 43
} | {
"line": 186,
"column": 44
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nr : R\ng : Γ\nn : ℕ\nhn : n ≠ 0\n⊢ (if n = 0 then r • (if 0 < x.orderTop then x else 0)... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 298,
"column": 89
} | {
"line": 298,
"column": 91
} | {
"line": 299,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng g' : Γ\nhg : ∀ (b : α), ∀ g' ∈ (s b).support, g ≤ g'\nhg' : g' ∈ s.hsum.support\n⊢ g ≤ g'",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"HahnSeries.suppo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 182,
"column": 17
} | {
"line": 182,
"column": 19
} | {
"line": 183,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\nσ : Type u_7\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nr : R\n⊢ (powerSeriesFamily x ((algebraMap R R⟦X⟧) r)).hsum = (algebraMap R R⟦Γ⟧) r",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 196,
"column": 39
} | {
"line": 196,
"column": 41
} | {
"line": 196,
"column": 42
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nr : R\ng : Γ\nn : ℕ\nhn : n ≠ 0\n⊢ (coeff n) (C r) * ((if 0 < x.orderTop then x else 0) ^ n).coeff g = 0",
"ppTerm": "?m.46",
"assigned": true,
"u... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 306,
"column": 37
} | {
"line": 306,
"column": 39
} | {
"line": 306,
"column": 40
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\na : α\nha : ↑g = (s a).orderTop\nhg : ∀ (b : α), ∀ g' ∈ (s b).support, g ≤ g'\nhna : ∀ (b : α), b ≠ a → (s b).coeff g = 0\n⊢ s.hsum.coeff g = (s a).coeff g",
"ppTerm": "?m.49... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 189,
"column": 11
} | {
"line": 189,
"column": 13
} | {
"line": 190,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nf : R →+* S\n⊢ subst ![subst ![X 0, X 1] ((MvPowerSeries.map f) F.toPowerSeries), X 2] ((MvPowerSeries.map f) F.toPowerSeries) =\n subst ![X 0, subst ![X 1, X 2] ((MvPow... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 207,
"column": 57
} | {
"line": 207,
"column": 59
} | {
"line": 208,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.constantCoeff F.Xzero = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Unit.unit",
"CommRing",
"MvPowerSeries.instZero",
"MvPowerSeries.HasSubst.X_zero",
"congrArg",
"CommSem... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 314,
"column": 26
} | {
"line": 314,
"column": 28
} | {
"line": 315,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\na : α\nha : ↑g = (s a).orderTop\nhg : ∀ (b : α), ∀ g' ∈ (s b).support, g ≤ g'\nhna : ∀ (b : α), b ≠ a → (s b).coeff g = 0\nthis : (if h : s.hsum = 0 then ⊤ else ↑(⋯.min ⋯)) = ↑g\... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 192,
"column": 51
} | {
"line": 192,
"column": 53
} | {
"line": 193,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nr : R\n⊢ (heval x) (C r) = r • 1",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithTop.decidableLT",
"Non... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 203,
"column": 51
} | {
"line": 203,
"column": 53
} | {
"line": 203,
"column": 54
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nhx : 0 < x.orderTop\ng : Γ\nn : ℕ\nhn : n ≠ 1\n⊢ ({ toFun := fun a ↦ if a = 1 then x ^ a else 0, isPWO_iUnion_support' := ⋯, finite_co_support' := ⋯ } n).coef... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 199,
"column": 57
} | {
"line": 199,
"column": 59
} | {
"line": 200,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nhx : 0 < x.orderTop\n⊢ (heval x) X = x",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HahnSeries.support",
"Set.IsPWO",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 311,
"column": 43
} | {
"line": 311,
"column": 45
} | {
"line": 312,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nα : Type u_5\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\ns : SummableFamily Γ R α\ng : Γ\na : α\nha : ↑g = (s a).orderTop\nhg : ∀ (b : α), ∀ g' ∈ (s b).support, g ≤ g'\nhna : ∀ (b : α), b ≠ a → (s b).coeff g = 0\n⊢ s.hsum.leadingCoeff = (s a).coeff g",
"ppTerm": "... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 330,
"column": 31
} | {
"line": 330,
"column": 33
} | {
"line": 331,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommGroup R\ns✝ t : SummableFamily Γ R α\na : α\ns : SummableFamily Γ R α\n⊢ (⋃ a, (-s a).support).IsPWO",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 333,
"column": 37
} | {
"line": 333,
"column": 39
} | {
"line": 334,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommGroup R\ns✝ t : SummableFamily Γ R α\na : α\ns : SummableFamily Γ R α\ng : Γ\n⊢ {a | (-s a).coeff g ≠ 0}.Finite",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 206,
