module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inl.inr.inl\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 1\nhb : ↑b ^ 3 = 8\nhc : ↑c ^ 3 = 1\n⊢ ¬1 + 8 = 1",
"ppTerm": "?inl.inr.inl",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inl.inr.inr\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 1\nhb : ↑b ^ 3 = 8\nhc : ↑c ^ 3 = 8\n⊢ ¬1 + 8 = 8",
"ppTerm": "?inl.inr.inr",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inr.inl.inl\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 8\nhb : ↑b ^ 3 = 1\nhc : ↑c ^ 3 = 1\n⊢ ¬8 + 1 = 1",
"ppTerm": "?inr.inl.inl",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inr.inl.inr\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 8\nhb : ↑b ^ 3 = 1\nhc : ↑c ^ 3 = 8\n⊢ ¬8 + 1 = 8",
"ppTerm": "?inr.inl.inr",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inr.inr.inl\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 8\nhb : ↑b ^ 3 = 8\nhc : ↑c ^ 3 = 1\n⊢ ¬8 + 8 = 1",
"ppTerm": "?inr.inr.inl",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inr.inr.inr\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 8\nhb : ↑b ^ 3 = 8\nhc : ↑c ^ 3 = 8\n⊢ ¬8 + 8 = 8",
"ppTerm": "?inr.inr.inr",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.Basic | {
"line": 55,
"column": 4
} | {
"line": 57,
"column": 23
} | {
"line": 58,
"column": 4
} | [
{
"pp": "case neg\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : (ZMod p)ˣ\nhc : ¬p = 2\nh₀ : IsSquare x ↔ x ^ (Fintype.card (ZMod p) / 2) = 1\n⊢ (∃ y, y ^ 2 = x) ↔ x ^ (p / 2) = 1",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Monoid.toMulOneClass",
"congrArg",
... | [
"case neg\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : (ZMod p)ˣ\nhc : ¬p = 2\nh₀ : IsSquare x ↔ x ^ (Fintype.card (ZMod p) / 2) = 1\nhs : (∃ y, y ^ 2 = x) ↔ IsSquare x\n⊢ (∃ y, y ^ 2 = x) ↔ x ^ (p / 2) = 1"
] | have hs : (∃ y : (ZMod p)ˣ, y ^ 2 = x) ↔ IsSquare x := by
rw [isSquare_iff_exists_sq x]
simp_rw [eq_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.NumberTheory.FLT.Three | {
"line": 98,
"column": 8
} | {
"line": 98,
"column": 31
} | {
"line": 98,
"column": 32
} | [
{
"pp": "case neg\na b c : ℤ\nha : a ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nh3a : 3 ∣ a\nHF : a ^ 3 + b ^ 3 + c ^ 3 = 0\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nhbc : IsCoprime (-b) (-c)\nh3b : ¬3 ∣ b\nh3c : ¬3 ∣ c\n⊢ (-b) ^ 3 + (-c) ^ 3 = a ^ 3",
"ppTerm": "?n... | [
"case neg\na b c : ℤ\nha : a ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nh3a : 3 ∣ a\nHF : a ^ 3 + b ^ 3 = -c ^ 3\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nhbc : IsCoprime (-b) (-c)\nh3b : ¬3 ∣ b\nh3c : ¬3 ∣ c\n⊢ (-b) ^ 3 + (-c) ^ 3 = a ^ 3"
] | add_eq_zero_iff_eq_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 98,
"column": 49
} | {
"line": 98,
"column": 55
} | {
"line": 98,
"column": 55
} | [
{
"pp": "a b c : ℤ\nha : a ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nh3a : 3 ∣ a\nHF : a ^ 3 + b ^ 3 = -c ^ 3\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nhbc : IsCoprime (-b) (-c)\nh3b : ¬3 ∣ b\nh3c : ¬3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.448",
"assigned": true,
"u... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 98,
"column": 49
} | {
"line": 98,
"column": 55
} | {
"line": 98,
"column": 55
} | [
{
"pp": "a b c : ℤ\nha : a ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nh3a : 3 ∣ a\nHF : a ^ 3 + b ^ 3 = -c ^ 3\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nhbc : IsCoprime (-b) (-c)\nh3b : ¬3 ∣ b\nh3c : ¬3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.448",
"assigned": true,
"u... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 98,
"column": 49
} | {
"line": 98,
"column": 55
} | {
"line": 98,
"column": 55
} | [
{
"pp": "a b c : ℤ\nha : a ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nh3a : 3 ∣ a\nHF : a ^ 3 + b ^ 3 = -c ^ 3\nH : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\nhbc : IsCoprime (-b) (-c)\nh3b : ¬3 ∣ b\nh3c : ¬3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.448",
"assigned": true,
"u... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum | {
"line": 59,
"column": 61
} | {
"line": 59,
"column": 67
} | {
"line": 59,
"column": 68
} | [
{
"pp": "F : Type u_1\ninst✝² : Field F\ninst✝¹ : Fintype F\ninst✝ : DecidableEq F\nhF : ringChar F ≠ 2\n⊢ 4 ∣ 8",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Dvd.dvd",
"of_decide_eq_true",
