module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Prime | {
"line": 70,
"column": 57
} | {
"line": 70,
"column": 78
} | {
"line": 70,
"column": 79
} | [
{
"pp": "α : Type u_1\ninst✝ : CommRing α\np : α\nh1 : p ≠ 0\nh2 : ¬IsUnit p\nh3 : ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b\n⊢ ∀ (a b : α), -p ∣ a * b → -p ∣ a ∨ -p ∣ b",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Semigroup.toMul",
... | [
"α : Type u_1\ninst✝ : CommRing α\np : α\nh1 : p ≠ 0\nh2 : ¬IsUnit p\nh3 : ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b\n⊢ ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 108,
"column": 8
} | {
"line": 108,
"column": 30
} | {
"line": 108,
"column": 31
} | [
{
"pp": "case refine_2.succ\np : ℕ\nhp : Fact (Nat.Prime p)\nn i k : ℕ\nhi : p * k < p * (p ^ n * (p - 1))\nhk : i = p * k\nhn : (Polynomial.map (Int.castRingHom (ZMod p)) ((cyclotomic (p ^ (n + 1)) ℤ).comp (X + C 1))).coeff k = 0\n⊢ ((cyclotomic (p ^ (n + 1)) (ZMod p)).comp (X + 1)).coeff k = 0",
"ppTerm":... | [
"case refine_2.succ\np : ℕ\nhp : Fact (Nat.Prime p)\nn i k : ℕ\nhi : p * k < p * (p ^ n * (p - 1))\nhk : i = p * k\nhn : (Polynomial.map (Int.castRingHom (ZMod p)) ((cyclotomic (p ^ (n + 1)) ℤ).comp (X + C 1))).coeff k = 0\n⊢ ((cyclotomic (p ^ (n + 1)) (ZMod p)).comp (X + 1)).coeff k = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.LinearDisjoint | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 55
} | {
"line": 52,
"column": 56
} | [
{
"pp": "A : Type u_1\nB : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝³⁴ : CommRing A\ninst✝³³ : Field K\ninst✝³² : Algebra A K\ninst✝³¹ : IsFractionRing A K\ninst✝³⁰ : CommRing B\ninst✝²⁹ : Field L\ninst✝²⁸ : Algebra B L\ninst✝²⁷ : Algebra A L\ninst✝²⁶ : Algebra K L\ninst✝²⁵ : FiniteDimensional K L\ninst✝²⁴ : ... | [
"A : Type u_1\nB : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝³⁴ : CommRing A\ninst✝³³ : Field K\ninst✝³² : Algebra A K\ninst✝³¹ : IsFractionRing A K\ninst✝³⁰ : CommRing B\ninst✝²⁹ : Field L\ninst✝²⁸ : Algebra B L\ninst✝²⁷ : Algebra A L\ninst✝²⁶ : Algebra K L\ninst✝²⁵ : FiniteDimensional K L\ninst✝²⁴ : IsScalarTowe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 101,
"column": 48
} | {
"line": 101,
"column": 59
} | {
"line": 101,
"column": 60
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn : ℕ\nhcycl : IsCyclotomicExtension {p ^ 0} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ 0)\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis : Fi... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn : ℕ\nhcycl : IsCyclotomicExtension {p ^ 0} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ 0)\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis : FiniteDimensio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 122,
"column": 56
} | {
"line": 122,
"column": 67
} | {
"line": 122,
"column": 68
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn n✝ : ℕ\nhcycl : IsCyclotomicExtension {p ^ (n✝ + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (n✝ + 1))\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn n✝ : ℕ\nhcycl : IsCyclotomicExtension {p ^ (n✝ + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (n✝ + 1))\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 262,
"column": 4
} | {
"line": 262,
"column": 15
} | {
"line": 262,
"column": 16
} | [
{
"pp": "case refine_1\np k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\nthis : NumberField K := numberField {p ^ (k + 1)} ℚ K\nh : hζ.toInteger = 1\n⊢ ζ ^ 1 = 1",
... | [
"case refine_1\np k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\nthis : NumberField K := numberField {p ^ (k + 1)} ℚ K\nh : hζ.toInteger = 1\n⊢ ζ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 375,
"column": 2
} | {
"line": 375,
"column": 38
} | {
"line": 376,
"column": 4
} | [
{
"pp": "p k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\n⊢ (Algebra.norm ℤ) (hζ.toInteger - 1) = ↑p",
"ppTerm": "?m.50",
"assigned": false,
"usedConstants"... | [
"p k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\n⊢ (Algebra.norm ℤ) (hζ.toInteger - 1) = ↑p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 385,
"column": 2
} | {
"line": 385,
"column": 13
} | {
"line": 385,
"column": 14
} | [
{
"pp": "K : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2} ℚ K\nhζ✝ : IsPrimitiveRoot ζ 2\nhζ : IsPrimitiveRoot ζ (2 ^ (0 + 1))\n⊢ (Algebra.norm ℤ) (hζ✝.toInteger - 1) = -2",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"K : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2} ℚ K\nhζ✝ : IsPrimitiveRoot ζ 2\nhζ : IsPrimitiveRoot ζ (2 ^ (0 + 1))\n⊢ (Algebra.norm ℤ) (hζ✝.toInteger - 1) = -2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 391,
"column": 55
} | {
"line": 391,
"column": 66
} | {
"line": 391,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Com... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 392,
"column": 53
} | {
"line": 392,
"column": 64
} | {
"line": 392,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.86",
"assigned": true,
"used... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 419,
"column": 55
} | {
"line": 419,
"column": 66
} | {
"line": 419,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 420,
"column": 53
} | {
"line": 420,
"column": 64
} | {
"line": 420,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.87",
"assigned": true,
"u... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 245,
"column": 43
} | {
"line": 245,
"column": 64
} | {
"line": 245,
"column": 65
} | [
{
"pp": "R : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : PowerBasis K L\nhp : _r... | [