"column": 66
} | {
"line": 206,
"column": 68
} | {
"line": 207,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nu : R⟦X⟧ˣ\n⊢ IsUnit ((heval x) ↑u)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Units.val",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 347,
"column": 31
} | {
"line": 347,
"column": 33
} | {
"line": 348,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommGroup R\ns✝ t : SummableFamily Γ R α\na : α\ns s' : SummableFamily Γ R α\n⊢ (⋃ a, ((⇑s - ⇑s') a).support).IsPWO",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 212,
"column": 71
} | {
"line": 212,
"column": 73
} | {
"line": 213,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nf : R⟦X⟧\ng : Γ\n⊢ ((heval x) f).coeff g = ∑ᶠ (n : ℕ), ((powerSeriesFamily x f).coeff g) n",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants":... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 350,
"column": 30
} | {
"line": 350,
"column": 32
} | {
"line": 351,
"column": 8
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommGroup R\ns✝ t : SummableFamily Γ R α\na : α\ns s' : SummableFamily Γ R α\ng : Γ\n⊢ {a | ((⇑s - ⇑s') a).coeff g ≠ 0}.Finite",
"ppTerm": "?m.40",
"assigned": true,
"use... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 377,
"column": 79
} | {
"line": 377,
"column": 81
} | {
"line": 378,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁴ : PartialOrder Γ\ninst✝³ : PartialOrder Γ'\ninst✝² : AddCommMonoid V\ninst✝¹ : AddCommMonoid R\ninst✝ : SMulWithZero R V\ns : SummableFamily Γ R α\nt : SummableFamily Γ' V β\ngh : Γ × Γ'\n⊢ (Function.support fun... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 217,
"column": 57
} | {
"line": 217,
"column": 59
} | {
"line": 218,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝³ : AddCommMonoid Γ\ninst✝² : LinearOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\nx : R⟦Γ⟧\nf : R⟦X⟧\n⊢ ((heval x) f).coeff 0 = constantCoeff f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finsupp.inst... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 212,
"column": 47
} | {
"line": 212,
"column": 49
} | {
"line": 213,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ (PowerSeries.coeff 1) F.Xzero = 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Unit.unit",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Fa... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 402,
"column": 46
} | {
"line": 402,
"column": 48
} | {
"line": 403,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : AddCommMonoid V\ninst✝³ : AddCommMonoid R\ninst✝² : SMulWithZero R V\ninst✝¹ : VAdd Γ Γ'\ninst✝ : IsOrderedCancelVAdd Γ Γ'\ns : α → R⟦Γ⟧\nt : β → V⟦Γ'⟧\nhs : ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 232,
"column": 11
} | {
"line": 232,
"column": 13
} | {
"line": 232,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ ∀ (i : Fin (Nat.succ 0).succ), constantCoeff (![X (), 0] i) = 0",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"Unit.unit",
"MvPowerSeries.instZero",
"congrArg",
"CommSemiring.toSemiring",
"and_... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 229,
"column": 90
} | {
"line": 229,
"column": 92
} | {
"line": 230,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.HasSubst (subst ![PowerSeries.X, 0] F.toPowerSeries)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"MvPowerSeries.instZero",
"MvPowerSeries.HasSubst.X_zero",
"... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 399,
"column": 55
} | {
"line": 399,
"column": 57
} | {
"line": 400,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : AddCommMonoid V\ninst✝³ : AddCommMonoid R\ninst✝² : SMulWithZero R V\ninst✝¹ : VAdd Γ Γ'\ninst✝ : IsOrderedCancelVAdd Γ Γ'\ns : α → R⟦Γ⟧\nt : β → V⟦Γ'⟧\nhs : ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 421,
"column": 22
} | {
"line": 421,
"column": 24
} | {
"line": 422,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : AddCommMonoid V\ninst✝³ : AddCommMonoid R\ninst✝² : SMulWithZero R V\ninst✝¹ : VAdd Γ Γ'\ninst✝ : IsOrderedCancelVAdd Γ Γ'\ns : SummableFamily Γ R α\nt : Summ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 417,
"column": 87
} | {
"line": 417,
"column": 89
} | {
"line": 418,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : AddCommMonoid V\ninst✝³ : AddCommMonoid R\ninst✝² : SMulWithZero R V\ninst✝¹ : VAdd Γ Γ'\ninst✝ : IsOrderedCancelVAdd Γ Γ'\ns : SummableFamily Γ R α\nt : Summ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 228,
"column": 81
} | {
"line": 228,