"Nat.decidable_dvd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum | {
"line": 59,
"column": 61
} | {
"line": 59,
"column": 67
} | {
"line": 59,
"column": 68
} | [
{
"pp": "F : Type u_1\ninst✝² : Field F\ninst✝¹ : Fintype F\ninst✝ : DecidableEq F\nhF : ringChar F ≠ 2\n⊢ 4 ∣ 8",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Dvd.dvd",
"of_decide_eq_true",
"Nat.decidable_dvd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum | {
"line": 59,
"column": 61
} | {
"line": 59,
"column": 67
} | {
"line": 59,
"column": 68
} | [
{
"pp": "F : Type u_1\ninst✝² : Field F\ninst✝¹ : Fintype F\ninst✝ : DecidableEq F\nhF : ringChar F ≠ 2\n⊢ 4 ∣ 8",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Dvd.dvd",
"of_decide_eq_true",
"Nat.decidable_dvd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 108,
"column": 32
} | {
"line": 108,
"column": 38
} | {
"line": 108,
"column": 38
} | [
{
"pp": "a 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\n⊢ ¬3 ∣ 1",
"ppTerm": "?m.165",
"assigned": true,
"usedConstants": [
"Int.decidableDvd",
"i... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 108,
"column": 32
} | {
"line": 108,
"column": 38
} | {
"line": 108,
"column": 38
} | [
{
"pp": "a 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\n⊢ ¬3 ∣ 1",
"ppTerm": "?m.165",
"assigned": true,
"usedConstants": [
"Int.decidableDvd",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 108,
"column": 32
} | {
"line": 108,
"column": 38
} | {
"line": 108,
"column": 38
} | [
{
"pp": "a 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\n⊢ ¬3 ∣ 1",
"ppTerm": "?m.165",
"assigned": true,
"usedConstants": [
"Int.decidableDvd",
"i... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 60
} | {
"line": 135,
"column": 60
} | [
{
"pp": "H : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\na b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nhc : c ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nhF : a ^ 3 + b ^ 3 + -c ^ 3 = 0\nh1 : (3 ∣ a ∨ 3 ∣ b) ∨ 3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.178",
"assigned": true,
"usedConstan... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 60
} | {
"line": 135,
"column": 60
} | [
{
"pp": "H : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\na b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nhc : c ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nhF : a ^ 3 + b ^ 3 + -c ^ 3 = 0\nh1 : (3 ∣ a ∨ 3 ∣ b) ∨ 3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.178",
"assigned": true,
"usedConstan... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 60
} | {
"line": 135,
"column": 60
} | [
{
"pp": "H : ∀ (a b c : ℤ), c ≠ 0 → ¬3 ∣ a → ¬3 ∣ b → 3 ∣ c → IsCoprime a b → a ^ 3 + b ^ 3 ≠ c ^ 3\na b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nhc : c ≠ 0\nHgcd : {a, b, c}.gcd id = 1\nhF : a ^ 3 + b ^ 3 + -c ^ 3 = 0\nh1 : (3 ∣ a ∨ 3 ∣ b) ∨ 3 ∣ c\n⊢ Odd 3",
"ppTerm": "?m.178",
"assigned": true,
"usedConstan... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 155,
"column": 82
} | {
"line": 155,
"column": 88
} | {
"line": 155,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 3 ≠ 0",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 155,
"column": 82
} | {
"line": 155,
"column": 88
} | {
"line": 155,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 3 ≠ 0",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 155,
"column": 82
} | {
"line": 155,
"column": 88
} | {
"line": 155,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 3 ≠ 0",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 172,
"column": 84
} | {
"line": 172,
"column": 90
} | {
"line": 172,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 172,
"column": 84
} | {
"line": 172,
"column": 90
} | {
"line": 172,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 172,
"column": 84
} | {
"line": 172,
"column": 90
} | {
"line": 172,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 173,
"column": 53
} | {
"line": 173,
"column": 59
} | {
"line": 173,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 173,
"column": 53
} | {
"line": 173,
"column": 59
} | {
"line": 173,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 173,
"column": 53
} | {
"line": 173,
"column": 59
} | {
"line": 173,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 174,
"column": 84
} | {
"line": 174,
"column": 90
} | {
"line": 174,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 174,