"R : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : PowerBasis K L\nhp : _root_.Prime p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 477,
"column": 55
} | {
"line": 477,
"column": 66
} | {
"line": 477,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 478,
"column": 53
} | {
"line": 478,
"column": 64
} | {
"line": 478,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.83",
"assigned": true,
"u... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 493,
"column": 55
} | {
"line": 493,
"column": 66
} | {
"line": 493,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CommRing",
... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 494,
"column": 53
} | {
"line": 494,
"column": 64
} | {
"line": 494,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants":... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 523,
"column": 55
} | {
"line": 523,
"column": 66
} | {
"line": 523,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CommRing",
... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 524,
"column": 53
} | {
"line": 524,
"column": 64
} | {
"line": 524,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants":... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 121,
"column": 74
} | {
"line": 121,
"column": 87
} | {
"line": 122,
"column": 6
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTowe... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTower A B L\nb :... | true_implies, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 21
} | {
"line": 125,
"column": 22
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTowe... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTower A B L\nb c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 29
} | {
"line": 195,
"column": 30
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : Field K\ninst✝¹⁵ : CommRing B\ninst✝¹⁴ : Field L\ninst✝¹³ : Algebra A K\ninst✝¹² : Algebra B L\ninst✝¹¹ : Algebra A B\ninst✝¹⁰ : Algebra K L\ninst✝⁹ : Algebra A L\ninst✝⁸ : IsScalarTower A K L\ninst✝⁷ : IsScalarTower ... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : Field K\ninst✝¹⁵ : CommRing B\ninst✝¹⁴ : Field L\ninst✝¹³ : Algebra A K\ninst✝¹² : Algebra B L\ninst✝¹¹ : Algebra A B\ninst✝¹⁰ : Algebra K L\ninst✝⁹ : Algebra A L\ninst✝⁸ : IsScalarTower A K L\ninst✝⁷ : IsScalarTower A B L\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 641,
"column": 2
} | {
"line": 641,
"column": 53
} | {
"line": 641,
"column": 54
} | [
{
"pp": "p k : ℕ\nK : Type u\ninst✝² : Field K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\n⊢ NumberField.discr K = (-1) ^ (p ^ k * (p - 1) / 2) * ↑p ^ (p ^ k * ((p - 1) * (k + 1) - 1))",
"ppTerm": "?m.107",
"assigned": false,
"usedConstants": [],
... | [
"p k : ℕ\nK : Type u\ninst✝² : Field K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\n⊢ NumberField.discr K = (-1) ^ (p ^ k * (p - 1) / 2) * ↑p ^ (p ^ k * ((p - 1) * (k + 1) - 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 420,
"column": 2
} | {
"line": 420,
"column": 13
} | {
"line": 420,
"column": 14
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝³⁸ : CommRing A\ninst✝³⁷ : Field K\ninst✝³⁶ : CommRing B\ninst✝³⁵ : Field L\ninst✝³⁴ : Algebra A K\ninst✝³³ : Algebra B L\ninst✝³² : Algebra A B\ninst✝³¹ : Algebra K L\ninst✝³⁰ : Algebra A L\ninst✝²⁹ : IsScalarTower A K L\ninst✝²⁸ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝³⁸ : CommRing A\ninst✝³⁷ : Field K\ninst✝³⁶ : CommRing B\ninst✝³⁵ : Field L\ninst✝³⁴ : Algebra A K\ninst✝³³ : Algebra B L\ninst✝³² : Algebra A B\ninst✝³¹ : Algebra K L\ninst✝³⁰ : Algebra A L\ninst✝²⁹ : IsScalarTower A K L\ninst✝²⁸ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 434,
"column": 2
} | {
"line": 435,
"column": 47
} | {
"line": 435,
"column": 48
} | [
{
"pp": "case h\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝⁴⁰ : CommRing A\ninst✝³⁹ : Field K\ninst✝³⁸ : CommRing B\ninst✝³⁷ : Field L\ninst✝³⁶ : Algebra A K\ninst✝³⁵ : Algebra B L\ninst✝³⁴ : Algebra A B\ninst✝³³ : Algebra K L\ninst✝³² : Algebra A L\ninst✝³¹ : IsScalarTower A K L\ninst✝³⁰ : IsS... | [
"case h\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝⁴⁰ : CommRing A\ninst✝³⁹ : Field K\ninst✝³⁸ : CommRing B\ninst✝³⁷ : Field L\ninst✝³⁶ : Algebra A K\ninst✝³⁵ : Algebra B L\ninst✝³⁴ : Algebra A B\ninst✝³³ : Algebra K L\ninst✝³² : Algebra A L\ninst✝³¹ : IsScalarTower A K L\ninst✝³⁰ : IsScalarTower A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 488,
"column": 6
} | {
"line": 488,
"column": 16
} | {
"line": 488,
"column": 17
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝... | [
"A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝ : FiniteDim... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 490,
"column": 4
} | {
"line": 490,
"column": 70
} | {
"line": 490,
"column": 71
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝... | [
"A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝ : FiniteDim... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 622,
"column": 6
} | {
"line": 622,
"column": 71
} | {
"line": 623,
"column": 6
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : Algebra A K\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra A L\ninst✝⁵ : IsScalarTower A K L\ninst✝⁴ : IsDomain A\ninst✝³ : IsFractionRing A K\ninst✝² : FiniteDimensional K L\ninst✝¹ : Algebra... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : Algebra A K\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra A L\ninst✝⁵ : IsScalarTower A K L\ninst✝⁴ : IsDomain A\ninst✝³ : IsFractionRing A K\ninst✝² : FiniteDimensional K L\ninst✝¹ : Algebra.IsSeparable... | rw [Function.comp_apply, coeff_eq_zero_of_natDegree_lt, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 370,
