module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 92,
"column": 4
} | {
"line": 92,
"column": 43
} | {
"line": 94,
"column": 0
} | [
{
"pp": "case «2»\nR : Type u_1\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ (t ^ 2 - C 4 * s * u).IsHomogeneous 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"HMul.hMul",
"C... | [] | exact isHomogeneous_X_pow .. |>.sub CXY | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 92,
"column": 4
} | {
"line": 92,
"column": 43
} | {
"line": 94,
"column": 0
} | [
{
"pp": "case «2»\nR : Type u_1\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ (t ^ 2 - C 4 * s * u).IsHomogeneous 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"HMul.hMul",
"C... | [] | exact isHomogeneous_X_pow .. |>.sub CXY | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 402,
"column": 35
} | {
"line": 402,
"column": 47
} | {
"line": 402,
"column": 48
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW' : Affine R\np q : R[X]\n⊢ (p • 1 + q • if 1 = 0 then 1 else 0) *\n (((q * (X ^ 3 + C W'.a₂ * X ^ 2 + C W'.a₄ * X + C W'.a₆)) • if 0 = 1 then 1 else 0) +\n (p - q * (C W'.a₁ * X + C W'.a₃)) • 1) -\n ((q * (X ^ 3 + C W'.a₂ * X ^ 2 + C W'.a₄ * X + C ... | [
"R : Type r\ninst✝ : CommRing R\nW' : Affine R\np q : R[X]\n⊢ (p • 1 + q • if False then 1 else 0) *\n (((q * (X ^ 3 + C W'.a₂ * X ^ 2 + C W'.a₄ * X + C W'.a₆)) • if 0 = 1 then 1 else 0) +\n (p - q * (C W'.a₁ * X + C W'.a₃)) • 1) -\n ((q * (X ^ 3 + C W'.a₂ * X ^ 2 + C W'.a₄ * X + C W'.a₆)) • 1 ... | one_ne_zero, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 32
} | {
"line": 120,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : W.IsElliptic\nx : Fin 3 → R\ni : Fin 3\n⊢ (eval x)\n (Function.uncurry\n ![![C (-W.b₂ ^ 2 * W.b₈ + 9 * W.b₂ * W.b₄ * W.b₆ - 8 * W.b₄ ^ 3 - 27 * W.b₆ ^ 2) * s ^ 2 +\n C (2 * W.b₂ * W.b₄ * ... | [
"R : Type u_1\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : W.IsElliptic\nx : Fin 3 → R\ni : Fin 3\n⊢ (eval x)\n (![![C (-W.b₂ ^ 2 * W.b₈ + 9 * W.b₂ * W.b₄ * W.b₆ - 8 * W.b₄ ^ 3 - 27 * W.b₆ ^ 2) * s ^ 2 +\n C (2 * W.b₂ * W.b₄ * W.b₈ - 2 * W.b₄ ^ 2 * W.b₆ - 10 * W.b₆ * W.b... | Function.uncurry_apply_pair, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 411,
"column": 50
} | {
"line": 412,
"column": 19
} | {
"line": 414,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ preNormEDS b c d 0 = 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
... | [] | by
simp [preNormEDS] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 415,
"column": 49
} | {
"line": 416,
"column": 19
} | {
"line": 418,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ preNormEDS b c d 1 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Int.cast",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.... | [] | by
simp [preNormEDS] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 431,
"column": 78
} | {
"line": 432,
"column": 19
} | {
"line": 434,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\nn : ℤ\n⊢ preNormEDS b c d (-n) = -preNormEDS b c d n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNo... | [] | by
simp [preNormEDS] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 489,
"column": 30
} | {
"line": 489,
"column": 36
} | {
"line": 489,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 489,
"column": 30
} | {
"line": 489,
"column": 36
} | {
"line": 489,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 489,
"column": 30
} | {
"line": 489,
"column": 36
} | {
"line": 489,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 494,
"column": 30
} | {
"line": 494,
"column": 36
} | {
"line": 494,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ Even 4",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",
"Int.instAdd",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 494,
"column": 30
} | {
"line": 494,
"column": 36
} | {
"line": 494,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ Even 4",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",
"Int.instAdd",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 494,
"column": 30
} | {
"line": 494,
"column": 36
} | {
"line": 494,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ Even 4",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",
"Int.instAdd",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 536,
"column": 39
} | {
"line": 536,
"column": 45
} | {
"line": 536,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 536,
"column": 39
} | {
"line": 536,
"column": 45
} | {
"line": 536,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 536,
"column": 39
} | {
"line": 536,
"column": 45
} | {
"line": 536,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Even 3",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
"Bool",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 540,
"column": 38
} | {
"line": 540,
"column": 44
} | {
"line": 540,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Odd 4",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 540,
"column": 38
} | {
"line": 540,
"column": 44
} | {
"line": 540,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Odd 4",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 540,
"column": 38
} | {
"line": 540,
"column": 44
} | {