"column": 84
} | {
"line": 174,
"column": 90
} | {
"line": 174,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 174,
"column": 84
} | {
"line": 174,
"column": 90
} | {
"line": 174,
"column": 90
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 175,
"column": 53
} | {
"line": 175,
"column": 59
} | {
"line": 175,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 175,
"column": 53
} | {
"line": 175,
"column": 59
} | {
"line": 175,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 175,
"column": 53
} | {
"line": 175,
"column": 59
} | {
"line": 175,
"column": 59
} | [
{
"pp": "K : 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\nh... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 845,
"column": 6
} | {
"line": 845,
"column": 30
} | {
"line": 846,
"column": 2
} | [
{
"pp": "case refine_2\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... | [] | exact Ideal.mul_le_right | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.FLT.Three | {
"line": 250,
"column": 48
} | {
"line": 250,
"column": 54
} | {
"line": 250,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 250,
"column": 48
} | {
"line": 250,
"column": 54
} | {
"line": 250,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 250,
"column": 48
} | {
"line": 250,
"column": 54
} | {
"line": 250,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 8
} | {
"line": 252,
"column": 4
} | [
{
"pp": "case inl.inl\nK : 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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = (hζ✝... | [
"case inl.inl\nK : 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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = (hζ✝.toInteger -... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.FLT.Three | {
"line": 261,
"column": 48
} | {
"line": 261,
"column": 54
} | {
"line": 261,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 261,
"column": 48
} | {
"line": 261,
"column": 54
} | {
"line": 261,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 261,
"column": 48
} | {
"line": 261,
"column": 54
} | {
"line": 261,
"column": 54
} | [
{
"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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = (hζ✝.toInteger - 1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 262,
"column": 4
} | {
"line": 262,
"column": 8
} | {
"line": 263,
"column": 4
} | [
{
"pp": "case inr.inr\nK : 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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = (hζ✝... | [
"case inr.inr\nK : 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\nz : 𝓞 K\nhz : S'.c = (hζ✝.toInteger - 1) * z\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = (hζ✝.toInteger - 1) ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = (hζ✝.toInteger -... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.FLT.Three | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 8
} | {
"line": 273,
"column": 4
} | [
{
"pp": "case inl\nK : 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\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = λ ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = λ ^ 4 * y\n⊢ S'.c ^ 3 = λ ^ 4 * (↑S'.u⁻¹ * (x + y))",
"ppTerm": "?inl",... | [
"case inl\nK : 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\nx : 𝓞 K\nhx : S'.a ^ 3 - 1 = λ ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 + 1 = λ ^ 4 * y\n⊢ λ ^ 4 * (↑S'.u⁻¹ * (x + y)) = S'.c ^ 3"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.FLT.Three | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 8
} | {
"line": 273,
"column": 4
} | [
{
"pp": "case inr\nK : 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\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = λ ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = λ ^ 4 * y\n⊢ S'.c ^ 3 = λ ^ 4 * (↑S'.u⁻¹ * (x + y))",
"ppTerm": "?inr",... | [
"case inr\nK : 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\nx : 𝓞 K\nhx : S'.a ^ 3 + 1 = λ ^ 4 * x\ny : 𝓞 K\nhy : S'.b ^ 3 - 1 = λ ^ 4 * y\n⊢ λ ^ 4 * (↑S'.u⁻¹ * (x + y)) = S'.c ^ 3"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.Fermat | {
"line": 90,
"column": 2
} | {
"line": 92,
"column": 60
} | {
"line": 94,
"column": 0
} | [
{
"pp": "n : ℕ\n⊢ ↑(n + 2).fermatNumber = ↑(n + 1).fermatNumber ^ 2 - 2 * (↑n.fermatNumber - 1) ^ 2",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"Nat.fermatNumber",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instOrdere... | [] | rw [Nat.fermatNumber_eq_fermatNumber_sq_sub_two_mul_fermatNumber_sub_one_sq,