"column": 83
} | {
"line": 229,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.subst F.Xzero F.Xzero = subst ![subst ![PowerSeries.X, 0] F.toPowerSeries, 0] F.toPowerSeries",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"CommRing",
"MvPowerSerie... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 240,
"column": 54
} | {
"line": 240,
"column": 56
} | {
"line": 241,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ ![0, 0] = 0",
"ppTerm": "?m.473",
"assigned": true,
"usedConstants": [
"MvPowerSeries.instZero",
"Fintype.elems",
"Nat.le_refl",
"CommSemiring.toSemiring",
"HEq.refl",
"Finset",
"List.Mem.tail",... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 442,
"column": 75
} | {
"line": 442,
"column": 77
} | {
"line": 443,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : AddCommMonoid V\ninst✝³ : AddCommMonoid R\ninst✝² : SMulWithZero R V\ninst✝¹ : VAdd Γ Γ'\ninst✝ : IsOrderedCancelVAdd Γ Γ'\ns : SummableFamily Γ R α\nt : Summ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 239,
"column": 13
} | {
"line": 239,
"column": 15
} | {
"line": 240,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ subst ![subst ![PowerSeries.X, 0] F.toPowerSeries, 0] F.toPowerSeries = F.Xzero",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"CommRing",
"MvPowerSeries.instZero",
"Fintype.elems",
"Nat.le_refl",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 226,
"column": 61
} | {
"line": 226,
"column": 63
} | {
"line": 227,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.subst F.Xzero F.Xzero = F.Xzero",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"CommRing",
"Trans.trans",
"MvPowerSeries.instZero",
"Fintype.elems",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 248,
"column": 58
} | {
"line": 248,
"column": 60
} | {
"line": 249,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\nthis : Invertible ((PowerSeries.coeff 1) F.Xzero)\n⊢ F.Xzero = PowerSeries.subst (PowerSeries.subst F.Xzero F.Xzero) F.Xzero.substInv",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 253,
"column": 13
} | {
"line": 253,
"column": 15
} | {
"line": 254,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\nthis : Invertible ((PowerSeries.coeff 1) F.Xzero)\n⊢ PowerSeries.subst (PowerSeries.subst F.Xzero F.Xzero) F.Xzero.substInv = PowerSeries.X",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 245,
"column": 46
} | {
"line": 245,
"column": 48
} | {
"line": 246,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ F.Xzero = PowerSeries.X",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Trans.trans",
"MvPowerSeries.instZero",
"Semiring.toModule",
"IsScalarTower.right",
"congrArg",
"CommS... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 259,
"column": 57
} | {
"line": 259,
"column": 59
} | {
"line": 260,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.constantCoeff F.zeroX = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Unit.unit",
"CommRing",
"MvPowerSeries.instZero",
"congrArg",
"CommSemiring.toSemiring",
"and_self",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 462,
"column": 56
} | {
"line": 462,
"column": 58
} | {
"line": 462,
"column": 59
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\nR : Type u_7\nV : Type u_8\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : Module R V\ns : SummableFamily Γ R α\nt : SummableFamily ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 455,
"column": 78
} | {
"line": 455,
"column": 80
} | {
"line": 456,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\nR : Type u_7\nV : Type u_8\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : Module R V\ns : SummableFamily Γ R α\nt : SummableFamily ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 264,
"column": 47
} | {
"line": 264,
"column": 49
} | {
"line": 265,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ (PowerSeries.coeff 1) F.zeroX = 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Unit.unit",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Fa... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 476,
"column": 36
} | {
"line": 476,
"column": 38
} | {
"line": 476,
"column": 39
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\nR : Type u_7\nV : Type u_8\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : Module R V\ns : SummableFamily Γ R α\nt : SummableFamily ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 284,
"column": 11
} | {
"line": 284,
"column": 13
} | {
"line": 284,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ ∀ (i : Fin (Nat.succ 0).succ), constantCoeff (![0, X ()] i) = 0",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"Unit.unit",