"line": 540,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nb c d : R\n⊢ ¬Odd 4",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 263,
"column": 35
} | {
"line": 263,
"column": 41
} | {
"line": 263,
"column": 41
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 263,
"column": 35
} | {
"line": 263,
"column": 41
} | {
"line": 263,
"column": 41
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 263,
"column": 35
} | {
"line": 263,
"column": 41
} | {
"line": 263,
"column": 41
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 267,
"column": 34
} | {
"line": 267,
"column": 40
} | {
"line": 267,
"column": 40
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 267,
"column": 34
} | {
"line": 267,
"column": 40
} | {
"line": 267,
"column": 40
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 267,
"column": 34
} | {
"line": 267,
"column": 40
} | {
"line": 267,
"column": 40
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 313,
"column": 33
} | {
"line": 313,
"column": 39
} | {
"line": 313,
"column": 39
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 313,
"column": 33
} | {
"line": 313,
"column": 39
} | {
"line": 313,
"column": 39
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 313,
"column": 33
} | {
"line": 313,
"column": 39
} | {
"line": 313,
"column": 39
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidablePredEven",
"id",
"Int",
"Bool.true",
"instOfNat",
"Even",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 317,
"column": 32
} | {
"line": 317,
"column": 38
} | {
"line": 317,
"column": 38
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 317,
"column": 32
} | {
"line": 317,
"column": 38
} | {
"line": 317,
"column": 38
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 317,
"column": 32
} | {
"line": 317,
"column": 38
} | {
"line": 317,
"column": 38
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Odd 4",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Odd",
"id",
"Int",
"Bool.true",
"Int.instDecidablePredOdd",
"instOfNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 734,
"column": 2
} | {
"line": 734,
"column": 36
} | {
"line": 735,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\nF : Type u_3\ninst✝¹ : FunLike F R S\ninst✝ : RingHomClass F R S\nf : F\nb c d : R\nn : ℕ\n⊢ f (preNormEDS' b c d n) = preNormEDS' (f b) (f c) (f d) n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.i... | [] | induction n using normEDSRec' with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 745,
"column": 90
} | {
"line": 746,
"column": 19
} | {
"line": 748,
"column": 0
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\nF : Type u_3\ninst✝¹ : FunLike F R S\ninst✝ : RingHomClass F R S\nf : F\nb c d : R\nn : ℤ\n⊢ f (preNormEDS b c d n) = preNormEDS (f b) (f c) (f d) n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.cas... | [] | by
simp [preNormEDS] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 379,
"column": 76
} | {
"line": 379,
"column": 82
} | {
"line": 379,
"column": 82
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ Even 2",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instA... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 379,
"column": 76
} | {
"line": 379,
"column": 82
} | {
"line": 379,
"column": 82
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ Even 2",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instA... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 379,
"column": 76
} | {
"line": 379,
"column": 82
} | {
"line": 379,
"column": 82
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ Even 2",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instA... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 384,
"column": 75
} | {
"line": 384,
"column": 81
} | {
"line": 384,
"column": 81
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 384,
"column": 75
} | {
"line": 384,
"column": 81
} | {
"line": 384,
"column": 81
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 384,
"column": 75
} | {
"line": 384,
"column": 81
} | {
"line": 384,
"column": 81
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.105",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 386,
"column": 48
} | {
"line": 386,
"column": 54
} | {
"line": 386,
"column": 54
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.182",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 386,
"column": 48
} | {
"line": 386,
"column": 54
} | {
"line": 386,
"column": 54
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.182",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | {
"line": 386,
"column": 48
} | {
"line": 386,
"column": 54
} | {
"line": 386,
"column": 54
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ ¬Even 3",
"ppTerm": "?m.182",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 21
} | {
"line": 220,
"column": 4
} | [
{
"pp": "F : Type u_1\ninst✝⁴ : Field F\ninst✝³ : IsSepClosed F\nE E' : WeierstrassCurve F\ninst✝² : E.IsElliptic\ninst✝¹ : E'.IsElliptic\np : ℕ\ninst✝ : CharP F p\nheq : E.j = E'.j\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝ : NeZero 2\nthis : 2 ^ 2 ≠ 0\n⊢ 4 ≠ 0",
"ppTerm": "?m.77",
"assigned": true,
"u... | [
"F : Type u_1\ninst✝⁴ : Field F\ninst✝³ : IsSepClosed F\nE E' : WeierstrassCurve F\ninst✝² : E.IsElliptic\ninst✝¹ : E'.IsElliptic\np : ℕ\ninst✝ : CharP F p\nheq : E.j = E'.j\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝ : NeZero 2\nthis : 4 ≠ 0\n⊢ 4 ≠ 0"
