module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 554,
"column": 4
} | {
"line": 554,
"column": 69
} | {
"line": 555,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z x✝¹ : R\nx✝ : ↥(posSubmonoid R)\n⊢ ValueGroupWithZero.mk x✝¹ x✝ * 0 = 0",
"ppTerm": "?m.372",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submonoid.mul",
"HMul.hMul",
"congrArg",
"Member... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z x✝¹ : R\nx✝ : ↥(posSubmonoid R)\n⊢ ValueGroupWithZero.mk (x✝¹ * 0) (x✝ * 1) = ValueGroupWithZero.mk 0 1"
] | rw [← ValueGroupWithZero.mk_zero 1, ValueGroupWithZero.mk_mul_mk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 141,
"column": 32
} | {
"line": 146,
"column": 54
} | {
"line": 146,
"column": 55
} | [
{
"pp": "R K : Type u\ninst✝² : Ring R\ninst✝¹ : DivisionRing K\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\n⊢ ∀ (s : Set R), s ∈ 𝓝 0 ↔ ∃ γ, {x | v.restrict x < ↑γ} ⊆ s",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"RingSubgroupsBasis.topology",
... | [] | by
letI := @IsTopologicalAddGroup.rightUniformSpace R _ v.subgroups_basis.topology _
intro s
rw [Filter.hasBasis_iff.mp v.subgroups_basis.hasBasis_nhds_zero s]
simp_rw [restrict_lt_iff_lt_embedding]
exact exists_congr fun γ ↦ by rw [true_and]; rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 46
} | {
"line": 116,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : Ring R\ninst✝⁴ : ValuativeRel R\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsTopologicalAddGroup R\nH : ∀ {s : Set R}, s ∈ 𝓝 0 ↔ ∃ γ, {z | v.restrict z < ↑γ} ⊆ s\n⊢ IsValuativeTopolo... | [
"R : Type u_1\ninst✝⁵ : Ring R\ninst✝⁴ : ValuativeRel R\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsTopologicalAddGroup R\nH : ∀ {s : Set R}, s ∈ 𝓝 0 ↔ ∃ γ, {z | v.restrict z < ↑γ} ⊆ s\ns : Set R\nx : R\n⊢ s ∈ 𝓝 x ↔ ... | apply of_mem_nhds_iff_vle v (fun {s x} ↦ ?_) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 71
} | {
"line": 219,
"column": 0
} | [
{
"pp": "case refine_5\nR : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_ad... | [] | · simpa [ContinuousAt] using (cts_add.1 (-x₀)).continuousAt (x := x₀) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 67
} | {
"line": 590,
"column": 67
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\n⊢ W.negAddY P Q = W.negAddY P Q * (P z * Q z) ^ 3 / (P z * Q z) ^ 3",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": ... | [
"F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\n⊢ W.negAddY P Q = W.negAddY P Q"
] | mul_div_cancel_right₀ _ <| pow_ne_zero 3 <| mul_ne_zero hPz hQz | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 647,
"column": 4
} | {
"line": 647,
"column": 67
} | {
"line": 647,
"column": 67
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\n⊢ W.addY P Q = W.addY P Q * (P z * Q z) ^ 3 / (P z * Q z) ^ 3",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
... | [
"F : Type u\ninst✝ : Field F\nW : Jacobian F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\n⊢ W.addY P Q = W.addY P Q"
] | mul_div_cancel_right₀ _ <| pow_ne_zero 3 <| mul_ne_zero hPz hQz | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 737,
"column": 60
} | {
"line": 739,
"column": 10
} | {
"line": 741,
"column": 0
} | [
{
"pp": "R : Type r\nS : Type s\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nW' : Jacobian R\nf : R →+* S\nP : Fin 3 → R\n⊢ (W'.map f).dblY (⇑f ∘ P) = f (W'.dblY P)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"RingHom.instRingHomClass",
... | [] | by
simp only [dblY, negY_eq, map_negDblY, map_dblX, map_dblZ]