Nat.cast_sub <| two_mul_fermatNumber_sub_one_sq_le_fermatNumber_sq n]
simp only [fermatNumber, push_cast, add_tsub_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Fermat | {
"line": 90,
"column": 2
} | {
"line": 92,
"column": 60
} | {
"line": 94,
"column": 0
} | [
{
"pp": "n : ℕ\n⊢ ↑(n + 2).fermatNumber = ↑(n + 1).fermatNumber ^ 2 - 2 * (↑n.fermatNumber - 1) ^ 2",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"Nat.fermatNumber",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instOrdere... | [] | rw [Nat.fermatNumber_eq_fermatNumber_sq_sub_two_mul_fermatNumber_sub_one_sq,
Nat.cast_sub <| two_mul_fermatNumber_sub_one_sq_le_fermatNumber_sq n]
simp only [fermatNumber, push_cast, add_tsub_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 6
} | {
"line": 304,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\n⊢ S'.a ^ 3 + S'.b ^ 3 = (S'.a + S'.b) * (S'.a + ↑η * S'.b) * (S'.a + ↑η ^ 2 * S'.b)",
"ppTerm": "?m.135",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"_privat... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS' : Solution' hζ\n⊢ (S'.a + S'.b) * (S'.a + ↑η * S'.b) * (S'.a + ↑η ^ 2 * S'.b) = S'.a ^ 3 + S'.b ^ 3"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.Fermat | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 74
} | {
"line": 217,
"column": 0
} | [
{
"pp": "n : ℕ\nhn1 : n ≠ 1\nhn0 : n ≠ 0\nhP : Prime (2 ^ n - 1)\nhan1 : 1 < 2 ^ n\nha1 : 1 < 2\nha0 : 0 < 2\nd : ℕ\nhdn : d ∣ n\nhinj : ∀ (x y : ℕ), 2 ^ x - 1 = 2 ^ y - 1 → x = y\nh : 2 ^ d - 1 ∣ 2 ^ n - 1\n⊢ d = 1 ∨ d = n",
"ppTerm": "?m.301",
"assigned": true,
"usedConstants": [
"Nat.instMo... | [] | exact (hP.eq_one_or_self_of_dvd (2 ^ d - 1) h).imp (hinj d 1) (hinj d n) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.FermatPsp | {
"line": 343,
"column": 2
} | {
"line": 343,
"column": 52
} | {
"line": 344,
"column": 2
} | [
{
"pp": "b : ℕ\nh : 1 ≤ b\nn : ℕ\n⊢ ∃ b_1, n ≤ b_1 ∧ b_1.FermatPsp b",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Nat.FermatPsp",
"Preorder.toLE",
"Exists",
"LE.le",
"instLENat",
"And",
"Exists.casesOn",
"Nat.instPreorder",
"Nat",
... | [
"b : ℕ\nh : 1 ≤ b\nn p : ℕ\nhp : p.FermatPsp b ∧ n ≤ p\n⊢ ∃ b_1, n ≤ b_1 ∧ b_1.FermatPsp b"
] | obtain ⟨p, hp⟩ := exists_infinite_pseudoprimes h n | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.NumberTheory.FLT.Three | {
"line": 383,
"column": 61
} | {
"line": 383,
"column": 67
} | {
"line": 383,
"column": 67
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 383,
"column": 61
} | {
"line": 383,
"column": 67
} | {
"line": 383,
"column": 67
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 383,
"column": 61
} | {
"line": 383,
"column": 67
} | {
"line": 383,
"column": 67
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 388,
"column": 56
} | {
"line": 388,
"column": 62
} | {
"line": 388,
"column": 62
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.212",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 388,
"column": 56
} | {
"line": 388,
"column": 62
} | {
"line": 388,
"column": 62
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.212",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 388,
"column": 56
} | {
"line": 388,
"column": 62
} | {
"line": 388,
"column": 62
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nS : Solution hζ\n⊢ 2 ≠ 0",
"ppTerm": "?m.212",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 451,
"column": 2
} | {
"line": 451,
"column": 6
} | {
"line": 452,
"column": 2
} | [
{
"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\np : 𝓞 K\nhp : Prime p\nhpaηb : p ∣ 1 * S.a + ↑η * S.b\nhpaηsqb : p ∣ 1 * S.a + ↑η ^ 2 * S.b\nthis : p ∣ ↑η ^ 2 - ↑η\n⊢ λ = (↑η ^ 2 - ↑η) * ↑η * ↑η",
"ppT... | [
"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\np : 𝓞 K\nhp : Prime p\nhpaηb : p ∣ 1 * S.a + ↑η * S.b\nhpaηsqb : p ∣ 1 * S.a + ↑η ^ 2 * S.b\nthis : p ∣ ↑η ^ 2 - ↑η\n⊢ (↑η ^ 2 - ↑η) * ↑η * ↑η = λ"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.FLT.Three | {
"line": 603,
"column": 81
} | {
"line": 603,
"column": 87
} | {
"line": 603,
"column": 87
} | [
{
"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 ∣ S.X\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 603,
"column": 81
} | {
"line": 603,
"column": 87
} | {
"line": 603,
"column": 87
} | [
{