] | norm_num1 at this | Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum1_1 | Mathlib.Tactic.normNum1 |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 223,
"column": 4
} | {
"line": 223,
"column": 21
} | {
"line": 224,
"column": 4
} | [
{
"pp": "F : Type u_1\ninst✝⁴ : Field F\ninst✝³ : IsSepClosed F\nE E' : WeierstrassCurve F\ninst✝² : E.IsElliptic\ninst✝¹ : E'.IsElliptic\np : ℕ\ninst✝ : CharP F p\nheq : E.j = E'.j\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝¹ : NeZero 2\nthis✝ : NeZero 4\nthis : 2 * 3 ≠ 0\n⊢ 6 ≠ 0",
"ppTerm": "?m.100",
"ass... | [
"F : Type u_1\ninst✝⁴ : Field F\ninst✝³ : IsSepClosed F\nE E' : WeierstrassCurve F\ninst✝² : E.IsElliptic\ninst✝¹ : E'.IsElliptic\np : ℕ\ninst✝ : CharP F p\nheq : E.j = E'.j\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝¹ : NeZero 2\nthis✝ : NeZero 4\nthis : 6 ≠ 0\n⊢ 6 ≠ 0"
] | norm_num1 at this | Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum1_1 | Mathlib.Tactic.normNum1 |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic | {
"line": 306,
"column": 2
} | {
"line": 306,
"column": 30
} | {
"line": 307,
"column": 2
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW' : Jacobian R\n⊢ W'.polynomialX = C W'.a₁ * Y * Z - (C 3 * X ^ 2 + C (2 * W'.a₂) * X * Z ^ 2 + C W'.a₄ * Z ^ 4)",
"ppTerm": "?m.150",
"assigned": true,
"usedConstants": [
"Derivation",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Weierstra... | [
"R : Type r\ninst✝ : CommRing R\nW' : Jacobian R\n⊢ (pderiv x)\n (Y ^ 2 + C W'.a₁ * X * Y * Z + C W'.a₃ * Y * Z ^ 3 -\n (X ^ 3 + C W'.a₂ * X ^ 2 * Z ^ 2 + C W'.a₄ * X * Z ^ 4 + C W'.a₆ * Z ^ 6)) =\n C W'.a₁ * Y * Z - (C 3 * X ^ 2 + C (2 * W'.a₂) * X * Z ^ 2 + C W'.a₄ * Z ^ 4)"
] | rw [polynomialX, polynomial] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 23
} | {
"line": 243,
"column": 6
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝⁴ : NeZero 2\nthis✝³ : NeZero 4\nthis✝² : NeZero 6\nthis✝¹ : Invertible 2 := invertibleOfNonzero hchar2\n... | [
"F : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝⁴ : NeZero 2\nthis✝³ : NeZero 4\nthis✝² : NeZero 6\nthis✝¹ : Invertible 2 := invertibleOfNonzero hchar2\nthis✝ : Inve... | norm_num1 at this | Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum1_1 | Mathlib.Tactic.normNum1 |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 291,
"column": 2
} | {
"line": 295,
"column": 60
} | {
"line": 297,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℤ\nh : ↑n ≠ 0\n⊢ (W.preΨ n).coeff ((n.natAbs ^ 2 - if Even n then 4 else 1) / 2) ≠ 0",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"AddGroup.toSubtractionMonoid",
"Int.cast",
... | [] | induction n using Int.negInduction with
| nat n => simpa only [preΨ_ofNat, Int.even_coe_nat]
using! W.coeff_preΨ'_ne_zero <| by exact_mod_cast h
| neg ih n => simpa only [preΨ_neg, coeff_neg, neg_ne_zero, Int.natAbs_neg, even_neg]
using! ih n <| neg_ne_zero.mp <| by exact_mod_cast h | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 291,
"column": 2
} | {
"line": 295,
"column": 60
} | {
"line": 297,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℤ\nh : ↑n ≠ 0\n⊢ (W.preΨ n).coeff ((n.natAbs ^ 2 - if Even n then 4 else 1) / 2) ≠ 0",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"AddGroup.toSubtractionMonoid",
"Int.cast",
... | [] | induction n using Int.negInduction with
| nat n => simpa only [preΨ_ofNat, Int.even_coe_nat]
using! W.coeff_preΨ'_ne_zero <| by exact_mod_cast h
| neg ih n => simpa only [preΨ_neg, coeff_neg, neg_ne_zero, Int.natAbs_neg, even_neg]
using! ih n <| neg_ne_zero.mp <| by exact_mod_cast h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 291,
"column": 2
} | {
"line": 295,
"column": 60
} | {
"line": 297,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℤ\nh : ↑n ≠ 0\n⊢ (W.preΨ n).coeff ((n.natAbs ^ 2 - if Even n then 4 else 1) / 2) ≠ 0",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"AddGroup.toSubtractionMonoid",
"Int.cast",
... | [] | induction n using Int.negInduction with
| nat n => simpa only [preΨ_ofNat, Int.even_coe_nat]
using! W.coeff_preΨ'_ne_zero <| by exact_mod_cast h
| neg ih n => simpa only [preΨ_neg, coeff_neg, neg_ne_zero, Int.natAbs_neg, even_neg]
using! ih n <| neg_ne_zero.mp <| by exact_mod_cast h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 325,
"column": 72
} | {
"line": 325,
"column": 75
} | {
"line": 325,
"column": 75
} | [
{
"pp": "case h.a₆\nF : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝³ : NeZero 2\nthis✝² : NeZero 4\nthis✝¹ : NeZero 6\nthis✝ : Invertible 2 := invertibleOfNonzer... | [
"case h.a₆\nF : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝³ : NeZero 2\nthis✝² : NeZero 4\nthis✝¹ : NeZero 6\nthis✝ : Invertible 2 := invertibleOfNonzero hchar2\nth... | hu6 | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 347,
"column": 13
} | {
"line": 347,
"column": 55
} | {
"line": 348,
"column": 2
} | [
{
"pp": "case nat\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℕ\n⊢ (W.ΨSq ↑n).natDegree ≤ (↑n).natAbs ^ 2 - 1",
"ppTerm": "?nat",
"assigned": true,
"usedConstants": [
"Int.cast",