map_simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 796,
"column": 25
} | {
"line": 796,
"column": 38
} | {
"line": 796,
"column": 39
} | [
{
"pp": "R : Type r\nS : Type s\nA : Type u\nB : Type v\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : CommRing A\ninst✝⁷ : CommRing B\nW' : Jacobian R\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra S A\ninst✝³ : IsScalarTower R S A\ninst✝² : Algebra R B\ninst✝¹ : Algebra S B\ninst✝ : IsSca... | [
"R : Type r\nS : Type s\nA : Type u\nB : Type v\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : CommRing A\ninst✝⁷ : CommRing B\nW' : Jacobian R\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra S A\ninst✝³ : IsScalarTower R S A\ninst✝² : Algebra R B\ninst✝¹ : Algebra S B\ninst✝ : IsScalarTower R S... | ← map_dblXYZ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 9
} | {
"line": 147,
"column": 2
} | [
{
"pp": "Γ : Type u_1\ninst✝² : LinearOrderedCommGroupWithZero Γ\nA : Type u_2\ninst✝¹ : Ring A\nv : Valuation A Γ\ninst✝ : v.IsRankOneDiscrete\ny : Γˣ\nx : A\nh1 : v x ≠ 0 → v x = 1\n⊢ (MonoidWithZeroHom.ofClass v) x = ↑y → ↑y = ↑1",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Un... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 172,
"column": 59
} | {
"line": 172,
"column": 64
} | {
"line": 172,
"column": 64
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nn : (WithZero (Multiplicative ℤ))ˣ\nhπ : (exp 1)⁻¹ ∈ range ⇑v\nx✝ :\n ∃ a,\n ¬(MonoidWithZeroHom.ofClass v) a = 0 ∧ ∃ x, (MonoidWithZeroHom.ofClass v) a * ↑n = (MonoidWithZeroHom.ofClass v) x\n⊢ U... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 172,
"column": 59
} | {
"line": 172,
"column": 64
} | {
"line": 172,
"column": 64
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nn : (WithZero (Multiplicative ℤ))ˣ\nhπ : (exp 1)⁻¹ ∈ range ⇑v\nx✝ :\n ∃ a,\n ¬(MonoidWithZeroHom.ofClass v) a = 0 ∧ ∃ x, (MonoidWithZeroHom.ofClass v) a * ↑n = (MonoidWithZeroHom.ofClass v) x\n⊢ U... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 172,
"column": 59
} | {
"line": 172,
"column": 64
} | {
"line": 172,
"column": 64
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nn : (WithZero (Multiplicative ℤ))ˣ\nhπ : (exp 1)⁻¹ ∈ range ⇑v\nx✝ :\n ∃ a,\n ¬(MonoidWithZeroHom.ofClass v) a = 0 ∧ ∃ x, (MonoidWithZeroHom.ofClass v) a * ↑n = (MonoidWithZeroHom.ofClass v) x\n⊢ U... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 176,
"column": 47
} | {
"line": 176,
"column": 56
} | {
"line": 177,
"column": 4
} | [
{
"pp": "case hH.ofNat.refine_1\nA : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nn✝ : (WithZero (Multiplicative ℤ))ˣ\nhπ✝ : (exp 1)⁻¹ ∈ range ⇑v\nx✝ : ∃ k, Units.mk0 (exp 1)⁻¹ ⋯ ^ k = n✝\nπ : A\nhπ : v π = (exp 1)⁻¹\nn : ℕ\nh : Units.mk0 (exp 1)⁻¹ ⋯ ^ Int.o... | [] | simp [hπ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 176,
"column": 47
} | {
"line": 176,
"column": 56
} | {
"line": 177,
"column": 4
} | [
{
"pp": "case hH.ofNat.refine_2\nA : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nn✝ : (WithZero (Multiplicative ℤ))ˣ\nhπ✝ : (exp 1)⁻¹ ∈ range ⇑v\nx✝ : ∃ k, Units.mk0 (exp 1)⁻¹ ⋯ ^ k = n✝\nπ : A\nhπ : v π = (exp 1)⁻¹\nn : ℕ\nh : Units.mk0 (exp 1)⁻¹ ⋯ ^ Int.o... | [] | simp [hπ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 183,
"column": 44
} | {
"line": 183,
"column": 49
} | {
"line": 183,
"column": 49
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nhsurj : Function.Surjective ⇑v\n⊢ exp (-1) ∈ range ⇑v",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddComm... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 183,