"MvPowerSeries.instZero",
"congrArg",
"CommSemiring.toSemiring",
"and_... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HahnEmbedding | {
"line": 38,
"column": 50
} | {
"line": 38,
"column": 52
} | {
"line": 39,
"column": 2
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module ℚ M\ninst✝ : IsOrderedModule ℚ M\n⊢ Nonempty (HahnEmbedding.Seed ℚ M ℝ)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Submodule.toIsOrderedAddMonoid",
"Norm... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 281,
"column": 90
} | {
"line": 281,
"column": 92
} | {
"line": 282,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.HasSubst (subst ![0, PowerSeries.X] F.toPowerSeries)",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"MvPowerSeries.instZero",
"congrArg",
"CommSemiring.toSemiri... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.HahnEmbedding | {
"line": 48,
"column": 86
} | {
"line": 48,
"column": 88
} | {
"line": 49,
"column": 2
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module ℚ M\ninst✝ : IsOrderedModule ℚ M\n⊢ ∃ f,\n StrictMono ⇑f ∧ ∀ (a : M), ArchimedeanClass.mk a = (FiniteArchimedeanClass.withTopOrderIso M) (ofLex (f a)).orderTop",
"ppTerm": "?m.49",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HahnEmbedding | {
"line": 78,
"column": 96
} | {
"line": 78,
"column": 98
} | {
"line": 79,
"column": 4
} | [
{
"pp": "M : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedAddMonoid M\nf₁ : M →+o DivisibleHull M := DivisibleHull.coeOrderAddMonoidHom M\nhf₁ : Function.Injective ⇑f₁\na : M\n⊢ ArchimedeanClass.mk a = (DivisibleHull.archimedeanClassOrderIso M).symm (ArchimedeanClass.mk (f₁ a))",
... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 280,
"column": 81
} | {
"line": 280,
"column": 83
} | {
"line": 281,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.subst F.zeroX F.zeroX = subst ![0, subst ![0, PowerSeries.X] F.toPowerSeries] F.toPowerSeries",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"CommRing",
"MvPowerSerie... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 292,
"column": 54
} | {
"line": 292,
"column": 56
} | {
"line": 292,
"column": 57
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ ![0, 0] = 0",
"ppTerm": "?m.473",
"assigned": true,
"usedConstants": [
"MvPowerSeries.instZero",
"Fintype.elems",
"Nat.le_refl",
"CommSemiring.toSemiring",
"HEq.refl",
"Finset",
"List.Mem.tail",... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 291,
"column": 13
} | {
"line": 291,
"column": 15
} | {
"line": 292,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ subst ![0, subst ![0, PowerSeries.X] F.toPowerSeries] F.toPowerSeries = F.zeroX",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"CommRing",
"MvPowerSeries.instZero",
"Fintype.elems",
"Nat.le_refl",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 278,
"column": 61
} | {
"line": 278,
"column": 63
} | {
"line": 279,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ PowerSeries.subst F.zeroX F.zeroX = F.zeroX",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"CommRing",
"Trans.trans",
"MvPowerSeries.instZero",
"Fintype.elems",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 299,
"column": 58
} | {
"line": 299,
"column": 60
} | {
"line": 300,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\nthis : Invertible ((PowerSeries.coeff 1) F.zeroX)\n⊢ F.zeroX = PowerSeries.subst (PowerSeries.subst F.zeroX F.zeroX) F.zeroX.substInv",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 304,
"column": 13
} | {
"line": 304,
"column": 15
} | {
"line": 305,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\nthis : Invertible ((PowerSeries.coeff 1) F.zeroX)\n⊢ PowerSeries.subst (PowerSeries.subst F.zeroX F.zeroX) F.zeroX.substInv = PowerSeries.X",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 298,
"column": 2
} | {
"line": 305,
"column": 79
} | {
"line": 307,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\nthis : Invertible ((PowerSeries.coeff 1) F.zeroX)\n⊢ F.zeroX = PowerSeries.X",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Trans.trans",
"MvPowerSeries.instZero",
"IsScalarTower.right",
... | [] | calc
_ = F.zeroX.substInv.subst (F.zeroX.subst F.zeroX) := by
have aux₀ : PowerSeries.HasSubst F.zeroX :=
PowerSeries.HasSubst.of_constantCoeff_zero' <| F.constantCoeff_zeroX
rw [← PowerSeries.subst_comp_subst_apply aux₀ aux₀, PowerSeries.subst_substInv_left _
F.constantCoeff_zeroX, Powe... | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 296,