"_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCur... | [] | exact (W.natDegree_coeff_ΨSq_ofNat n).left | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 347,
"column": 13
} | {
"line": 347,
"column": 55
} | {
"line": 348,
"column": 2
} | [
{
"pp": "case nat\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℕ\n⊢ (W.ΨSq ↑n).natDegree ≤ (↑n).natAbs ^ 2 - 1",
"ppTerm": "?nat",
"assigned": true,
"usedConstants": [
"Int.cast",
"_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCur... | [] | exact (W.natDegree_coeff_ΨSq_ofNat n).left | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 347,
"column": 13
} | {
"line": 347,
"column": 55
} | {
"line": 348,
"column": 2
} | [
{
"pp": "case nat\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℕ\n⊢ (W.ΨSq ↑n).natDegree ≤ (↑n).natAbs ^ 2 - 1",
"ppTerm": "?nat",
"assigned": true,
"usedConstants": [
"Int.cast",
"_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCur... | [] | exact (W.natDegree_coeff_ΨSq_ofNat n).left | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 121,
"column": 14
} | {
"line": 121,
"column": 37
} | {
"line": 121,
"column": 38
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ ![P x, -P y, 0] =\n ![P x ^ 2 * P x / P x ^ 2 * ![1, 1, 0] x, (-(P y / P x)) ^ 3 * ![1, 1, 0] y, -(P y / P x) * ![1, 1, 0] z]",
"ppTerm": "?m.103",
"assigned":... | [
"F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ ![P x, -P y, 0] = ![P x * ![1, 1, 0] x, (-(P y / P x)) ^ 3 * ![1, 1, 0] y, -(P y / P x) * ![1, 1, 0] z]"
] | hX.mul_div_cancel_left, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 121,
"column": 65
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 71
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ Odd 3",
"ppTerm": "?m.118",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 121,
"column": 65
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 71
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ Odd 3",
"ppTerm": "?m.118",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 121,
"column": 65
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 71
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ Odd 3",
"ppTerm": "?m.118",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 122,
"column": 44
} | {
"line": 122,
"column": 67
} | {
"line": 122,
"column": 68
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ ![P x, -P y, 0] = ![P x, -(P x ^ 3 * P y / P x ^ 3) * ![1, 1, 0] y, -(P y / P x) * ![1, 1, 0] z]",
"ppTerm": "?m.140",
"assigned": true,
"usedConstants": [
... | [
"F : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nhP : W.Nonsingular P\nhPz : P z = 0\nhX : ∀ {n : ℕ}, IsUnit (P x ^ n)\n⊢ ![P x, -P y, 0] = ![P x, -P y * ![1, 1, 0] y, -(P y / P x) * ![1, 1, 0] z]"
] | hX.mul_div_cancel_left, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 69
} | {
"line": 221,
"column": 2
} | [
{
"pp": "case pos\nR : Type r\ninst✝ : CommRing R\nW' : Jacobian R\nP Q : Fin 3 → R\nu v : R\nhu : IsUnit u\nhv : IsUnit v\nh : P ≈ Q\n⊢ W'.add (u • P) (v • Q) ≈ W'.add P Q",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WeierstrassCurve.Jacobian.add",
"Units.i... | [
"case neg\nR : Type r\ninst✝ : CommRing R\nW' : Jacobian R\nP Q : Fin 3 → R\nu v : R\nhu : IsUnit u\nhv : IsUnit v\nh : ¬P ≈ Q\n⊢ W'.add (u • P) (v • Q) ≈ W'.add P Q"
] | · exact ⟨hu.unit ^ 4, by convert! (add_smul_of_equiv h hu hv).symm⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 373,
"column": 42
} | {
"line": 373,
"column": 69
} | {
"line": 373,
"column": 70
} | [
{
"pp": "R : Type r\ninst✝¹ : CommRing R\nW' : Jacobian R\ninst✝ : NoZeroDivisors R\nP Q : Fin 3 → R\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\nhy : P y * Q z ^ 3 = Q y * P z ^ 3\nhy' : P y * Q z ^ 3 = W'.negY Q * P z ^ 3\n⊢ ![W'.dblU P ^ 2, W'.dblY P, W'.dblZ P] = ![W'.dblU P ^ 2, W'.dblU P ^ 3, 0]",
... | [
"R : Type r\ninst✝¹ : CommRing R\nW' : Jacobian R\ninst✝ : NoZeroDivisors R\nP Q : Fin 3 → R\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\nhy : P y * Q z ^ 3 = Q y * P z ^ 3\nhy' : P y * Q z ^ 3 = W'.negY Q * P z ^ 3\n⊢ ![W'.dblU P ^ 2, W'.dblU P ^ 3, W'.dblZ P] = ![W'.dblU P ^ 2, W'.dblU P ^ 3, 0]"
] | dblY_of_Y_eq hQz hx hy hy', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 325,
"column": 2
} | {
"line": 326,
"column": 71
} | {
"line": 328,
"column": 0
} | [
{
"pp": "case neg\nF : Type u\ninst✝ : Field F\nW : Jacobian F\nP : Fin 3 → F\nQ✝ : PointClass F\nhP : W.Nonsingular P\nhPz : P z = 0\nQ : Fin 3 → F\nhQ : W.NonsingularLift ⟦Q⟧\nhQz : ¬Q z = 0\n⊢ W.addMap ⟦P⟧ ⟦Q⟧ = ⟦Q⟧",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZ... | [] | · rw [addMap_eq, add_of_Z_eq_zero_left hP.left hPz hQz,
smul_eq _ <| (isUnit_X_of_Z_eq_zero hP hPz).mul <| Ne.isUnit hQz] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 560,
"column": 6
} | {
"line": 560,
"column": 20
} | {
"line": 560,
"column": 21
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\n⊢ W.negAddY P Q =\n ((P y * Q z ^ 3 - Q y * P z ^ 3) * (W.addX P Q * (P z * Q z) ^ 2 - P x * Q z ^ 2 * addZ P Q ^ 2) +\n P y * Q z ^ 3 * addZ P Q ^ 3) /\n (P z * Q z) ^ 3",
"ppTerm": "?m.220",... | [
"F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\n⊢ W.negAddY P Q = W.negAddY P Q * (P z * Q z) ^ 3 / (P z * Q z) ^ 3"
] | ← negAddY_eq', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 93,
"column": 8
} | {