"column": 12
} | {
"line": 370,
"column": 23
} | {
"line": 370,
"column": 24
} | [
{
"pp": "case zero\nR : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : PowerBasis K... | [
"case zero\nR : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : PowerBasis K L\nhp : _ro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 38
} | {
"line": 100,
"column": 39
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nh : ∑ i, ↑(↑i).mult * Real.log (↑i ((algebraMap (𝓞 K) K) ↑x)) = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))\n⊢ ∑ w, (logEmbedding K) (Additive.ofMul x) w = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))",
"ppTerm": ... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nh : ∑ i, ↑(↑i).mult * Real.log (↑i ((algebraMap (𝓞 K) K) ↑x)) = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))\n⊢ ∑ x_1, ↑(↑x_1).mult * Real.log (↑x_1 ((algebraMap (𝓞 K) K) ↑x)) =\n -(↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x)))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Fintype | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 45
} | {
"line": 66,
"column": 46
} | [
{
"pp": "M₀ : Type u_1\ninst✝² : MonoidWithZero M₀\ninst✝¹ : Nontrivial M₀\ninst✝ : Finite M₀\nthis : Fintype M₀\n⊢ Nat.card M₀ˣ < Nat.card M₀",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_1\ninst✝² : MonoidWithZero M₀\ninst✝¹ : Nontrivial M₀\ninst✝ : Finite M₀\nthis : Fintype M₀\n⊢ Nat.card M₀ˣ < Nat.card M₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 696,
"column": 42
} | {
"line": 696,
"column": 59
} | {
"line": 696,
"column": 60
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 86,
"column": 22
} | {
"line": 86,
"column": 33
} | {
"line": 86,
"column": 34
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ (algebraMap (𝓞 K) K) ↑η ^ 2 + (algebraMap (𝓞 K) K) ↑η + 1 - 3 * (algebraMap (𝓞 K) K) ↑η =\n 0 - 3 * (algebraMap (𝓞 K) K) ↑η",
"ppTerm": "?m.169",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_is... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ζ ^ 2 + ζ + 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 92,
"column": 7
} | {
"line": 92,
"column": 18
} | {
"line": 92,
"column": 19
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ↑(↑⋯.unit ^ 2 + ↑⋯.unit + 1) = ↑0",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"No... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ζ ^ 2 + ζ + 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 718,
"column": 49
} | {
"line": 718,
"column": 60
} | {
"line": 718,
"column": 61
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 720,
"column": 59
} | {
"line": 720,
"column": 70
} | {
"line": 720,
"column": 71
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 721,
"column": 74
} | {
"line": 721,
"column": 85
} | {
"line": 721,
"column": 86
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 29
} | {
"line": 193,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nx : 𝓞 K\nh : λ ∣ x + 1\n⊢ -x - 1 = -(x + 1)",
"ppTerm": "?m.163",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"NumberField.instCommRing... | [] | exact (neg_add' x 1).symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 13
} | {
"line": 147,
"column": 14
} | [
{
"pp": "p : ℕ\nh : Prime p\ns : Finset ℕ\nhs : s ⊆ {1}\n⊢ ∑ i ∈ s, i ≤ 1",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℕ\nh : Prime p\ns : Finset ℕ\nhs : s ⊆ {1}\n⊢ ∑ i ∈ s, i ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 15
} | {
"line": 155,
"column": 16
} | [
{
"pp": "case inl\nn : ℕ\nh : Prime n\n⊢ (n ^ 0).Deficient",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"id",
"instOfNatNat",
"NPow.toPow",
"pow_zero",
... | [
"case inl\nn : ℕ\nh : Prime n\n⊢ Deficient 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic | {
"line": 236,
"column": 6
} | {
"line": 236,
"column": 54
} | {
"line": 236,
"column": 55
} | [
{
"pp": "case neg\nF : Type u_1\ninst✝² : Field F\ninst✝¹ : Fintype F\ninst✝ : DecidableEq F\nhF : ringChar F ≠ 2\na : F\nh₀ : ¬a = 0\ns : Finset F := {x | x ^ 2 = a}.toFinset\nh : ¬IsSquare a\n⊢ ∀ (x : F), x ∉ s",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset... | [
"case neg\nF : Type u_1\ninst✝² : Field F\ninst✝¹ : Fintype F\ninst✝ : DecidableEq F\nhF : ringChar F ≠ 2\na : F\nh₀ : ¬a = 0\ns : Finset F := {x | x ^ 2 = a}.toFinset\nh : ¬IsSquare a\n⊢ ∀ (x : F), ¬a = x ^ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 802,
"column": 6
} | {
"line": 802,
"column": 95
} | {
"line": 803,
"column": 8
} | [
{
"pp": "case neg.refine_1.smul\nA : Type u_1\nB : Type u_3\ninst✝⁸ : CommRing A\ninst✝⁷ : CommRing B\ninst✝⁶ : Algebra A B\ninst✝⁵ : IsDomain A\ninst✝⁴ : IsDedekindDomain A\ninst✝³ : IsDedekindDomain B\ninst✝² : IsTorsionFree A B\ninst✝¹ : Module.Finite A B\ninst✝ : Algebra.IsSeparable (FractionRing A) (Fracti... | [
"case neg.refine_1.smul\nA : Type u_1\nB : Type u_3\ninst✝⁸ : CommRing A\ninst✝⁷ : CommRing B\ninst✝⁶ : Algebra A B\ninst✝⁵ : IsDomain A\ninst✝⁴ : IsDedekindDomain A\ninst✝³ : IsDedekindDomain B\ninst✝² : IsTorsionFree A B\ninst✝¹ : Module.Finite A B\ninst✝ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LegendreSymbol.Basic | {
"line": 63,
"column": 25
} | {
"line": 63,
"column": 45
} | {
"line": 63,
"column": 45
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ZMod p\nha : a ≠ 0\n⊢ Units.mk0 a ha ^ (p / 2) = 1 ↔ a ^ (p / 2) = 1",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"AddGroupWithOne.toAddMonoidWit... | [] | simp [Units.ext_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LegendreSymbol.Basic | {
"line": 63,
"column": 25
} | {
"line": 63,
"column": 45