"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 ∣ S.X\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 603,
"column": 81
} | {
"line": 603,
"column": 87
} | {
"line": 603,
"column": 87
} | [
{
"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 ∣ S.X\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 606,
"column": 81
} | {
"line": 606,
"column": 87
} | {
"line": 606,
"column": 87
} | [
{
"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 ∣ S.Y\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 606,
"column": 81
} | {
"line": 606,
"column": 87
} | {
"line": 606,
"column": 87
} | [
{
"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 ∣ S.Y\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 606,
"column": 81
} | {
"line": 606,
"column": 87
} | {
"line": 606,
"column": 87
} | [
{
"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 ∣ S.Y\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 609,
"column": 81
} | {
"line": 609,
"column": 87
} | {
"line": 609,
"column": 87
} | [
{
"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 ∣ S.Z\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 609,
"column": 81
} | {
"line": 609,
"column": 87
} | {
"line": 609,
"column": 87
} | [
{
"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 ∣ S.Z\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 609,
"column": 81
} | {
"line": 609,
"column": 87
} | {
"line": 609,
"column": 87
} | [
{
"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 ∣ S.Z\n⊢ 3 ≠ 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 48
} | {
"line": 612,
"column": 54
} | {
"line": 612,
"column": 54
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 48
} | {
"line": 612,
"column": 54
} | {
"line": 612,
"column": 54
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 48
} | {
"line": 612,
"column": 54
} | {
"line": 612,
"column": 54
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 60
} | {
"line": 612,
"column": 66
} | {
"line": 612,
"column": 66
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 60
} | {
"line": 612,
"column": 66
} | {
"line": 612,
"column": 66
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FLT.Three | {
"line": 612,
"column": 60
} | {
"line": 612,
"column": 66
} | {
"line": 612,
"column": 66
} | [
{
"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⊢ 0 < 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Harmonic.ZetaAsymp | {
"line": 183,
"column": 8
} | {
"line": 183,
"column": 91
} | {
"line": 184,
"column": 8
} | [
{
"pp": "case hf\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ IntervalIntegrable (fun x ↦ x ^ (-s)) volume (↑n) (↑n + 1)",
"ppTerm": "?hf✝",
"assigned": true,
"usedConstants": [
"Real.instLE",
"Real",
"Real.lattice",
"Real.instZero",
"S... | [
"case hf.refine_1\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ 0 < ↑n",
"case hf.refine_2\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ 0 < ↑n + 1"
] | refine intervalIntegral.intervalIntegrable_rpow (Or.inr <| notMem_uIcc_of_lt ?_ ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.Harmonic.ZetaAsymp | {
"line": 183,
"column": 8
} | {
"line": 183,
"column": 91
} | {
"line": 184,
"column": 8
} | [
{
"pp": "case hg\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ IntervalIntegrable (fun x ↦ x ^ (-(s + 1))) volume (↑n) (↑n + 1)",
"ppTerm": "?hg",
"assigned": true,
"usedConstants": [
"Real.instLE",
"Real",
"Real.lattice",
"Real.instZero",
... | [
"case hg.refine_1\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ 0 < ↑n",
"case hg.refine_2\nn : ℕ\nhn : 0 < n\ns : ℝ\nhs : 1 < s\nhv : ∀ x ∈ uIcc (↑n) (↑n + 1), 0 < x\n⊢ 0 < ↑n + 1"
] | refine intervalIntegral.intervalIntegrable_rpow (Or.inr <| notMem_uIcc_of_lt ?_ ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.Height.MvPolynomial | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 57
} | {
"line": 263,
"column": 2
} | [
{
"pp": "K : Type u_4\ninst✝² : Field K\nι : Type u_5\nι' : Type u_6\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Finite ι'\nh : Nonempty ι'\np : ι' → MvPolynomial ι K\nj : ι'\n⊢ HasFiniteMulSupport fun v ↦ max (⨆ s, ↑v (coeff (↑s) (p j))) 1",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
... | [
"case inl\nK : Type u_4\ninst✝² : Field K\nι : Type u_5\nι' : Type u_6\ninst✝¹ : AdmissibleAbsValues K\ninst✝ : Finite ι'\nh : Nonempty ι'\np : ι' → MvPolynomial ι K\nj : ι'\nhs₀ : IsEmpty ↥(p j).support\n⊢ HasFiniteMulSupport fun v ↦ max (⨆ s, ↑v (coeff (↑s) (p j))) 1",