"line": 94,
"column": 61
} | {
"line": 95,
"column": 8
} | [
{
"pp": "case inr\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯... | [
"case inr\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu : embed... | have hu : ValueGroup₀.embedding u⁻¹.1 = γx⁻¹ := by
simp [restrict₀_apply, embedding_apply, hu_def, Hx] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Algebra.WithZeroTopology | {
"line": 51,
"column": 86
} | {
"line": 53,
"column": 66
} | {
"line": 55,
"column": 0
} | [
{
"pp": "Γ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n⊢ 𝓝 = update pure 0 (⨅ γ, ⨅ (_ : γ ≠ 0), 𝓟 (Iio γ))",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Pure.pure",
"WithZeroTopology.topologicalSpace",
"Filter.instMembership",
"Iff.mpr",
"Eq.m... | [] | by
rw [nhds_nhdsAdjoint, sup_of_le_right]
exact le_iInf₂ fun γ hγ ↦ le_principal_iff.2 <| zero_lt_iff.2 hγ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.WithZeroTopology | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 34
} | {
"line": 62,
"column": 0
} | [
{
"pp": "Γ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n⊢ 𝓝 0 = ⨅ γ, ⨅ (_ : γ ≠ 0), 𝓟 (Iio γ)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Pure.pure",
"WithZeroTopology.topologicalSpace",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrde... | [] | rw [nhds_eq_update, update_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.WithZeroTopology | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 34
} | {
"line": 62,
"column": 0
} | [
{
"pp": "Γ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n⊢ 𝓝 0 = ⨅ γ, ⨅ (_ : γ ≠ 0), 𝓟 (Iio γ)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Pure.pure",
"WithZeroTopology.topologicalSpace",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrde... | [] | rw [nhds_eq_update, update_self] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.WithZeroTopology | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 34
} | {
"line": 62,
"column": 0
} | [
{
"pp": "Γ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n⊢ 𝓝 0 = ⨅ γ, ⨅ (_ : γ ≠ 0), 𝓟 (Iio γ)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Pure.pure",
"WithZeroTopology.topologicalSpace",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrde... | [] | rw [nhds_eq_update, update_self] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 540,
"column": 2
} | {
"line": 540,
"column": 27
} | {
"line": 542,
"column": 0
} | [
{
"pp": "case mk.mk\nR : Type u_1\ninst✝² : Semiring R\ninst✝¹ : ValuativeRel R\nα : Type u_2\ninst✝ : Mul α\nf : R → ↥(posSubmonoid R) → α\nhf : ∀ (x y : R) (t s : ↥(posSubmonoid R)), x * ↑t ≤ᵥ y * ↑s → y * ↑s ≤ᵥ x * ↑t → f x s = f y t\nhdist : ∀ (a b : R) (r s : ↥(posSubmonoid R)), f (a * b) (r * s) = f a r *... | [] | simpa using hdist _ _ _ _ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.Algebra.Valued.WithVal | {
"line": 478,
"column": 2
} | {
"line": 478,
"column": 23
} | {
"line": 478,
"column": 24
} | [
{
"pp": "Γ₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\nR : Type u_3\ninst✝ : Ring R\nv : Valuation R Γ₀\nb : R\n⊢ (WithZero.map' ↑(valueGroupEquiv v).symm) (if h : v b = 0 then 0 else ↑⟨Units.mk0 (v b) ⋯, ⋯⟩) =\n if h : v b = 0 then 0 else ↑⟨Units.mk0 (v b) ⋯, ⋯⟩",
"ppTerm": "?m.35",
"as... | [
"case pos\nΓ₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\nR : Type u_3\ninst✝ : Ring R\nv : Valuation R Γ₀\nb : R\nhb : v b = 0\n⊢ (WithZero.map' ↑(valueGroupEquiv v).symm) (if h : v b = 0 then 0 else ↑⟨Units.mk0 (v b) ⋯, ⋯⟩) =\n if h : v b = 0 then 0 else ↑⟨Units.mk0 (v b) ⋯, ⋯⟩",
"case neg\nΓ₀ : ... | by_cases hb : v b = 0 | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Topology.Algebra.Valued.WithVal | {
"line": 549,
"column": 25
} | {
"line": 549,
"column": 42
} | {
"line": 549,
"column": 43
} | [
{
"pp": "case h\nR : Type u_4\nΓ₀ : Type u_5\nΓ₀' : Type u_6\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : LinearOrderedCommGroupWithZero Γ₀'\nv : Valuation R Γ₀\nw : Valuation R Γ₀'\nhval : Valued R Γ₀'\nhv : Valued.v = w\nh : v.IsEquiv w\nγ : (ofClass Valued.v).ValueGroup₀ˣ\nr s : R\nh... | [
"case h\nR : Type u_4\nΓ₀ : Type u_5\nΓ₀' : Type u_6\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : LinearOrderedCommGroupWithZero Γ₀'\nv : Valuation R Γ₀\nw : Valuation R Γ₀'\nhval : Valued R Γ₀'\nhv : Valued.v = w\nh : v.IsEquiv w\nγ : (ofClass Valued.v).ValueGroup₀ˣ\nr s : R\nhr₀ : 0 < Val... | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 59
} | {
"line": 77,
"column": 4
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nx : K\nπ : A\nhπ : Irreducible π\na b : A\nH : (valuation K (maximalIdeal A)) ((algebraMap A K) a / (algebraMap A K) b)... | [
"case neg\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nx : K\nπ : A\nhπ : Irreducible π\nb : A\nhb : b ∈ nonZeroDivisors A\nn : ℕ\nu : Aˣ\nH : (valuation K (maximalIdeal A)) ((algebraMap... | obtain ⟨n, u, rfl⟩ := eq_unit_mul_pow_irreducible ha hπ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 128,
"column": 2
} | {
"line": 131,
"column": 27
} | {
"line": 132,
"column": 2
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\n⊢ ContinuousAt (⇑v.restrict) 0",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"WithZeroTopology.topologicalSpace",
"Filter.instMembership",
... | [