"column": 44
} | {
"line": 183,
"column": 49
} | {
"line": 183,
"column": 49
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nhsurj : Function.Surjective ⇑v\n⊢ exp (-1) ∈ range ⇑v",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddComm... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 183,
"column": 44
} | {
"line": 183,
"column": 49
} | {
"line": 183,
"column": 49
} | [
{
"pp": "A : Type u_2\ninst✝ : Ring A\nv : Valuation A (WithZero (Multiplicative ℤ))\nhv : v.IsRankOneDiscrete\nhsurj : Function.Surjective ⇑v\n⊢ exp (-1) ∈ range ⇑v",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddComm... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 36
} | {
"line": 230,
"column": 2
} | [
{
"pp": "Γ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nA : Type u_2\ninst✝ : Ring A\nv : Valuation A Γ\nhv : v.IsRankOneDiscrete\nπ : A\nhπ : v.IsUniformizer π\n⊢ Subgroup.genLTOne (MonoidWithZeroHom.ofClass v).valueGroup = Units.mk0 (v π) ⋯",
"ppTerm": "?m.63",
"assigned": true,
"usedCon... | [
"Γ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nA : Type u_2\ninst✝ : Ring A\nv : Valuation A Γ\nhv : v.IsRankOneDiscrete\nπ : A\nhπ : v.IsUniformizer π\n⊢ Subgroup.genLTOne (MonoidWithZeroHom.ofClass v).valueGroup = IsRankOneDiscrete.generator v"
] | simp only [val, Units.mk0_val, hπ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 357,
"column": 35
} | {
"line": 357,
"column": 44
} | {
"line": 357,
"column": 45
} | [
{
"pp": "Γ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝ : Field K\nv : Valuation K Γ\nhv : v.IsRankOneDiscrete\nr : ↥v.valuationSubring\nhr : r ≠ 0\nπ : v.Uniformizer\nhr₀ : v ↑r ≠ 0\nvr : Γˣ := Units.mk0 (v ↑r) hr₀\nhvr_def : vr = Units.mk0 (v ↑r) hr₀\nm : ℤ\nhm : Units.mk0 (v ↑π.... | [
"Γ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝ : Field K\nv : Valuation K Γ\nhv : v.IsRankOneDiscrete\nr : ↥v.valuationSubring\nhr : r ≠ 0\nπ : v.Uniformizer\nhr₀ : v ↑r ≠ 0\nvr : Γˣ := Units.mk0 (v ↑r) hr₀\nhvr_def : vr = Units.mk0 (v ↑r) hr₀\nm : ℤ\nhm : Units.mk0 (v ↑π.val) ⋯ ^ m =... | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 367,
"column": 58
} | {
"line": 367,
"column": 67
} | {
"line": 367,
"column": 68
} | [
{
"pp": "case h\nΓ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝ : Field K\nv : Valuation K Γ\nhv : v.IsRankOneDiscrete\nr : ↥v.valuationSubring\nhr : r ≠ 0\nπ : v.Uniformizer\nhr₀ : v ↑r ≠ 0\nvr : Γˣ := Units.mk0 (v ↑r) hr₀\nhvr_def : vr = Units.mk0 (v ↑r) hr₀\nm : ℤ\nhm : Units.mk... | [
"case h\nΓ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝ : Field K\nv : Valuation K Γ\nhv : v.IsRankOneDiscrete\nr : ↥v.valuationSubring\nhr : r ≠ 0\nπ : v.Uniformizer\nhr₀ : v ↑r ≠ 0\nvr : Γˣ := Units.mk0 (v ↑r) hr₀\nhvr_def : vr = Units.mk0 (v ↑r) hr₀\nm : ℤ\nhm : Units.mk0 (v ↑π.val)... | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 55,
"column": 28
} | {
"line": 55,
"column": 37
} | {
"line": 55,
"column": 37
} | [
{
"pp": "A : 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\nv : Valuation K (WithZero (Multiplicative ℤ)) := valuation K (maximalIdeal A)\nπ : K := ⋯.choose\nhπ : v π = ↑(ofAdd (-1))\n⊢ v π... | [] | simp [hπ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 55,
"column": 28
} | {
"line": 55,
"column": 37
} | {
"line": 55,
"column": 37
} | [
{
"pp": "A : 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\nv : Valuation K (WithZero (Multiplicative ℤ)) := valuation K (maximalIdeal A)\nπ : K := ⋯.choose\nhπ : v π = ↑(ofAdd (-1))\n⊢ v π... | [] | simp [hπ] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 55,
