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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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simp [PreTilt, coeff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.WittVector.Identities | {
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Mathlib.RingTheory.Perfection | {
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simp [PreTilt, coeff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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simp [PreTilt, coeff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.Perfection | {
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{
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.WittVector.Identities | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Domain | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.Identities | {
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Mathlib.RingTheory.WittVector.Domain | {
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Mathlib.RingTheory.WittVector.Identities | {
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Mathlib.RingTheory.WittVector.Domain | {
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Mathlib.RingTheory.WittVector.Identities | {
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Mathlib.RingTheory.WittVector.Domain | {
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Mathlib.RingTheory.WittVector.Domain | {
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Mathlib.RingTheory.Perfection | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
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Mathlib.RingTheory.Perfection | {
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} | [
{
"pp": "K : Type u₁\ninst✝⁴ : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝³ : CommRing O\ninst✝² : Algebra O K\nhv : v.Integers O\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact ¬IsUnit ↑p\n⊢ ModP.preVal K v O p ((coeff 0) 1) ^ p ^ 0 = 1",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants":... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.InitTail | {
"line": 73,
"column": 61
} | {
"line": 73,
"column": 63
} | {
"line": 74,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝ : CommRing R\nP : ℕ → Prop\nx : 𝕎 R\nn : ℕ\n⊢ (select P x).coeff n = (aeval x.coeff) (selectPoly P n)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 753,
"column": 2
} | {
"line": 753,
"column": 56
} | {
"line": 754,
"column": 2
} | [
{
"pp": "case inr.inr\nK : Type u₁\ninst✝⁴ : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝³ : CommRing O\ninst✝² : Algebra O K\nhv : v.Integers O\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact ¬IsUnit ↑p\nf g : PreTilt O p\nhf : f ≠ 0\nhg : g ≠ 0\nm : ℕ\nhm : (coeff m) f ≠ 0\nn : ℕ\nhn : (coeff n) g ≠ 0\n... | [
"case inr.inr\nK : Type u₁\ninst✝⁴ : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝³ : CommRing O\ninst✝² : Algebra O K\nhv : v.Integers O\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact ¬IsUnit ↑p\nf g : PreTilt O p\nhf : f ≠ 0\nhg : g ≠ 0\nm n : ℕ\nhn : (coeff n) g ≠ 0\nhm : (Perfection.coeff (ModP O p) p (ma... | replace hm := coeff_ne_zero_of_le hm (le_max_left m n) | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.RingTheory.WittVector.InitTail | {
"line": 77,
"column": 76
} | {
"line": 77,
"column": 78
} | {
"line": 78,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nP✝ P : ℕ → Prop\n⊢ IsPoly p fun x x_1 x_2 ↦ select P x_2",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"WittVector.select",
"MvPolynomial.aeva... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 358,
"column": 45
} | {
"line": 358,
"column": 47
} | {
"line": 361,
"column": 2
} | [
{
"pp": "p : ℕ\nR S : Type u\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\nf : ⦃R : Type u⦄ → [CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\nhf : IsPoly₂ p f\ng : R →+* S\nx y : 𝕎 R\n⊢ (WittVector.map g) (f x y) = f ((WittVector.map g) x) ((WittVector.map g) y)",
"ppTerm": "?m.30",
"assign... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 90,
"column": 84
} | {
"line": 90,
"column": 86
} | {
"line": 91,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\nx : TruncatedWittVector p n R\n⊢ (mk p fun i ↦ coeff i x) = x",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TruncatedWittVector.coeff",
"TruncatedWittVector.ext",
"congrArg",
"id",
"TruncatedWittVector.coeff_mk... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.InitTail | {
"line": 96,
"column": 27
} | {
"line": 96,
"column": 29
} | {
"line": 97,
"column": 4
} | [
{
"pp": "p : ℕ\nP : ℕ → Prop\nhp : Fact (Nat.Prime p)\nthis✝ : IsPoly p fun {R} [CommRing R] x ↦ select P x + select (fun i ↦ ¬P i) x\nR : Type u_1\nR._inst : CommRing R\nx : 𝕎 R\nn : ℕ\nthis :\n (bind₁ (selectPoly P)) (wittPolynomial p ℤ n) + (bind₁ (selectPoly fun i ↦ ¬P i)) (wittPolynomial p ℤ n) =\n wi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 102,
"column": 93
} | {
"line": 102,