"case inr\nK : Type u_4\ninst✝² : Field K\... | rcases isEmpty_or_nonempty (p j).support with hs₀ | hs₀ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.RingTheory.RootsOfUnity.Lemmas | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 92
} | {
"line": 49,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nμ : R\nhμ : IsPrimitiveRoot μ (n + 1)\nthis : (-1) ^ n = ∏ k ∈ range n, -1\n⊢ (-1) ^ n * ∏ k ∈ range n, (μ ^ (k + 1) - 1) = ↑n + 1",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"MulOn... | [] | simp only [this, ← prod_mul_distrib, neg_one_mul, neg_sub, ← prod_one_sub_pow_eq_order hμ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.JacobiSum.Basic | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 27
} | {
"line": 93,
"column": 28
} | [
{
"pp": "case e_a.e_a\nF : Type u_1\nR : Type u_2\ninst✝⁴ : CommRing F\ninst✝³ : Nontrivial F\ninst✝² : Fintype F\ninst✝¹ : DecidableEq F\ninst✝ : CommRing R\nχ ψ : MulChar F R\n⊢ 0 = ∑ x ∈ {0, 1}, (χ x - 1) * (ψ (1 - x) - 1)",
"ppTerm": "?e_a.e_a✝",
"assigned": true,
"usedConstants": [
"Eq.mp... | [
"case e_a.e_a\nF : Type u_1\nR : Type u_2\ninst✝⁴ : CommRing F\ninst✝³ : Nontrivial F\ninst✝² : Fintype F\ninst✝¹ : DecidableEq F\ninst✝ : CommRing R\nχ ψ : MulChar F R\n⊢ 0 = (χ 0 - 1) * (ψ (1 - 0) - 1) + (χ 1 - 1) * (ψ (1 - 1) - 1)"
] | sum_pair zero_ne_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Height.NumberField | {
"line": 99,
"column": 20
} | {
"line": 99,
"column": 68
} | {
"line": 99,
"column": 68
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : NumberField K\nM : Type u_2\ninst✝ : AddCommMonoid M\nf : AbsoluteValue K ℝ → M\n⊢ ∀ a ∈ univ, ↑a ∈ archAbsVal.toFinset",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Real.partialOrder",
"Real",
... | [] | simp [InfinitePlace.isInfinitePlace, archAbsVal] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.Height.NumberField | {
"line": 99,
"column": 20
} | {
"line": 99,
"column": 68
} | {
"line": 99,
"column": 68
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : NumberField K\nM : Type u_2\ninst✝ : AddCommMonoid M\nf : AbsoluteValue K ℝ → M\n⊢ ∀ a ∈ univ, ↑a ∈ archAbsVal.toFinset",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Real.partialOrder",
"Real",
... | [] | simp [InfinitePlace.isInfinitePlace, archAbsVal] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Height.NumberField | {
"line": 99,
"column": 20
} | {
"line": 99,
"column": 68
} | {
"line": 99,
"column": 68
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : NumberField K\nM : Type u_2\ninst✝ : AddCommMonoid M\nf : AbsoluteValue K ℝ → M\n⊢ ∀ a ∈ univ, ↑a ∈ archAbsVal.toFinset",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Real.partialOrder",
"Real",
... | [] | simp [InfinitePlace.isInfinitePlace, archAbsVal] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Height.NumberField | {
"line": 99,
"column": 17
} | {
"line": 99,
"column": 68
} | {
"line": 99,
"column": 68
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : NumberField K\nM : Type u_2\ninst✝ : AddCommMonoid M\nf : AbsoluteValue K ℝ → M\n⊢ ∀ a ∈ univ, ↑a ∈ archAbsVal.toFinset",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Real.partialOrder",
"Real",
... | [] | by simp [InfinitePlace.isInfinitePlace, archAbsVal] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Harmonic.ZetaAsymp | {
"line": 504,
"column": 75
} | {
"line": 504,
"column": 96
} | {
"line": 504,
"column": 96
} | [
{
"pp": "h₁ :\n HasDerivAt (id * completedRiemannZeta₀ - 1 - id / (1 - id))\n (1 * completedRiemannZeta₀ 0 + id 0 * deriv completedRiemannZeta₀ 0 - 0 -\n (1 * (1 - id) 0 - id 0 * (0 - 1)) / (1 - id) 0 ^ 2)\n 0\n⊢ ↑π ∈ slitPlane",
"ppTerm": "?m.276",
"assigned": true,
"usedConstants": [
... | [] | by simp [Real.pi_pos] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.JacobiSum.Basic | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 76
} | {
"line": 169,
"column": 2
} | [
{
"pp": "F : Type u_1\nR : Type u_2\ninst✝³ : Field F\ninst✝² : Fintype F\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nχ φ : MulChar F R\nh : χ * φ ≠ 1\nψ : AddChar F R\n⊢ gaussSum (χ * φ) ψ * jacobiSum χ φ = gaussSum χ ψ * gaussSum φ ψ",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"F... | [