"column": 28
} | {
"line": 55,
"column": 37
} | {
"line": 55,
"column": 37
} | [
{
"pp": "A : 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\nv : Valuation K (WithZero (Multiplicative ℤ)) := valuation K (maximalIdeal A)\nπ : K := ⋯.choose\nhπ : v π = ↑(ofAdd (-1))\n⊢ v π... | [] | simp [hπ] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 62
} | {
"line": 287,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\ne : G ≃o Additive G := OrderIso.refl G\n⊢ Nonempty (Additive G ≃+o ℤ) ↔ ¬DenselyOrdered G",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.in... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\ne : G ≃o Additive G := OrderIso.refl G\n⊢ ¬DenselyOrdered (Additive G) ↔ ¬DenselyOrdered G"
] | LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 410,
"column": 6
} | {
"line": 410,
"column": 72
} | {
"line": 411,
"column": 4
} | [
{
"pp": "case refine_3\nG₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero G₀\ninst✝ : Nontrivial G₀ˣ\ng : G₀\nhg : g ≠ 0\nthis : ({x | g ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2) ↔ {x | Units.mk0 g hg ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2\nf : G₀ ≃*o WithZero (Multiplicative ℤ)\n⊢ G₀ˣ ≃* Multiplicative ℤ",
... | [] | exact MulEquiv.withZero.symm (WithZero.withZeroUnitsEquiv.trans f) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 410,
"column": 6
} | {
"line": 410,
"column": 72
} | {
"line": 411,
"column": 4
} | [
{
"pp": "case refine_3\nG₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero G₀\ninst✝ : Nontrivial G₀ˣ\ng : G₀\nhg : g ≠ 0\nthis : ({x | g ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2) ↔ {x | Units.mk0 g hg ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2\nf : G₀ ≃*o WithZero (Multiplicative ℤ)\n⊢ G₀ˣ ≃* Multiplicative ℤ",
... | [] | exact MulEquiv.withZero.symm (WithZero.withZeroUnitsEquiv.trans f) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 410,
"column": 6
} | {
"line": 410,
"column": 72
} | {
"line": 411,
"column": 4
} | [
{
"pp": "case refine_3\nG₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero G₀\ninst✝ : Nontrivial G₀ˣ\ng : G₀\nhg : g ≠ 0\nthis : ({x | g ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2) ↔ {x | Units.mk0 g hg ≤ x}.WellFoundedOn fun x1 x2 ↦ x1 < x2\nf : G₀ ≃*o WithZero (Multiplicative ℤ)\n⊢ G₀ˣ ≃* Multiplicative ℤ",
... | [] | exact MulEquiv.withZero.symm (WithZero.withZeroUnitsEquiv.trans f) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 455,
"column": 12
} | {
"line": 455,
"column": 17
} | {
"line": 456,
"column": 8
} | [
{
"pp": "case neg.hxy\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embeddin... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 455,
"column": 12
} | {
"line": 455,
"column": 17
} | {
"line": 456,
"column": 8
} | [
{
"pp": "case neg.hxy\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embeddin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 455,
"column": 12
} | {
"line": 455,
"column": 17
} | {
"line": 456,
"column": 8
} | [
{
"pp": "case neg.hxy\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embeddin... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 299,
"column": 9
} | {
"line": 299,
"column": 14
} | {
"line": 299,
"column": 14
} | [
{
"pp": "R : 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\nπ : R\nhπ : v.intValuation π = exp (-1)\n⊢ v.intValuation π ≠ 0 ∧ v.intValuation π ≠ 1",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 299,
"column": 9
} | {
"line": 299,