} | {
"line": 63,
"column": 45
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ZMod p\nha : a ≠ 0\n⊢ Units.mk0 a ha ^ (p / 2) = 1 ↔ a ^ (p / 2) = 1",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"AddGroupWithOne.toAddMonoidWit... | [] | simp [Units.ext_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.Basic | {
"line": 63,
"column": 25
} | {
"line": 63,
"column": 45
} | {
"line": 63,
"column": 45
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ZMod p\nha : a ≠ 0\n⊢ Units.mk0 a ha ^ (p / 2) = 1 ↔ a ^ (p / 2) = 1",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"AddGroupWithOne.toAddMonoidWit... | [] | simp [Units.ext_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.Basic | {
"line": 119,
"column": 6
} | {
"line": 120,
"column": 75
} | {
"line": 121,
"column": 6
} | [
{
"pp": "case pos\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ℤ\nhc : ringChar (ZMod p) = 2\nha : ↑a = 0\n⊢ ↑(legendreSym p a) = ↑a ^ (p / 2)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Nat.Prime",
"instHDiv",
"legendreSym._proof_1",
... | [
"case pos\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ℤ\nhc : ringChar (ZMod p) = 2\nha : ↑a = 0\n⊢ ↑0 = 0"
] | rw [legendreSym, ha, quadraticChar_zero,
zero_pow (Nat.div_pos (@Fact.out p.Prime).two_le (succ_pos 1)).ne'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum | {
"line": 85,
"column": 4
} | {
"line": 85,
"column": 87
} | {
"line": 86,
"column": 6
} | [
{
"pp": "F : Type u_1\ninst✝⁵ : Field F\ninst✝⁴ : Fintype F\ninst✝³ : DecidableEq F\nhF : ringChar F ≠ 2\nF' : Type u_2\ninst✝² : Field F'\ninst✝¹ : Fintype F'\ninst✝ : DecidableEq F'\nhF' : ringChar F' ≠ 2\nh : ringChar F' ≠ ringChar F\nχ : MulChar F F' := (quadraticChar F).ringHomComp (algebraMap ℤ F')\na : F... | [
"F : Type u_1\ninst✝⁵ : Field F\ninst✝⁴ : Fintype F\ninst✝³ : DecidableEq F\nhF : ringChar F ≠ 2\nF' : Type u_2\ninst✝² : Field F'\ninst✝¹ : Fintype F'\ninst✝ : DecidableEq F'\nhF' : ringChar F' ≠ 2\nh : ringChar F' ≠ ringChar F\nχ : MulChar F F' := (quadraticChar F).ringHomComp (algebraMap ℤ F')\na : Fˣ\nha : (qua... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 825,
"column": 4
} | {
"line": 825,
"column": 35
} | {
"line": 825,
"column": 36
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : Algebra A B\ninst✝⁹ : IsDomain A\ninst✝⁸ : IsDedekindDomain A\ninst✝⁷ : IsDedekindDomain B\ninst✝⁶ : IsTorsionFree A B\ninst✝⁵ : Module.Finite A B\ninst✝⁴ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal... | [
"A : Type u_1\nB : Type u_3\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : Algebra A B\ninst✝⁹ : IsDomain A\ninst✝⁸ : IsDedekindDomain A\ninst✝⁷ : IsDedekindDomain B\ninst✝⁶ : IsTorsionFree A B\ninst✝⁵ : Module.Finite A B\ninst✝⁴ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\ninst✝³ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 20
} | {
"line": 118,
"column": 21
} | [
{
"pp": "case inr.inr\na b c : ℤ\nha : a ≠ 0\nh3a : 3 ∣ a\nHgcd : {a, b, c}.gcd id = 1\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nHF : a ^ 3 + b ^ 3 + c ^ 3 = 0\nx : ℤ\nh3b : 3 ∣ b\nhx : x = c\n⊢ 3 ∣ id x",
"ppTerm": "?inr.inr",
"assigned": true,
"us... | [
"case inr.inr\na b c : ℤ\nha : a ≠ 0\nh3a : 3 ∣ a\nHgcd : {a, b, c}.gcd id = 1\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nHF : a ^ 3 + b ^ 3 + c ^ 3 = 0\nx : ℤ\nh3b : 3 ∣ b\nhx : x = c\n⊢ 3 ∣ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 830,
"column": 4
} | {
"line": 830,
"column": 51
} | {
"line": 830,
"column": 52
} | [
{
"pp": "case refine_1\nA : Type u_1\nB : Type u_3\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : Algebra A B\ninst✝⁹ : IsDomain A\ninst✝⁸ : IsDedekindDomain A\ninst✝⁷ : IsDedekindDomain B\ninst✝⁶ : IsTorsionFree A B\ninst✝⁵ : Module.Finite A B\ninst✝⁴ : Algebra.IsSeparable (FractionRing A) (FractionRin... | [
"case refine_1\nA : Type u_1\nB : Type u_3\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : Algebra A B\ninst✝⁹ : IsDomain A\ninst✝⁸ : IsDedekindDomain A\ninst✝⁷ : IsDedekindDomain B\ninst✝⁶ : IsTorsionFree A B\ninst✝⁵ : Module.Finite A B\ninst✝⁴ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Id... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 15
} | {
"line": 178,
"column": 16
} | [
{
"pp": "case refine_5\nK : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nH : FermatLastTheoremForThreeGen hζ\na b c : ℤ\nhc : c ≠ 0\nha : ¬3 ∣ a\nhb : ¬3 ∣ b\nx✝ : 3 ∣ c\nhcoprime : IsCoprime a b\nh : a ^ 3 + b ^ 3 = c ^ 3\nx : ℤ\nhx... | [
"case refine_5\nK : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nH : FermatLastTheoremForThreeGen hζ\na b c : ℤ\nhc : c ≠ 0\nha : ¬3 ∣ a\nhb : ¬3 ∣ b\nx✝ : 3 ∣ c\nhcoprime : IsCoprime a b\nh : a ^ 3 + b ^ 3 = c ^ 3\nx : ℤ\nhx : c = 3 * x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 843,
"column": 6
} | {
"line": 843,
"column": 17
} | {
"line": 843,
"column": 18
} | [
{
"pp": "case refine_1\nA : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing... | [
"case refine_1\nA : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ide... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 67
} | {
"line": 129,
"column": 68
} | [
{
"pp": "case inr\np q : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact (Nat.Prime q)\nhp : p ≠ 2\nhq : q ≠ 2\nh : p ≠ q\nqr : legendreSym q ↑p * legendreSym p ↑q * legendreSym p ↑q = (-1) ^ (p / 2 * (q / 2)) * legendreSym p ↑q\nthis : ↑↑q ≠ 0\n⊢ legendreSym q ↑p = (-1) ^ (p / 2 * (q / 2)) * legendreSym p ↑q",
... | [