"F : Type u_1\nR : Type u_2\ninst✝³ : Field F\ninst✝² : Fintype F\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nχ φ : MulChar F R\nh : χ * φ ≠ 1\nψ : AddChar F R\n⊢ gaussSum (χ * φ) ψ * jacobiSum χ φ = ∑ x ∈ univ \\ {0}, ∑ x_1, χ x_1 * φ (x - x_1) * ψ x + ∑ x, χ x * φ (0 - x) * ψ 0"
] | rw [gaussSum_mul _ _ ψ, sum_eq_sum_sdiff_singleton_add (mem_univ (0 : F))] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Height.NumberField | {
"line": 157,
"column": 2
} | {
"line": 175,
"column": 45
} | {
"line": 178,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : NumberField K\nι : Type u_2\ninst✝¹ : Finite ι\nx : ι → 𝓞 K\ninst✝ : Nonempty ι\nhx : ∀ (i : ι), x i ≠ 0\n⊢ ↑(absNorm (span (Set.range x))) * ∏ᶠ (v : FinitePlace K), ⨆ i, v ↑(x i) = 1",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"... | [] | have H j : span {x j} ≠ ⊥ := mt span_singleton_eq_bot.mp (hx j)
have hx' : ⨆ i, span {x i} ≠ ⊥ :=
iSup_eq_bot.not.mpr <| not_forall.mpr ⟨Classical.ofNonempty, H _⟩
rw [span_range_eq_iSup, ← finprod_finitePlace_pow_multiplicity hx',
map_finprod _ <| hasFiniteMulSupport_fun_pow_multiplicity hx' (·), Nat.cast_... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Height.NumberField | {
"line": 157,
"column": 2
} | {
"line": 175,
"column": 45
} | {
"line": 178,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : NumberField K\nι : Type u_2\ninst✝¹ : Finite ι\nx : ι → 𝓞 K\ninst✝ : Nonempty ι\nhx : ∀ (i : ι), x i ≠ 0\n⊢ ↑(absNorm (span (Set.range x))) * ∏ᶠ (v : FinitePlace K), ⨆ i, v ↑(x i) = 1",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"... | [] | have H j : span {x j} ≠ ⊥ := mt span_singleton_eq_bot.mp (hx j)
have hx' : ⨆ i, span {x i} ≠ ⊥ :=
iSup_eq_bot.not.mpr <| not_forall.mpr ⟨Classical.ofNonempty, H _⟩
rw [span_range_eq_iSup, ← finprod_finitePlace_pow_multiplicity hx',
map_finprod _ <| hasFiniteMulSupport_fun_pow_multiplicity hx' (·), Nat.cast_... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.IsAdjoinRoot | {
"line": 439,
"column": 4
} | {
"line": 439,
"column": 14
} | {
"line": 440,
"column": 4
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring S\nf : R[X]\ninst✝ : Algebra R S\nh : IsAdjoinRootMonic S f\ng : Fin f.natDegree →₀ R\na✝ : Nontrivial R\ni : Fin f.natDegree\n⊢ ∀ (m : ℕ), f.natDegree ≤ m → { toFinsupp := AddMonoidAlgebra.ofCoeff (Finsupp.mapDomain Fin.val g) }.coeff m = 0",
... | [
"R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring S\nf : R[X]\ninst✝ : Algebra R S\nh : IsAdjoinRootMonic S f\ng : Fin f.natDegree →₀ R\na✝ : Nontrivial R\ni : Fin f.natDegree\nm : ℕ\nhm : f.natDegree ≤ m\n⊢ { toFinsupp := AddMonoidAlgebra.ofCoeff (Finsupp.mapDomain Fin.val g) }.coeff m = 0"
] | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.NumberTheory.LSeries.ZMod | {
"line": 212,
"column": 6
} | {
"line": 212,
"column": 51
} | {
"line": 213,
"column": 6
} | [
{
"pp": "case neg\nN : ℕ\ninst✝ : NeZero N\nΦ : ZMod N → ℂ\ns : ℂ\nhs : Φ 0 = 0 ∨ s ≠ 1\nj : ZMod N\nh : ¬(-j ≠ 0 ∨ s ≠ 1)\n⊢ Φ j * LFunction (fun k ↦ 𝕖 (-j * k)) s = Φ j * expZeta (toAddCircle (-j)) s",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"ZMod... | [
"case neg\nN : ℕ\ninst✝ : NeZero N\nΦ : ZMod N → ℂ\ns : ℂ\nhs : Φ 0 = 0 ∨ s ≠ 1\nj : ZMod N\nh : j = 0 ∧ s = 1\n⊢ Φ j * LFunction (fun k ↦ 𝕖 (-j * k)) s = Φ j * expZeta (toAddCircle (-j)) s"
] | simp only [neg_ne_zero, not_or, not_not] at h | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LSeries.ZMod | {
"line": 452,
"column": 4
} | {
"line": 453,
"column": 8
} | {
"line": 454,
"column": 2
} | [
{
"pp": "N : ℕ\ninst✝ : NeZero N\nΦ : ZMod N → ℂ\nhΦ : Function.Odd Φ\ns : ℂ\nhs : 1 < s.re\n⊢ (∑ x, Φ (-x) * expZeta (toAddCircle (-x)) s) / (2 * I) - (∑ x, Φ x * expZeta (toAddCircle (-x)) s) / (2 * I) =\n -I⁻¹ * LFunction (𝓕 Φ) s",
"ppTerm": "?m.260",
"assigned": true,
"usedConstants": [
... | [] | simp only [hΦ _, neg_mul, sum_neg_distrib, LFunction_dft Φ (.inl hΦ.map_zero)]
ring | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LSeries.ZMod | {
"line": 452,
"column": 4
} | {
"line": 453,
"column": 8
} | {
"line": 454,
"column": 2
} | [
{
"pp": "N : ℕ\ninst✝ : NeZero N\nΦ : ZMod N → ℂ\nhΦ : Function.Odd Φ\ns : ℂ\nhs : 1 < s.re\n⊢ (∑ x, Φ (-x) * expZeta (toAddCircle (-x)) s) / (2 * I) - (∑ x, Φ x * expZeta (toAddCircle (-x)) s) / (2 * I) =\n -I⁻¹ * LFunction (𝓕 Φ) s",
"ppTerm": "?m.260",
"assigned": true,
"usedConstants": [
... | [] | simp only [hΦ _, neg_mul, sum_neg_distrib, LFunction_dft Φ (.inl hΦ.map_zero)]