"column": 14
} | {
"line": 299,
"column": 14
} | [
{
"pp": "R : 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\nπ : R\nhπ : v.intValuation π = exp (-1)\n⊢ v.intValuation π ≠ 0 ∧ v.intValuation π ≠ 1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 299,
"column": 9
} | {
"line": 299,
"column": 14
} | {
"line": 299,
"column": 14
} | [
{
"pp": "R : 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\nπ : R\nhπ : v.intValuation π = exp (-1)\n⊢ v.intValuation π ≠ 0 ∧ v.intValuation π ≠ 1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 367,
"column": 60
} | {
"line": 369,
"column": 43
} | {
"line": 371,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nr : R\n⊢ (valuation K v) ((algebraMap R K) r) = 1 ↔ r ∉ v.asIdeal",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants"... | [] | by
rw [← HeightOneSpectrum.valuation_lt_one_iff_mem (K := K), le_antisymm_iff]
simp [HeightOneSpectrum.valuation_le_one] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 407,
"column": 9
} | {
"line": 407,
"column": 14
} | {
"line": 407,
"column": 14
} | [
{
"pp": "R : 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\nπ : K\nhπ : (valuation K v) π = exp (-1)\n⊢ (valuation K v) π ≠ 0 ∧ (valuation K v) π ≠ 1",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 407,
"column": 9
} | {
"line": 407,
"column": 14
} | {
"line": 407,
"column": 14
} | [
{
"pp": "R : 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\nπ : K\nhπ : (valuation K v) π = exp (-1)\n⊢ (valuation K v) π ≠ 0 ∧ (valuation K v) π ≠ 1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 407,
"column": 9
} | {
"line": 407,
"column": 14
} | {
"line": 407,
"column": 14
} | [
{
"pp": "R : 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\nπ : K\nhπ : (valuation K v) π = exp (-1)\n⊢ (valuation K v) π ≠ 0 ∧ (valuation K v) π ≠ 1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 552,
"column": 6
} | {
"line": 552,
"column": 47
} | {
"line": 553,
"column": 6
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\ns : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nthis✝ : (𝓝 0).HasBasis (fun x ↦ True) fun γ ↦ {x | extensionValuation x < ↑((Units.map ↑embedd... | [
"case refine_1\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\ns : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nthis✝ : (𝓝 0).HasBasis (fun x ↦ True) fun γ ↦ {x | extensionValuation x < ↑((Units.map ↑emb... | refine ⟨fun ⟨γ, h⟩ ↦ ?_, fun ⟨γ, h⟩ ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 693,
"column": 10
} | {
"line": 693,
"column": 31
} | {
"line": 693,
"column": 31
} | [
{
"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)\nu v : σ →₀ ... | [
"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)\nu v : σ →₀ ℕ\nx : ι →₀ ... | Finset.prod_congr rfl | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 487,
"column": 49
} | {
"line": 487,
"column": 54
} | {
"line": 487,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\na s : R\nhs : s ∈ v.asIdeal.primeCompl\n⊢ s ≠ 0",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"False",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 487,
"column": 49
} | {
"line": 487,
"column": 54
} | {
"line": 487,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\na s : R\nhs : s ∈ v.asIdeal.primeCompl\n⊢ s ≠ 0",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"False",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 487,
"column": 49
} | {
"line": 487,
"column": 54
} | {