"case inr\np q : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fact (Nat.Prime q)\nhp : p ≠ 2\nhq : q ≠ 2\nh : p ≠ q\nqr : legendreSym q ↑p * legendreSym p ↑q * legendreSym p ↑q = (-1) ^ (p / 2 * (q / 2)) * legendreSym p ↑q\nthis : ↑↑q ≠ 0\n⊢ legendreSym q ↑p = (-1) ^ (p / 2 * (q / 2)) * legendreSym p ↑q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 856,
"column": 4
} | {
"line": 856,
"column": 15
} | {
"line": 856,
"column": 16
} | [
{
"pp": "case pos\nA : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\n... | [
"case pos\nA : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 862,
"column": 42
} | {
"line": 862,
"column": 59
} | {
"line": 862,
"column": 60
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal ... | [
"A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FermatPsp | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 41
} | {
"line": 146,
"column": 4
} | [
{
"pp": "a b : ℕ\nha : 2 ≤ a\nhb : 2 < b\n⊢ a ^ 2 * a = a ^ 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.instMonoid",
"Nat.pow_succ",
"id",
"instMulNat",
"instOfNatNat",
"... | [] | rw [Nat.pow_succ a 2] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.FermatPsp | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 41
} | {
"line": 146,
"column": 4
} | [
{
"pp": "a b : ℕ\nha : 2 ≤ a\nhb : 2 < b\n⊢ a ^ 2 * a = a ^ 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.instMonoid",
"Nat.pow_succ",
"id",
"instMulNat",
"instOfNatNat",
"... | [] | rw [Nat.pow_succ a 2] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FermatPsp | {
"line": 145,
"column": 20
} | {
"line": 145,
"column": 41
} | {
"line": 146,
"column": 4
} | [
{
"pp": "a b : ℕ\nha : 2 ≤ a\nhb : 2 < b\n⊢ a ^ 2 * a = a ^ 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.instMonoid",
"Nat.pow_succ",
"id",
"instMulNat",
"instOfNatNat",
"... | [] | rw [Nat.pow_succ a 2] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FermatPsp | {
"line": 150,
"column": 36
} | {
"line": 150,
"column": 62
} | {
"line": 150,
"column": 63
} | [
{
"pp": "b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\n⊢ b - 1 ∣ b ^ p - 1",
"ppTerm": "?m.108",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\n⊢ b - 1 ∣ b ^ p - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FermatPsp | {
"line": 151,
"column": 36
} | {
"line": 151,
"column": 62
} | {
"line": 151,
"column": 63
} | [
{
"pp": "b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\nq₁ : b - 1 ∣ b ^ p - 1\n⊢ b + 1 ∣ b ^ p + 1",
"ppTerm": "?m.140",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"b p : ℕ\nx✝ : 2 ≤ b\nhp : Odd p\nq₁ : b - 1 ∣ b ^ p - 1\n⊢ b + 1 ∣ b ^ p + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 875,
"column": 49
} | {
"line": 875,
"column": 60
} | {
"line": 875,
"column": 61
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal ... | [
"A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FermatPsp | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 39
} | {
"line": 215,
"column": 40
} | [
{
"pp": "b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^... | [
"b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^ (p - 1)\np_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 877,
"column": 59
} | {
"line": 877,
"column": 70
} | {
"line": 877,
"column": 71
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal ... | [
"A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Fermat | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 35
} | {
"line": 105,
"column": 36
} | [
{
"pp": "case inr\nm n : ℕ\nhmn : m ≠ n\nthis : ∀ {m n : ℕ}, m ≠ n → m < n → m.fermatNumber.Coprime n.fermatNumber\nhmn' : ¬m < n\n⊢ m.fermatNumber.Coprime n.fermatNumber",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nm n : ℕ\nhmn : m ≠ n\nthis : ∀ {m n : ℕ}, m ≠ n → m < n → m.fermatNumber.Coprime n.fermatNumber\nhmn' : ¬m < n\n⊢ m.fermatNumber.Coprime n.fermatNumber"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 878,
"column": 74
} | {
"line": 878,
"column": 85
} | {
"line": 878,
"column": 86
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal ... | [
"A : Type u_1\nB : Type u_3\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : CommRing B\ninst✝⁹ : Algebra A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\ninst✝⁶ : IsDedekindDomain B\ninst✝⁵ : IsTorsionFree A B\ninst✝⁴ : Module.Finite A B\ninst✝³ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\np : Ideal A\ninst✝² : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 38
} | {
"line": 290,
"column": 4
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 2 ≤ S'.multiplicity",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"id",
"instOfNatNat",
"LE.le",
"instLENa... | [
"K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 2 ≤ _root_.multiplicity λ S'.c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 307,
"column": 32
} | {
"line": 307,
"column": 49
} | {
"line": 309,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\n⊢ S'.a ^ 3 + S'.a ^ 2 * S'.b * (↑η ^ 2 + ↑η + 1) + S'.a * S'.b ^ 2 * (↑η ^ 2 + ↑η + 1) + S'.b ^ 3 = S'.a ^ 3 + S'.b ^ 3",
"ppTerm": "?m.606",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInte... | [] | rw [eta_sq]; ring | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 307,
"column": 32
} | {
"line": 307,
"column": 49
} | {
"line": 309,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\n⊢ S'.a ^ 3 + S'.a ^ 2 * S'.b * (↑η ^ 2 + ↑η + 1) + S'.a * S'.b ^ 2 * (↑η ^ 2 + ↑η + 1) + S'.b ^ 3 = S'.a ^ 3 + S'.b ^ 3",
"ppTerm": "?m.606",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInte... | [] | rw [eta_sq]; ring | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FermatPsp | {
"line": 248,
"column": 6
} | {
"line": 248,
"column": 32
} | {
"line": 248,
"column": 33
} | [
{