"case inr\nK : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : K\nh : x ≠ 0\n⊢ ContinuousAt (⇑v.restrict) x"
] | · rw [ContinuousAt, map_zero, WithZeroTopology.tendsto_zero]
intro γ hγ
rw [Filter.Eventually, Valued.mem_nhds_zero]
use Units.mk0 γ hγ; rfl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 245,
"column": 2
} | {
"line": 248,
"column": 27
} | {
"line": 249,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\n⊢ ∃ C, IsMinimal R (C • W)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"i... | [
"R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nC : VariableChange K\nhC : MaximalFor (fun C ↦ IsIntegral R (C • W)) (fun C ↦ valuation_Δ_aux R (C • W)) C\n⊢ ∃ C, Is... | obtain ⟨C, hC⟩ := exists_maximalFor_of_wellFoundedGT
(fun (C : VariableChange K) ↦ IsIntegral R (C • W))
(fun (C : VariableChange K) ↦ valuation_Δ_aux R (C • W))
(exists_isIntegral R W) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 509,
"column": 4
} | {
"line": 509,
"column": 14
} | {
"line": 510,
"column": 4
} | [
{
"pp": "case mpr\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : (coeff 0) φ = 0\n⊢ ∀ m < 1, (coeff m) φ = 0",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"instOfNatNat",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat"
],
"usedFVars": [],
"usedGoals"... | [
"case mpr\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : (coeff 0) φ = 0\nm : ℕ\nhm : m < 1\n⊢ (coeff m) φ = 0"
] | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 679,
"column": 8
} | {
"line": 679,
"column": 14
} | {
"line": 681,
"column": 0
} | [
{
"pp": "case inr.succ\nR : Type u_2\ninst✝ : CommSemiring R\nφ : R⟦X⟧\nn' : ℕ\nih : n' > 0 → (coeff 1) (φ ^ n') = ↑n' * (coeff 1) φ * constantCoeff φ ^ (n' - 1)\nhn : n' + 1 > 0\nh₁ : ∀ (m : ℕ), φ ^ (m + 1) = φ ^ m * φ\nh₂ : antidiagonal 1 = {(0, 1), (1, 0)}\n⊢ (0, 1) ∉ {(1, 0)}",
"ppTerm": "?inr.succ✝",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 679,
"column": 8
} | {
"line": 679,
"column": 14
} | {
"line": 681,
"column": 0
} | [
{
"pp": "case inr.succ\nR : Type u_2\ninst✝ : CommSemiring R\nφ : R⟦X⟧\nn' : ℕ\nih : n' > 0 → (coeff 1) (φ ^ n') = ↑n' * (coeff 1) φ * constantCoeff φ ^ (n' - 1)\nhn : n' + 1 > 0\nh₁ : ∀ (m : ℕ), φ ^ (m + 1) = φ ^ m * φ\nh₂ : antidiagonal 1 = {(0, 1), (1, 0)}\n⊢ (0, 1) ∉ {(1, 0)}",
"ppTerm": "?inr.succ✝",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 679,
"column": 8
} | {
"line": 679,
"column": 14
} | {
"line": 681,
"column": 0
} | [
{
"pp": "case inr.succ\nR : Type u_2\ninst✝ : CommSemiring R\nφ : R⟦X⟧\nn' : ℕ\nih : n' > 0 → (coeff 1) (φ ^ n') = ↑n' * (coeff 1) φ * constantCoeff φ ^ (n' - 1)\nhn : n' + 1 > 0\nh₁ : ∀ (m : ℕ), φ ^ (m + 1) = φ ^ m * φ\nh₂ : antidiagonal 1 = {(0, 1), (1, 0)}\n⊢ (0, 1) ∉ {(1, 0)}",
"ppTerm": "?inr.succ✝",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 697,
"column": 6
} | {
"line": 705,
"column": 26
} | {
"line": 707,
"column": 0
} | [
{
"pp": "case insert\nσ : Type u_1\nR : Type u_3\ninst✝² : CommSemiring R\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq σ\nf : ι → MvPowerSeries σ R\na : ι\ns : Finset ι\nha : a ∉ s\nih : ∀ (d : σ →₀ ℕ), (coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (coeff (l i)) (f i)\nd : σ →₀ ℕ\... | [] | simp only [Set.PairwiseDisjoint, Set.Pairwise, mem_coe, mem_antidiagonal, ne_eq,
disjoint_left, mem_map, mem_attach, Function.Embedding.coeFn_mk, true_and, Subtype.exists,
exists_prop, not_exists, not_and, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂,
Prod.forall, Prod.mk.injEq]
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 697,
"column": 6
} | {
"line": 705,
"column": 26
} | {
"line": 707,
"column": 0
} | [
{
"pp": "case insert\nσ : Type u_1\nR : Type u_3\ninst✝² : CommSemiring R\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq σ\nf : ι → MvPowerSeries σ R\na : ι\ns : Finset ι\nha : a ∉ s\nih : ∀ (d : σ →₀ ℕ), (coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (coeff (l i)) (f i)\nd : σ →₀ ℕ\... | [] | simp only [Set.PairwiseDisjoint, Set.Pairwise, mem_coe, mem_antidiagonal, ne_eq,
disjoint_left, mem_map, mem_attach, Function.Embedding.coeFn_mk, true_and, Subtype.exists,
exists_prop, not_exists, not_and, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂,
Prod.forall, Prod.mk.injEq]
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 810,
"column": 6
} | {
"line": 810,
"column": 44
} | {
"line": 811,
"column": 6
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\nB : Type u_4\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : Nonempty σ\ninst✝ : Nontrivial R\ninhabited_h : Inhabited σ\nx : R\n⊢ ¬(algebraMap R (MvPowerSeries σ R)) x = X default",
"... | [
"σ : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\nB : Type u_4\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : Nonempty σ\ninst✝ : Nontrivial R\ninhabited_h : Inhabited σ\nx : R\n⊢ ∃ x_1, ¬(coeff x_1) ((algebraMap R (MvPowerSeries σ R)) x) = (coeff x... | rw [MvPowerSeries.ext_iff, not_forall] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 61
} | {
"line": 138,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns t : Finset (σ →₀ ℕ)\nhs : IsLowerSet ↑s\nht : IsLowerSet ↑t\nx : σ →₀ ℕ\nf g : MvPowerSeries σ R\nhxs : x ∈ s\nhxt : x ∈ t\n⊢ MvPolynomial.coeff x ((truncFinset R s) f * (truncFinset R t) g) = (coeff x) (f * g)",