"column": 46
} | {
"line": 296,
"column": 48
} | {
"line": 297,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nF : FormalGroup R\n⊢ F.zeroX = PowerSeries.X",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Trans.trans",
"MvPowerSeries.instZero",
"Semiring.toModule",
"IsScalarTower.right",
"congrArg",
"CommS... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 310,
"column": 84
} | {
"line": 310,
"column": 86
} | {
"line": 311,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ subst ![f, 0] F.toPowerSeries = PowerSeries.subst f (subst ![PowerSeries.X, 0] F.toPowerSeries)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"dite_cond... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 317,
"column": 13
} | {
"line": 317,
"column": 15
} | {
"line": 318,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ PowerSeries.subst f (subst ![PowerSeries.X, 0] F.toPowerSeries) = f",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"CommRing",
"MvPowerSeries.instZ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 308,
"column": 41
} | {
"line": 308,
"column": 43
} | {
"line": 309,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ subst ![f, 0] F.toPowerSeries = f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"UniformSpace",
"Eq.mpr",
"Unit.u... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HahnEmbedding | {
"line": 93,
"column": 33
} | {
"line": 93,
"column": 35
} | {
"line": 94,
"column": 4
} | [
{
"pp": "M : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedAddMonoid M\nf₁ : M →+o DivisibleHull M := DivisibleHull.coeOrderAddMonoidHom M\nhf₁ : Function.Injective ⇑f₁\nhf₁class :\n ∀ (a : M), ArchimedeanClass.mk a = (DivisibleHull.archimedeanClassOrderIso M).symm (ArchimedeanCla... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 323,
"column": 84
} | {
"line": 323,
"column": 86
} | {
"line": 324,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ subst ![0, f] F.toPowerSeries = PowerSeries.subst f (subst ![0, PowerSeries.X] F.toPowerSeries)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"dite_cond... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 323,
"column": 84
} | {
"line": 329,
"column": 29
} | {
"line": 330,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ subst ![0, f] F.toPowerSeries = PowerSeries.subst f (subst ![0, PowerSeries.X] F.toPowerSeries)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"dite_cond... | [] | by
rw [PowerSeries.subst, subst_comp_subst_apply _ hf.const]
· congr! 2 with s
fin_cases s
· simp [subst, eval₂]
· simp [PowerSeries.X, subst]
· exact HasSubst.zero_X | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 330,
"column": 13
} | {
"line": 330,
"column": 15
} | {
"line": 331,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ PowerSeries.subst f (subst ![0, PowerSeries.X] F.toPowerSeries) = f",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"CommRing",
"MvPowerSeries.instZ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
"line": 472,
"column": 64
} | {
"line": 472,
"column": 66
} | {
"line": 473,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nα : Type u_5\nβ : Type u_6\ninst✝⁶ : PartialOrder Γ\ninst✝⁵ : PartialOrder Γ'\ninst✝⁴ : VAdd Γ Γ'\ninst✝³ : IsOrderedCancelVAdd Γ Γ'\nR : Type u_7\nV : Type u_8\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : Module R V\ns : SummableFamily Γ R α\nt : SummableFamily ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 321,
"column": 41
} | {
"line": 321,
"column": 43
} | {
"line": 322,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\n⊢ subst ![0, f] F.toPowerSeries = f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"UniformSpace",
"Eq.mpr",
"Unit.u... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.PowerSeries | {
"line": 58,
"column": 16
} | {
"line": 58,
"column": 18
} | {
"line": 59,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : R⟦ℕ⟧\n⊢ (fun f ↦ { coeff := fun n ↦ (PowerSeries.coeff n) f, isPWO_support' := ⋯ }) ((fun f ↦ PowerSeries.mk f.coeff) f) = f",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"congrArg",
"Hahn... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.PowerSeries | {
"line": 61,
"column": 17
} | {
"line": 61,
"column": 19
} | {
"line": 62,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : PowerSeries R\n⊢ (fun f ↦ PowerSeries.mk f.coeff) ((fun f ↦ { coeff := fun n ↦ (PowerSeries.coeff n) f, isPWO_support' := ⋯ }) f) = f",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"congrArg",
... | [] | by | [anonymous] | by |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.