"pp": "b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^... | [
"b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^ (p - 1)\nAB... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Fermat | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 70
} | {
"line": 170,
"column": 71
} | [
{
"pp": "a n p : ℕ\nhp : Prime p\nhp2 : p ≠ 2\nhpdvd : p ∣ a ^ 2 ^ n + 1\nthis✝ : Fact (2 < p)\nthis : Fact (Prime p)\nha1 : ↑a ^ 2 ^ n = -1\nha0 : ↑a ≠ 0\nha : orderOf ↑a = 2 ^ (n + 1)\n⊢ ∃ k, p = k * 2 ^ (n + 1) + 1",
"ppTerm": "?m.187",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"a n p : ℕ\nhp : Prime p\nhp2 : p ≠ 2\nhpdvd : p ∣ a ^ 2 ^ n + 1\nthis✝ : Fact (2 < p)\nthis : Fact (Prime p)\nha1 : ↑a ^ 2 ^ n = -1\nha0 : ↑a ≠ 0\nha : orderOf ↑a = 2 ^ (n + 1)\n⊢ ∃ k, p = k * 2 ^ (n + 1) + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FermatPsp | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 86
} | {
"line": 276,
"column": 87
} | [
{
"pp": "case h\nb : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone :... | [
"case h\nb : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^ (p ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.NatInt | {
"line": 63,
"column": 4
} | {
"line": 63,
"column": 46
} | {
"line": 64,
"column": 4
} | [
{
"pp": "case refine_1.inr.inl\n⊢ (maximalIdeal ℕ).IsPrime",
"ppTerm": "?refine_1.inr.inl",
"assigned": true,
"usedConstants": [
"IsLocalRing.maximalIdeal",
"Ideal.IsMaximal.isPrime",
"instIsLocalRingNat",
"IsLocalRing.maximalIdeal.isMaximal",
"Nat",
"Nat.instComm... | [
"case refine_1.inr.inr\np : ℕ\nhp : Nat.Prime p\n⊢ (span {p}).IsPrime"
] | · exact (maximalIdeal.isMaximal ℕ).isPrime | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.FermatPsp | {
"line": 282,
"column": 4
} | {
"line": 282,
"column": 43
} | {
"line": 282,
"column": 44
} | [
{
"pp": "b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^... | [
"b : ℕ\nb_ge_two : 2 ≤ b\np : ℕ\np_prime : Prime p\np_gt_two : 2 < p\nnot_dvd : ¬p ∣ b * (b ^ 2 - 1)\nA : ℕ := (b ^ p - 1) / (b - 1)\nB : ℕ := (b ^ p + 1) / (b + 1)\nhA : p < A\nhi_A : 1 < A\nhi_B : 1 < B\nhi_b : 0 < b\nhi_bsquared : 0 < b ^ 2 - 1\nhi_bpowtwop : 1 ≤ b ^ (2 * p)\nhi_bpowpsubone : 1 ≤ b ^ (p - 1)\np_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 946,
"column": 10
} | {
"line": 946,
"column": 40
} | {
"line": 946,
"column": 41
} | [
{
"pp": "case hgt\nA : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsDedekindDomain A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Module.Finite A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\nP ... | [
"case hgt\nA : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsDedekindDomain A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Module.Finite A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\nP : Ideal B\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FrobeniusNumber | {
"line": 142,
"column": 28
} | {
"line": 142,
"column": 63
} | {
"line": 142,
"column": 64
} | [
{
"pp": "s : Set ℕ\nh0 : ¬setGcd s = 0\nt : Finset ℕ\nhts : ↑t ⊆ s\na : ↥t → ℤ\neq : ∑ i, a i • ↑↑i = ↑(setGcd s)\nx : ℕ\nhxs : x ∈ s\nhx : x ≠ 0\nn : ℕ := x / setGcd s * ∑ i, (-a i).toNat * ↑i\n⊢ ↑(insert x t) ⊆ s",
"ppTerm": "?m.213",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"con... | [
"s : Set ℕ\nh0 : ¬setGcd s = 0\nt : Finset ℕ\nhts : ↑t ⊆ s\na : ↥t → ℤ\neq : ∑ i, a i • ↑↑i = ↑(setGcd s)\nx : ℕ\nhxs : x ∈ s\nhx : x ≠ 0\nn : ℕ := x / setGcd s * ∑ i, (-a i).toNat * ↑i\n⊢ x ∈ s ∧ ↑t ⊆ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 386,
"column": 65
} | {
"line": 389,
"column": 22
} | {
"line": 391,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ λ ∣ S.a + ↑η ^ 2 * S.b",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"_private.Mathlib.Numb... | [] | by
rw [show S.a + η ^ 2 * S.b = (S.a + S.b) + λ ^ 2 * S.b + 2 * λ * S.b by rw [coe_eta]; ring]
exact dvd_add (dvd_add (dvd_trans (dvd_pow_self _ (by decide)) S.hab) ⟨λ * S.b, by ring⟩)
⟨2 * S.b, by ring⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.FrobeniusNumber | {
"line": 188,
"column": 6
} | {
"line": 188,
"column": 17
} | {
"line": 188,
"column": 18
} | [
{
"pp": "case refine_1\nm n✝¹ : ℕ\ns✝ t✝ : Set ℕ\nn✝ : ℕ\ns : Submodule ℕ ℕ\nt : Finset ℕ\nn : ℕ\nhts : ↑t ⊆ ↑s\nhn : ∀ m ≥ n, setGcd ↑s ∣ m → m ∈ Ideal.span ↑t\n⊢ ↑(t ∪ {m ∈ Finset.range n | m ∈ s}) ⊆ ↑s",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule"... | [
"case refine_1\nm n✝¹ : ℕ\ns✝ t✝ : Set ℕ\nn✝ : ℕ\ns : Submodule ℕ ℕ\nt : Finset ℕ\nn : ℕ\nhts : ↑t ⊆ ↑s\nhn : ∀ m ≥ n, setGcd ↑s ∣ m → m ∈ Ideal.span ↑t\n⊢ ↑t ⊆ ↑s ∧ {x | x < n ∧ x ∈ s} ⊆ ↑s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FrobeniusNumber | {
"line": 191,
"column": 38
} | {
"line": 191,
"column": 49
} | {
"line": 191,
"column": 50
} | [
{
"pp": "m✝ n✝¹ : ℕ\ns✝ t✝ : Set ℕ\nn✝ : ℕ\ns : Submodule ℕ ℕ\nt : Finset ℕ\nn : ℕ\nhts : ↑t ⊆ ↑s\nhn : ∀ m ≥ n, setGcd ↑s ∣ m → m ∈ Ideal.span ↑t\nm : ℕ\nhm : m ∈ s\ngt : m < n\n⊢ m ∈ ↑(t ∪ {m ∈ Finset.range n | m ∈ s})",
"ppTerm": "?m.124",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"m✝ n✝¹ : ℕ\ns✝ t✝ : Set ℕ\nn✝ : ℕ\ns : Submodule ℕ ℕ\nt : Finset ℕ\nn : ℕ\nhts : ↑t ⊆ ↑s\nhn : ∀ m ≥ n, setGcd ↑s ∣ m → m ∈ Ideal.span ↑t\nm : ℕ\nhm : m ∈ s\ngt : m < n\n⊢ m ∈ t ∨ m < n ∧ m ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 489,
"column": 4
} | {
"line": 489,
"column": 86
} | {
"line": 489,
"column": 86
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nh : λ ^ (3 * S.multiplicity - 2) * λ * λ ∣ (S.a + S.b) * (λ * S.y) * (λ * S.z)\nthis : 2 ≤ S.multiplicity\n⊢ λ ^ (3 * S.multiplicity - 2) ∣ S.y * (S.z * (S.a ... | [