"ppTerm": "?m.38",
"assigned... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns t : Finset (σ →₀ ℕ)\nhs : IsLowerSet ↑s\nht : IsLowerSet ↑t\nx : σ →₀ ℕ\nf g : MvPowerSeries σ R\nhxs : x ∈ s\nhxt : x ∈ t\n⊢ ∑ x ∈ antidiagonal x, MvPolynomial.coeff x.1 ((truncFinset R s) f) * MvPolynomial.coeff x.2 ((truncFinset R t) g) =\n ∑ p ∈ antidiag... | simp only [MvPowerSeries.coeff_mul, MvPolynomial.coeff_mul] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 727,
"column": 12
} | {
"line": 727,
"column": 29
} | {
"line": 727,
"column": 30
} | [
{
"pp": "case refine_2.refine_2\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ γ, {x | (valuation K v).restrict... | [
"case refine_2.refine_2\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ γ, {x | (valuation K v).restrict x < ↑γ} ⊆ s... | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 852,
"column": 4
} | {
"line": 857,
"column": 30
} | {
"line": 859,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝⁴ : Field K\ninst✝³ : CommSemiring S\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nv : HeightOneSpectrum R\ninst✝ : Algebra S K\nr : S\nx : (valuation K v).Completion\n⊢ r • x = (Completion.coeRingHom... | [] | induction x using Completion.induction_on with
| hp =>
exact isClosed_eq (continuous_const_smul _) (continuous_const_mul _)
| ih x =>
simp [Algebra.smul_def, Completion.algebraMap_def, WithVal.algebraMap_right_apply,
Completion.coeRingHom] | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 852,
"column": 4
} | {
"line": 857,
"column": 30
} | {
"line": 859,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝⁴ : Field K\ninst✝³ : CommSemiring S\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nv : HeightOneSpectrum R\ninst✝ : Algebra S K\nr : S\nx : (valuation K v).Completion\n⊢ r • x = (Completion.coeRingHom... | [] | induction x using Completion.induction_on with
| hp =>
exact isClosed_eq (continuous_const_smul _) (continuous_const_mul _)
| ih x =>
simp [Algebra.smul_def, Completion.algebraMap_def, WithVal.algebraMap_right_apply,
Completion.coeRingHom] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 852,
"column": 4
} | {
"line": 857,
"column": 30
} | {
"line": 859,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝⁴ : Field K\ninst✝³ : CommSemiring S\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nv : HeightOneSpectrum R\ninst✝ : Algebra S K\nr : S\nx : (valuation K v).Completion\n⊢ r • x = (Completion.coeRingHom... | [] | induction x using Completion.induction_on with
| hp =>
exact isClosed_eq (continuous_const_smul _) (continuous_const_mul _)
| ih x =>
simp [Algebra.smul_def, Completion.algebraMap_def, WithVal.algebraMap_right_apply,
Completion.coeRingHom] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 28
} | {
"line": 193,
"column": 0
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nr : R\nd : σ →₀ ℕ\nh✝ : ¬d = 0\n⊢ Tendsto (fun i ↦ 0) (𝓝 r) (𝓝 0)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"tendsto_const_nhds",
"nhds",
"Zero.toOfNat0",
"OfNat.... | [] | exact tendsto_const_nhds | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 28
} | {
"line": 193,
"column": 0
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nr : R\nd : σ →₀ ℕ\nh✝ : ¬d = 0\n⊢ Tendsto (fun i ↦ 0) (𝓝 r) (𝓝 0)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"tendsto_const_nhds",
"nhds",
"Zero.toOfNat0",
"OfNat.... | [] | exact tendsto_const_nhds | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 28
} | {
"line": 193,
"column": 0
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nr : R\nd : σ →₀ ℕ\nh✝ : ¬d = 0\n⊢ Tendsto (fun i ↦ 0) (𝓝 r) (𝓝 0)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"tendsto_const_nhds",
"nhds",
"Zero.toOfNat0",
"OfNat.... | [] | exact tendsto_const_nhds | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 676,
"column": 4
} | {
"line": 676,
"column": 8
} | {
"line": 677,
"column": 4
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf g : MvPowerSeries σ R\np q : ℕ\nhf : ↑p ≤ weightedOrder w f\nhg : ↑q ≤ weightedOrder w g\nd : σ →₀ ℕ\nhd : ¬(weight w) d = p + q\n⊢ 0 = (coeff d) ((weightedHomogeneousComponent w p) f * (weightedHomogeneousComponent w q) g)",
"p... | [
"case neg\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf g : MvPowerSeries σ R\np q : ℕ\nhf : ↑p ≤ weightedOrder w f\nhg : ↑q ≤ weightedOrder w g\nd : σ →₀ ℕ\nhd : ¬(weight w) d = p + q\n⊢ (coeff d) ((weightedHomogeneousComponent w p) f * (weightedHomogeneousComponent w q) g) = 0"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 1028,
"column": 80
} | {
"line": 1033,
"column": 44
} | {
"line": 1035,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nb : ℝ≥0\nhb : 1 < b\n⊢ IsNonarchimedean (v.intAdicAbvDef hb)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero... | [] | by
intro x y
simp only [intAdicAbvDef]
have h_mono := (toNNReal_strictMono hb).monotone
rw [← h_mono.map_max]
exact h_mono <| v.intValuation.map_add x y | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.PowerSeries.Trunc | {
"line": 82,
"column": 83
} | {
"line": 83,
"column": 64
} | {
"line": 85,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nf : R⟦X⟧\nn : ℕ\n⊢ ((trunc (n + 1)) f).natDegree < n + 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_trunc",