"line": 487,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\na s : R\nhs : s ∈ v.asIdeal.primeCompl\n⊢ s ≠ 0",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"False",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Finsupp | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 23
} | {
"line": 72,
"column": 4
} | [
{
"pp": "case refine_1\nι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι →₀ Finset α\nht : t.support ⊆ s\ni : ι\nh : (i ∈ f.support → i ∈ s) ∧ (i ∈ s → f i ∈ t i)\n⊢ f i ∈ t i",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
... | [
"case pos\nι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι →₀ Finset α\nht : t.support ⊆ s\ni : ι\nh : (i ∈ f.support → i ∈ s) ∧ (i ∈ s → f i ∈ t i)\nhi : i ∈ s\n⊢ f i ∈ t i",
"case neg\nι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι →₀ Finset α\nht : t.sup... | by_cases hi : i ∈ s | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 262,
"column": 2
} | {
"line": 267,
"column": 12
} | {
"line": 269,
"column": 0
} | [
{
"pp": "case right\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf g : MvPowerSeries σ R\nH : weightedOrder w f < weightedOrder w g\nn : ℕ\nhn : ↑n = weightedOrder w f\nd : σ →₀ ℕ\nhd' : (coeff d) f ≠ 0\nhd : (weight w) d = n\n⊢ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff d) (f + g) = 0",
"ppTe... | [] | · intro b hb
suffices weight w b < weightedOrder w f by
rw [(coeff _).map_add, coeff_eq_zero_of_lt_weightedOrder w this,
coeff_eq_zero_of_lt_weightedOrder w (lt_trans this H), add_zero]
rw [← hn, Nat.cast_lt]
exact hb | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 275,
"column": 4
} | {
"line": 276,
"column": 55
} | {
"line": 277,
"column": 2
} | [
{
"pp": "case inr\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf g : MvPowerSeries σ R\nh : weightedOrder w f ≠ weightedOrder w g\nthis :\n ∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},\n weightedOrder w f ≠ weightedOrder w g →\n weightedOrder... | [] | rw [add_comm f g, inf_comm]
exact this _ h.symm ((le_of_not_gt H₁).lt_of_ne' h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 275,
"column": 4
} | {
"line": 276,
"column": 55
} | {
"line": 277,
"column": 2
} | [
{
"pp": "case inr\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf g : MvPowerSeries σ R\nh : weightedOrder w f ≠ weightedOrder w g\nthis :\n ∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},\n weightedOrder w f ≠ weightedOrder w g →\n weightedOrder... | [] | rw [add_comm f g, inf_comm]
exact this _ h.symm ((le_of_not_gt H₁).lt_of_ne' h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 864,
"column": 4
} | {
"line": 865,
"column": 61
} | {
"line": 867,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nn : σ →₀ ℕ\n⊢ (MvPowerSeries.coeff n) ↑(φ * ψ) = (MvPowerSeries.coeff n) (↑φ * ↑ψ)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Nat.instMulZeroClass",
"... | [] | classical
simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul] | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 864,
"column": 4
} | {
"line": 865,
"column": 61
} | {
"line": 867,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nn : σ →₀ ℕ\n⊢ (MvPowerSeries.coeff n) ↑(φ * ψ) = (MvPowerSeries.coeff n) (↑φ * ↑ψ)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Nat.instMulZeroClass",
"... | [] | classical
simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 864,
"column": 4
} | {
"line": 865,
"column": 61
} | {
"line": 867,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nn : σ →₀ ℕ\n⊢ (MvPowerSeries.coeff n) ↑(φ * ψ) = (MvPowerSeries.coeff n) (↑φ * ↑ψ)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Nat.instMulZeroClass",