"K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nh : λ ^ (3 * S.multiplicity - 2) * λ * λ ∣ (S.a + S.b) * S.y * S.z * λ * λ\nthis : 2 ≤ S.multiplicity\n⊢ λ ^ (3 * S.multiplicity - 2) ∣ S.y * (S.z * (S.a + S.b))"
] | show (S.a + S.b) * (λ * y S) * (λ * z S) = (S.a + S.b) * y S * z S * λ * λ by ring | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 551,
"column": 2
} | {
"line": 565,
"column": 6
} | {
"line": 567,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ S.x * S.y * S.z = ↑S.u * S.w ^ 3",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
... | [] | suffices hh : λ ^ (3 * S.multiplicity - 2) * S.x * λ * S.y * λ * S.z =
S.u * λ ^ (3 * S.multiplicity) * S.w ^ 3 by
rw [show λ ^ (3 * multiplicity S - 2) * x S * λ * y S * λ * z S =
λ ^ (3 * multiplicity S - 2) * λ * λ * x S * y S * z S by ring] at hh
have := S.two_le_multiplicity
rw [mul_comm _ ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 551,
"column": 2
} | {
"line": 565,
"column": 6
} | {
"line": 567,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ S.x * S.y * S.z = ↑S.u * S.w ^ 3",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
... | [] | suffices hh : λ ^ (3 * S.multiplicity - 2) * S.x * λ * S.y * λ * S.z =
S.u * λ ^ (3 * S.multiplicity) * S.w ^ 3 by
rw [show λ ^ (3 * multiplicity S - 2) * x S * λ * y S * λ * z S =
λ ^ (3 * multiplicity S - 2) * λ * λ * x S * y S * z S by ring] at hh
have := S.two_le_multiplicity
rw [mul_comm _ ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Height.Basic | {
"line": 356,
"column": 4
} | {
"line": 356,
"column": 15
} | {
"line": 356,
"column": 16
} | [
{
"pp": "case inr.refine_1\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0\nhx' : (x i)⁻¹ • x ≠ 0\nv : AbsoluteValue K ℝ\nx✝ : v ∈ archAbsVal\n⊢ 1 = v (((x i)⁻¹ • x) i)",
"ppTerm": "?inr.refine_1",
"assigned": tr... | [
"case inr.refine_1\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0\nhx' : (x i)⁻¹ • x ≠ 0\nv : AbsoluteValue K ℝ\nx✝ : v ∈ archAbsVal\n⊢ 1 = (v (x i))⁻¹ * v (x i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 623,
"column": 14
} | {
"line": 623,
"column": 31
} | {
"line": 625,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ S.a + S.b + ↑η ^ 2 * S.b - S.a + ↑η ^ 2 * S.b + 2 * ↑η * S.b + S.b = 0",
"ppTerm": "?m.428",
"assigned": true,
"usedConstants": [
"IsPrimi... | [] | rw [eta_sq]; ring | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 623,
"column": 14
} | {
"line": 623,
"column": 31
} | {
"line": 625,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ S.a + S.b + ↑η ^ 2 * S.b - S.a + ↑η ^ 2 * S.b + 2 * ↑η * S.b + S.b = 0",
"ppTerm": "?m.428",
"assigned": true,
"usedConstants": [
"IsPrimi... | [] | rw [eta_sq]; ring | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Height.Basic | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 20
} | {
"line": 373,
"column": 21
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nf : ι → ι'\nx : ι' → K\nh₀ : x ∘ f = 0\n⊢ mulHeight (x ∘ f) ≤ mulHeight x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case inl\nK : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nf : ι → ι'\nx : ι' → K\nh₀ : x ∘ f = 0\n⊢ 1 ≤ mulHeight x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 392,
"column": 2
} | {
"line": 392,
"column": 42
} | {
"line": 392,
"column": 43
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nf : ι → ι'\nx : ι' → K\n⊢ logHeight (x ∘ f) ≤ logHeight x",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Real.instLE",
"Real",
"Fu... | [
"K : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nf : ι → ι'\nx : ι' → K\n⊢ log (mulHeight (x ∘ f)) ≤ log (mulHeight x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 401,
"column": 67
} | {
"line": 401,
"column": 78
} | {
"line": 401,
"column": 79
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\n⊢ Sum.elim x 0 (Sum.inl i) ≠ 0 (Sum.inl i)",
"ppTerm": "?m.77",
"assigned": true,
"usedConstant... | [
"K : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\n⊢ ¬x i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 408,
"column": 15
} | {
"line": 408,
"column": 26
} | {
"line": 408,
"column": 27
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\nhx' : Sum.elim x 0 ≠ 0\nv : AbsoluteValue K ℝ\nval✝ : ι'\n⊢ v (Sum.elim x 0 (Sum.inr val✝)) ≤ ⨆ i... | [
"case inr\nK : Type u_1\ninst✝³ : Field K\ninst✝² : AdmissibleAbsValues K\nι : Type u_2\nι' : Type u_3\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\nhx' : Sum.elim x 0 ≠ 0\nv : AbsoluteValue K ℝ\nval✝ : ι'\n⊢ 0 ≤ ⨆ i, v (x i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 444,
"column": 2
} | {
"line": 444,
"column": 37
} | {
"line": 444,
"column": 38
} | [
{
"pp": "case e'_5\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_5\ninst✝ : Subsingleton ι\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\nj : ι\n⊢ ((x i)⁻¹ • x) j = 1 j",
"ppTerm": "?e'_5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"D... | [
"case e'_5\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_5\ninst✝ : Subsingleton ι\nx : ι → K\nhx : x ≠ 0\ni : ι\nhi : x i ≠ 0 i\nthis : Nonempty ι\nj : ι\n⊢ (x i)⁻¹ * x i = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 559,
"column": 4
} | {
"line": 559,
"column": 22
} | {
"line": 559,
"column": 23
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : AdmissibleAbsValues K\nx✝ : K\nv : AbsoluteValue K ℝ\nx : K\nthis : ∀ (i : Fin 2), v (![x, 1] i) = ![v x, 1] i\n⊢ max (v x) 1 = ⨆ i, v (![x, 1] i)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : AdmissibleAbsValues K\nx✝ : K\nv : AbsoluteValue K ℝ\nx : K\nthis : ∀ (i : Fin 2), v (![x, 1] i) = ![v x, 1] i\n⊢ max (v x) 1 = ⨆ i, ![v x, 1] i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 561,