ring | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LSeries.HurwitzZetaValues | {
"line": 170,
"column": 2
} | {
"line": 174,
"column": 43
} | {
"line": 177,
"column": 0
} | [
{
"pp": "k : ℕ\nx : ℝ\nhk : k ≠ 0\nhx : x ∈ Icc 0 1\n⊢ hurwitzZeta (↑x) (1 - 2 * ↑k) =\n -1 / (2 * ↑k) * Polynomial.eval (↑x) (Polynomial.map (algebraMap ℚ ℂ) (Polynomial.bernoulli (2 * k)))",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.neg_zero",
... | [] | suffices hurwitzZetaOdd x (1 - 2 * k) = 0 by
rw [hurwitzZeta, this, add_zero, hurwitzZetaEven_one_sub_two_mul_nat hk hx]
obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hk
rw [Nat.cast_succ, show (1 : ℂ) - 2 * (k + 1) = -2 * k - 1 by ring,
hurwitzZetaOdd_neg_two_mul_nat_sub_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LSeries.HurwitzZetaValues | {
"line": 170,
"column": 2
} | {
"line": 174,
"column": 43
} | {
"line": 177,
"column": 0
} | [
{
"pp": "k : ℕ\nx : ℝ\nhk : k ≠ 0\nhx : x ∈ Icc 0 1\n⊢ hurwitzZeta (↑x) (1 - 2 * ↑k) =\n -1 / (2 * ↑k) * Polynomial.eval (↑x) (Polynomial.map (algebraMap ℚ ℂ) (Polynomial.bernoulli (2 * k)))",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.neg_zero",
... | [] | suffices hurwitzZetaOdd x (1 - 2 * k) = 0 by
rw [hurwitzZeta, this, add_zero, hurwitzZetaEven_one_sub_two_mul_nat hk hx]
obtain ⟨k, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hk
rw [Nat.cast_succ, show (1 : ℂ) - 2 * (k + 1) = -2 * k - 1 by ring,
hurwitzZetaOdd_neg_two_mul_nat_sub_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LSeries.HurwitzZetaValues | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 27
} | {
"line": 222,
"column": 4
} | [
{
"pp": "case inl\n⊢ riemannZeta (2 * ↑0) = (-1) ^ (0 + 1) * 2 ^ (2 * ↑0 - 1) * ↑π ^ (2 * 0) * ↑(bernoulli (2 * 0)) / ↑(2 * 0)!",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"CharP.cast_eq_zero",
"Rat.instOfNat",
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClas... | [
"case inl\n⊢ -1 / 2 = -2⁻¹"
] | simp [riemannZeta_zero] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LSeries.HurwitzZetaValues | {
"line": 232,
"column": 57
} | {
"line": 237,
"column": 13
} | {
"line": 239,
"column": 0
} | [
{
"pp": "⊢ riemannZeta 4 = ↑π ^ 4 / 90",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Preorder.toLT",
"instHDiv",
"Nat.instIsOrderedAddMonoid",
"Real.pi",
"riemannZeta",
"congrA... | [] | by
convert! congr_arg ((↑) : ℝ → ℂ) hasSum_zeta_four.tsum_eq
· rw [← Nat.cast_one, show (4 : ℂ) = (4 : ℕ) by simp,
zeta_nat_eq_tsum_of_gt_one (by simp : 1 < 4)]
simp only [push_cast]
· norm_cast | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LSeries.PrimesInAP | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 32
} | {
"line": 154,
"column": 2
} | [
{
"pp": "case e'_5\nq : ℕ\na : ZMod q\ny : ℝ\nhy : 1 < y\nthis : LSeriesSummable (fun n ↦ ↑(Λ n)) ↑y\nn : ℕ\n⊢ term (fun n ↦ ↑(residueClass a n)) (↑y) n = {n | ↑n = a}.indicator (term (fun n ↦ ↑(Λ n)) ↑y) n",
"ppTerm": "?e'_5",
"assigned": true,
"usedConstants": [
"ArithmeticFunction.vonMangol... | [
"case pos\nq : ℕ\na : ZMod q\ny : ℝ\nhy : 1 < y\nthis : LSeriesSummable (fun n ↦ ↑(Λ n)) ↑y\nn : ℕ\nhn : ↑n = a\n⊢ term (fun n ↦ ↑(residueClass a n)) (↑y) n = {n | ↑n = a}.indicator (term (fun n ↦ ↑(Λ n)) ↑y) n",
"case neg\nq : ℕ\na : ZMod q\ny : ℝ\nhy : 1 < y\nthis : LSeriesSummable (fun n ↦ ↑(Λ n)) ↑y\nn : ℕ\nh... | by_cases hn : (n : ZMod q) = a | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.NumberTheory.ZetaValues | {
"line": 454,
"column": 44
} | {
"line": 454,
"column": 50
} | {
"line": 454,
"column": 51
} | [
{
"pp": "⊢ 2 ≠ 1",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.ZetaValues | {
"line": 454,
"column": 44
} | {
"line": 454,
"column": 50
} | {
"line": 454,
"column": 51
} | [
{
"pp": "⊢ 2 ≠ 1",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ZetaValues | {
"line": 454,
"column": 44
} | {
"line": 454,
"column": 50
} | {
"line": 454,
"column": 51
} | [
{
"pp": "⊢ 2 ≠ 1",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ZetaValues | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 10
} | {
"line": 464,
"column": 0
} | [
{
"pp": "⊢ 4 ≠ 1",
"ppTerm": "?m.116",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.ZetaValues | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 10
} | {
"line": 464,
"column": 0
} | [
{
"pp": "⊢ 4 ≠ 1",
"ppTerm": "?m.116",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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