"Preorder.toLT",
"Semiring.toModule",
"ite_eq_right_iff._simp_1",
"Nat.instOne",
... | [] | by
simp +contextual [natDegree_le_iff_coeff_eq_zero, coeff_trunc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 158,
"column": 8
} | {
"line": 158,
"column": 19
} | {
"line": 158,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nH : φ.order < ψ.order\nthis : (φ + ψ).order = φ.order\n⊢ (φ + ψ).order ≤ min φ.order ψ.order",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instLinearOrderENat",
"congrArg",
"PartialOrder.toPreorder"... | [
"R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nH : φ.order < ψ.order\nthis : (φ + ψ).order = φ.order\n⊢ (φ + ψ).order ≤ φ.order ∧ (φ + ψ).order ≤ ψ.order"
] | le_inf_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.PowerSeries.Trunc | {
"line": 213,
"column": 20
} | {
"line": 213,
"column": 24
} | {
"line": 214,
"column": 4
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nf : R[X]\nhn : f.natDegree < n\nm : ℕ\nh : n ≤ m\n⊢ 0 = f.coeff m",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"CommSemiring.toSemiring",
"Polynomial.coeff",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq.symm",
... | [
"R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nf : R[X]\nhn : f.natDegree < n\nm : ℕ\nh : n ≤ m\n⊢ f.coeff m = 0"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.RingTheory.PowerSeries.Trunc | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 6
} | {
"line": 227,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn a b : ℕ\nf g : R⟦X⟧\nha : n < a\nhb : n < b\n⊢ (coeff n) (f * g) = (coeff n) (↑((trunc a) f) * ↑((trunc b) g))",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
... | [
"R : Type u_2\ninst✝ : CommSemiring R\nn a b : ℕ\nf g : R⟦X⟧\nha : n < a\nhb : n < b\n⊢ (coeff n) (↑((trunc a) f) * ↑((trunc b) g)) = (coeff n) (f * g)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.RingTheory.PowerSeries.PiTopology | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 12
} | {
"line": 232,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝¹ : CommRing R\ninst✝ : TopologicalSpace R\na✝ : Nontrivial R\nn : ℕ\n⊢ ∀ (b : ℕ), n ≤ b → ↑n < (-X ^ (b + 1)).order",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | [
"R : Type u_2\ninst✝¹ : CommRing R\ninst✝ : TopologicalSpace R\na✝ : Nontrivial R\nn m : ℕ\nhm : n ≤ m\n⊢ ↑n < (-X ^ (m + 1)).order"
] | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 476,
"column": 4
} | {
"line": 476,
"column": 94
} | {
"line": 477,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : Ring R\np : R⟦X⟧\nT : Subring R\nhp : ∀ (n : ℕ), (coeff n) p ∈ T\n⊢ (p.toSubring T hp).order ≤ p.order",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_toSubring",
"PowerSeries.coeff_of_lt_order",
"Semiri... | [] | refine le_order _ _ fun d hd => by simp [coeff_of_lt_order d hd, ← coeff_toSubring p T hp] | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 476,
"column": 4
} | {
"line": 476,
"column": 94
} | {
"line": 477,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : Ring R\np : R⟦X⟧\nT : Subring R\nhp : ∀ (n : ℕ), (coeff n) p ∈ T\n⊢ (p.toSubring T hp).order ≤ p.order",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_toSubring",
"PowerSeries.coeff_of_lt_order",
"Semiri... | [] | refine le_order _ _ fun d hd => by simp [coeff_of_lt_order d hd, ← coeff_toSubring p T hp] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 476,
"column": 4
} | {
"line": 476,
"column": 94
} | {
"line": 477,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝ : Ring R\np : R⟦X⟧\nT : Subring R\nhp : ∀ (n : ℕ), (coeff n) p ∈ T\n⊢ (p.toSubring T hp).order ≤ p.order",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_toSubring",
"PowerSeries.coeff_of_lt_order",
"Semiri... | [] | refine le_order _ _ fun d hd => by simp [coeff_of_lt_order d hd, ← coeff_toSubring p T hp] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 336,
"column": 53
} | {
"line": 336,
"column": 74
} | {
"line": 336,
"column": 74
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nha' : ∀ (i : σ), constantCoeff (a i) = 0\nf : MvPowerSeries σ R\nhf : constantCoeff f = 0\nd : σ →₀ ℕ\nhd : ¬d = 0\ni : σ\nhi : d i ≠ 0\n⊢ (... | [] | by simp [zero_pow hi] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Real.Cardinality | {
"line": 137,
"column": 4
} | {
"line": 141,
"column": 19
} | {
"line": 142,
"column": 4
} | [
{
"pp": "case zero\nc : ℝ\nh1 : 0 < c\nh2 : c < 1 / 2\nh3 : c < 1\nf g : ℕ → Bool\nhn : ∀ k < 0, f k = g k\nfn : f 0 = false\ngn : g 0 = true\nf_max : ℕ → Bool := fun n ↦ rec false (fun x x_1 ↦ true) n\nhf_max : ∀ (n : ℕ), f n = true → f_max n = true\ng_min : ℕ → Bool := fun n ↦ rec true (fun x x_1 ↦ false) n\n... | [
"case zero\nc : ℝ\nh1 : 0 < c\nh2 : c < 1 / 2\nh3 : c < 1\nf g : ℕ → Bool\nhn : ∀ k < 0, f k = g k\nfn : f 0 = false\ngn : g 0 = true\nf_max : ℕ → Bool := fun n ↦ rec false (fun x x_1 ↦ true) n\nhf_max : ∀ (n : ℕ), f n = true → f_max n = true\ng_min : ℕ → Bool := fun n ↦ rec true (fun x x_1 ↦ false) n\nhg_min : ∀ (... | have : c / (1 - c) < 1 := by
rw [div_lt_one, lt_sub_iff_add_lt]
· convert! _root_.add_lt_add h2 h2
norm_num
rwa [sub_pos] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
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