"column": 95
} | {
"line": 103,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nx : TruncatedWittVector p n R\ni : Fin n\n⊢ x.out.coeff ↑i = coeff i x",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TruncatedWittVector.coeff",
"congrArg",
"CommSemiring.toSemiring",
"dif_pos",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 105,
"column": 52
} | {
"line": 105,
"column": 54
} | {
"line": 106,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝ : CommRing R\n⊢ Injective out",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"TruncatedWittVector.coeff",
"TruncatedWittVector.ext",
"congrArg",
"TruncatedWittVector.coeff_out",
"Eq.mp",
"Fin.val",
"WittVector"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 130,
"column": 91
} | {
"line": 130,
"column": 93
} | {
"line": 131,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\nx : 𝕎 R\ni : Fin n\n⊢ TruncatedWittVector.coeff i (truncateFun n x) = x.coeff ↑i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TruncatedWittVector.coeff",
"congrArg",
"WittVector.truncateFun.eq_1",
"id",
"Fin.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 755,
"column": 48
} | {
"line": 755,
"column": 50
} | {
"line": 756,
"column": 4
} | [
{
"pp": "K : Type u₁\ninst✝⁴ : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝³ : CommRing O\ninst✝² : Algebra O K\nhv : v.Integers O\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact ¬IsUnit ↑p\nf g : PreTilt O p\nhf : f ≠ 0\nhg : g ≠ 0\nm n : ℕ\nhm : (Perfection.coeff (ModP O p) p (max m n)) f ≠ 0\nhn : (Per... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 136,
"column": 72
} | {
"line": 136,
"column": 74
} | {
"line": 137,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nx : 𝕎 R\n⊢ (truncateFun n x).out = init n x",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TruncatedWittVector.coeff",
"congrArg",
"CommSemiring.toSemiring",
"Classical.propDecidable",
"Fin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 149,
"column": 85
} | {
"line": 149,
"column": 87
} | {
"line": 150,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nx : TruncatedWittVector p n R\n⊢ WittVector.truncateFun n x.out = x",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"TruncatedWittVector.coeff",
"congrArg",
"TruncatedWittVector.coeff_out",
"TruncatedWittVector.mk_c... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 63,
"column": 57
} | {
"line": 63,
"column": 59
} | {
"line": 64,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nr : R\nn : ℕ\n⊢ (ghostComponent n) (teichmullerFun p r) = r ^ p ^ n",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"MulOne.toOne",
"wittPolynomial",
"False",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 191,
"column": 80
} | {
"line": 191,
"column": 82
} | {
"line": 192,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\ni : Fin n\n⊢ coeff i 0 = 0",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"WittVector.instZero",
"Eq.mpr",
"TruncatedWittVector.coeff",
"congrArg",
"CommSemiring.toSemiring",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 232,
"column": 65
} | {
"line": 232,
"column": 67
} | {
"line": 233,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx y : 𝕎 R\n⊢ truncateFun n (x + y) = truncateFun n x + truncateFun n y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"TruncatedWittVector.instAdd",
"id",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 237,
"column": 65
} | {
"line": 237,
"column": 67
} | {
"line": 238,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx y : 𝕎 R\n⊢ truncateFun n (x * y) = truncateFun n x * truncateFun n y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"WittVector.init_mul",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 240,
"column": 77
} | {
"line": 240,
"column": 79
} | {
"line": 241,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx : 𝕎 R\n⊢ truncateFun n (-x) = -truncateFun n x",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WittVector.instNeg",
"congrArg",
"WittVector.init_neg",
"id",
"T... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 244,
"column": 65
} | {
"line": 244,
"column": 67
} | {
"line": 245,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx y : 𝕎 R\n⊢ truncateFun n (x - y) = truncateFun n x - truncateFun n y",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"id",
"TruncatedWittVect... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 247,
"column": 93
} | {
"line": 247,
"column": 95
} | {
"line": 248,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nm : ℕ\nx : 𝕎 R\n⊢ truncateFun n (m • x) = m • truncateFun n x",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"WittVector.hasNatScalar",
"congrArg",
"id",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 250,
"column": 93
} | {
"line": 250,
"column": 95
} | {
"line": 251,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nm : ℤ\nx : 𝕎 R\n⊢ truncateFun n (m • x) = m • truncateFun n x",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"WittVector.hasIntScalar",