"column": 2
} | {
"line": 561,
"column": 47
} | {
"line": 563,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : AdmissibleAbsValues K\nx : K\nH : ∀ (v : AbsoluteValue K ℝ) (x : K), max (v x) 1 = ⨆ i, v (![x, 1] i)\nhx : ![x, 1] ≠ 0\n⊢ mulHeight₁ x = mulHeight ![x, 1]",
"ppTerm": "?m.336",
"assigned": true,
"usedConstants": [
"Real.partialOrder",
"Re... | [] | simp only [mulHeight₁_eq, mulHeight_eq hx, H] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.Height.Basic | {
"line": 758,
"column": 4
} | {
"line": 758,
"column": 15
} | {
"line": 758,
"column": 16
} | [
{
"pp": "case inr.inl\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\ny : ι → K\nhι : Nonempty ι\n⊢ mulHeight (0 * y) ≤ mulHeight 0 * mulHeight y",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"... | [
"case inr.inl\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\ny : ι → K\nhι : Nonempty ι\n⊢ 1 ≤ mulHeight y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 760,
"column": 4
} | {
"line": 760,
"column": 15
} | {
"line": 760,
"column": 16
} | [
{
"pp": "case inr.inr.inl\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\nx : ι → K\nhι : Nonempty ι\nhx : x ≠ 0\n⊢ mulHeight (x * 0) ≤ mulHeight x * mulHeight 0",
"ppTerm": "?inr.inr.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"R... | [
"case inr.inr.inl\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : AdmissibleAbsValues K\nι : Type u_2\ninst✝ : Finite ι\nx : ι → K\nhι : Nonempty ι\nhx : x ≠ 0\n⊢ 1 ≤ mulHeight x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.Basic | {
"line": 793,
"column": 61
} | {
"line": 800,
"column": 30
} | {
"line": 802,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : AdmissibleAbsValues K\nι : Type u_2\ns : Finset ι\nx : ι → K\n⊢ mulHeight₁ (∏ i ∈ s, x i) ≤ ∏ i ∈ s, mulHeight₁ (x i)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Eq.mpr",
"MulOne.toOne",
... | [] | by
classical
induction s using Finset.induction with
| empty => simp
| insert b s hb ih =>
simp only [Finset.prod_insert hb]
grw [← ih]
exact mulHeight₁_mul_le .. | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 53,
"column": 8
} | {
"line": 53,
"column": 19
} | {
"line": 53,
"column": 20
} | [
{
"pp": "case insert.refine_2.inl\nα : Type u_2\nβ : Type u_3\nF : Type u_4\ninst✝³ : AddCommMonoid β\ninst✝² : FunLike F β ℝ\ninst✝¹ : NonnegHomClass F β ℝ\ninst✝ : ZeroHomClass F β ℝ\nv : F\nl : α → β\nhv : IsNonarchimedean ⇑v\na : α\ns : Finset α\nha : a ∉ s\nih : v (∑ i ∈ s, l i) ≤ ⨆ i, v (l ↑i)\nhs : IsEmp... | [
"case insert.refine_2.inl\nα : Type u_2\nβ : Type u_3\nF : Type u_4\ninst✝³ : AddCommMonoid β\ninst✝² : FunLike F β ℝ\ninst✝¹ : NonnegHomClass F β ℝ\ninst✝ : ZeroHomClass F β ℝ\nv : F\nl : α → β\nhv : IsNonarchimedean ⇑v\na : α\ns : Finset α\nha : a ∉ s\nih : v (∑ i ∈ s, l i) ≤ ⨆ i, v (l ↑i)\nhs : IsEmpty ↥s\n⊢ 0 ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 64
} | {
"line": 131,
"column": 65
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nx : ι → K\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight x\nhι' : IsEmpty ι'\n⊢ (mulHeight fun j ↦ ∑ i, A... | [
"case inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nx : ι → K\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight x\nhι' : IsEmpty ι'\n⊢ 1 ≤ ↑(Nat.card ι) ^ totalWeight K * m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 40
} | {
"line": 133,
"column": 41
} | [
{
"pp": "case inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nx : ι → K\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight x\nhι' : Nonempty ι'\nh : (fun j ↦ ∑ i, A (j... | [
"case inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nx : ι → K\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight x\nhι' : Nonempty ι'\nh : (fun j ↦ ∑ i, A (j, i) * x i) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 135,
"column": 4
} | {
"line": 135,
"column": 15
} | {
"line": 135,
"column": 16
} | [
{
"pp": "case inr.inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nx : ι → K\nhι' : Nonempty ι'\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight 0 * mulHeight x\nh : (fun j ↦ ∑ i, 0 (j, i) * x i) ... | [
"case inr.inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nx : ι → K\nhι' : Nonempty ι'\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight 0 * mulHeight x\nh : (fun j ↦ ∑ i, 0 (j, i) * x i) ≠ 0\n⊢ 1 ≤ ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 15
} | {
"line": 137,
"column": 16
} | [
{
"pp": "case inr.inr.inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nhι' : Nonempty ι'\nhA : A ≠ 0\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight 0\nh : (fun j ↦ ... | [
"case inr.inr.inr.inl\nK : Type u_1\ninst✝⁴ : Field K\nι : Type u_2\nι' : Type u_3\ninst✝³ : Fintype ι\ninst✝² : Finite ι'\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Nonempty ι\nA : ι' × ι → K\nhι' : Nonempty ι'\nhA : A ≠ 0\nH₀ : 1 ≤ ↑(Nat.card ι) ^ totalWeight K * mulHeight A * mulHeight 0\nh : (fun j ↦ ∑ i, A (j, i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 709,
"column": 34
} | {
"line": 709,
"column": 78
} | {
"line": 709,
"column": 79
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\nS' : Solution' hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nh : λ ^ (S.multiplicity - 1) * S.X = 0\n⊢ S.X = 0",
"ppTerm": "?m.117",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\nS' : Solution' hζ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nh : λ ^ (S.multiplicity - 1) * S.X = 0\n⊢ S.X = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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