"congrArg",
"WittV... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 72,
"column": 59
} | {
"line": 72,
"column": 61
} | {
"line": 73,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R →+* S\nr : R\n⊢ (map f) (teichmullerFun p r) = teichmullerFun p (f r)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"WittVector.instCommRing",
"CommSemiring.toS... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 253,
"column": 91
} | {
"line": 253,
"column": 93
} | {
"line": 254,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx : 𝕎 R\nm : ℕ\n⊢ truncateFun n (x ^ m) = truncateFun n x ^ m",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WittVector.init_pow",
"congrArg",
"id",
"WittVector.hasNa... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 309,
"column": 70
} | {
"line": 309,
"column": 72
} | {
"line": 310,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx : 𝕎 R\n⊢ x ∈ RingHom.ker (truncate n) ↔ ∀ i < n, x.coeff i = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TruncatedWittVector.coeff",
"RingHom.instRingHomClass",
"Mul... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 78,
"column": 74
} | {
"line": 78,
"column": 76
} | {
"line": 79,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nR : Type u_3\nx y : MvPolynomial R ℚ\n⊢ teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"WittVector.ghostMap.bijective_of_invertible",
"Eq.mpr",
"RingHom.instRingHo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 318,
"column": 71
} | {
"line": 318,
"column": 73
} | {
"line": 319,
"column": 2
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nf : ℕ → R\n⊢ (truncate n) { coeff := f } = TruncatedWittVector.mk p fun k ↦ f ↑k",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"TruncatedWittVector.coeff",
"WittVector.coeff_truncate",
"Tru... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 85,
"column": 74
} | {
"line": 85,
"column": 76
} | {
"line": 86,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nR : Type u_3\nx y : MvPolynomial R ℤ\n⊢ teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"HMul.hMul",
"AddM... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 98,
"column": 10
} | {
"line": 98,
"column": 52
} | {
"line": 98,
"column": 52
} | [
{
"pp": "case succ\np : ℕ\nR : Type u_1\nS : Type u_2\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn✝ : ℕ\n⊢ (teichmullerFun p 1).coeff (n✝ + 1) = coeff 1 (n✝ + 1)",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WittVector.instOne",
"MulOn... | [
"case succ\np : ℕ\nR : Type u_1\nS : Type u_2\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn✝ : ℕ\n⊢ (teichmullerFun p 1).coeff (n✝ + 1) = 0"
] | one_coeff_eq_of_pos _ _ _ (Nat.succ_pos _) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 336,
"column": 28
} | {
"line": 336,
"column": 30
} | {
"line": 337,
"column": 6
} | [
{
"pp": "p n : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nm : ℕ\nhm : n ≤ m\n⊢ RingHom.ker (WittVector.truncate m) ≤ RingHom.ker (WittVector.truncate n)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"RingHom.instRingHomClass... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 95,
"column": 14
} | {
"line": 95,
"column": 16
} | {
"line": 96,
"column": 4
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ teichmullerFun p 1 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WittVector.instOne",
"MulOne.toOne",
"congrArg",
"WittVector.instC... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 355,
"column": 64
} | {
"line": 355,
"column": 66
} | {
"line": 356,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nn₁ n₂ n₃ : ℕ\nh1 : n₁ ≤ n₂\nh2 : n₂ ≤ n₃\nx : TruncatedWittVector p n₃ R\n⊢ (truncate h1) ((truncate h2) x) = (truncate ⋯) x",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"TruncatedWittVector.truncate_wi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.InitTail | {
"line": 85,
"column": 88
} | {
"line": 85,
"column": 90
} | {
"line": 88,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝ : CommRing R\nP : ℕ → Prop\nhp : Fact (Nat.Prime p)\n⊢ ∀ (x : 𝕎 R), select P x + select (fun i ↦ ¬P i) x = x",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"AddMonoidAlgebra.instIsLeftCancelAddZeroOfIsCancelAddOfUniqueSums",
"IsRightCancelA... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Truncated | {
"line": 361,
"column": 83
} | {
"line": 361,
"column": 85
} | {
"line": 362,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nn₁ n₂ n₃ : ℕ\nh1 : n₁ ≤ n₂\nh2 : n₂ ≤ n₃\n⊢ (truncate h1).comp (truncate h2) = truncate ⋯",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"congrArg",
"CommSemiring.toSemiring",
"RingHom",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Teichmuller | {
"line": 99,
"column": 14
} | {
"line": 99,
"column": 16
} | {
"line": 100,
"column": 4
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ ∀ (x y : R), teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.i... | [] | by | [anonymous] | by |
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