"... | [] | classical
simp only [coeff_coe, MvPowerSeries.coeff_mul, coeff_mul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 719,
"column": 4
} | {
"line": 722,
"column": 93
} | {
"line": 723,
"column": 4
} | [
{
"pp": "case refine_1\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✝ : ∃ t ∈ 𝓝 0, toCompletion ⁻¹' t ⊆ s\nt : Set... | [
"case 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\nγ : (of... | · obtain ⟨δ, hδ⟩ := Valued.mem_nhds_zero.1 ht
refine ⟨Units.mapEquiv (valueGroupOrderIso K v).symm.toMulEquiv δ, fun x hx ↦ hts (hδ ?_)⟩
rw [Set.mem_setOf_eq] at hx ⊢
simpa [← map_lt_map_iff (valueGroupOrderIso K v), valueGroupOrderIso_restrict] using hx | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 62
} | {
"line": 172,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPolynomial σ R\n⊢ (truncFinset R s) ↑p = p ↔ p.support ⊆ s",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
... | [
"case refine_1\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPolynomial σ R\nh : (truncFinset R s) ↑p = p\n⊢ p.support ⊆ s",
"case refine_2\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPolynomial σ R\nh : p.support ⊆ s\nx : σ →₀ ℕ\n⊢ MvPolynomia... | refine ⟨fun h ↦ ?_, fun h ↦ MvPolynomial.ext _ _ fun x ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 363,
"column": 52
} | {
"line": 363,
"column": 75
} | {
"line": 363,
"column": 76
} | [
{
"pp": "case ind\nσ : Type u_1\nR : Type u_2\nn : ℕ\ninst✝¹ : Finite σ\ninst✝ : CommSemiring R\np : MvPowerSeries σ R\nk : ℕ\nih : ∀ m ≤ k, ∀ {x : σ →₀ ℕ}, degree x < n → MvPolynomial.coeff x ((truncTotal n) p ^ m) = (coeff x) (p ^ m)\nx : σ →₀ ℕ\nh : degree x < n\n⊢ MvPolynomial.coeff x ((truncTotal n) p ^ k ... | [
"case ind\nσ : Type u_1\nR : Type u_2\nn : ℕ\ninst✝¹ : Finite σ\ninst✝ : CommSemiring R\np : MvPowerSeries σ R\nk : ℕ\nih : ∀ m ≤ k, ∀ {x : σ →₀ ℕ}, degree x < n → MvPolynomial.coeff x ((truncTotal n) p ^ m) = (coeff x) (p ^ m)\nx : σ →₀ ℕ\nh : degree x < n\n⊢ ∑ x ∈ antidiagonal x, MvPolynomial.coeff x.1 ((truncTot... | MvPolynomial.coeff_mul, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 75
} | {
"line": 217,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : CommSemiring R\nf : MvPowerSeries σ R\nm : ℕ\nhm : constantCoeff f ^ m = 0\n⊢ IsTopologicallyNilpotent f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Semiring.t... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : CommSemiring R\nf : MvPowerSeries σ R\nm : ℕ\nhm : constantCoeff f ^ m = 0\n⊢ ∀ (d : σ →₀ ℕ), Tendsto (fun i ↦ (coeff d) (f ^ i)) atTop (𝓝 0)"
] | simp_rw [IsTopologicallyNilpotent, tendsto_iff_coeff_tendsto, coeff_zero] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.Algebra.LinearTopology | {
"line": 220,
"column": 2
} | {
"line": 226,
"column": 52
} | {
"line": 227,
"column": 2
} | [
{
"pp": "R : Type u_1\nR' : Type u_2\nM : Type u_3\ninst✝⁸ : Ring R\ninst✝⁷ : Ring R'\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\ninst✝⁴ : Module R' M\ninst✝³ : SMulCommClass R R' M\ninst✝² : TopologicalSpace M\ninst✝¹ : IsLinearTopology R M\ninst✝ : IsLinearTopology R' M\nI : Submodule R M\nhI : ↑I ∈ 𝓝 0\n... | [
"R : Type u_1\nR' : Type u_2\nM : Type u_3\ninst✝⁸ : Ring R\ninst✝⁷ : Ring R'\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\ninst✝⁴ : Module R' M\ninst✝³ : SMulCommClass R R' M\ninst✝² : TopologicalSpace M\ninst✝¹ : IsLinearTopology R M\ninst✝ : IsLinearTopology R' M\nI : Submodule R M\nhI : ↑I ∈ 𝓝 0\nJ : Submodul... | have hR'A : ∀ r' : R', ∀ i ∈ A, r' • i ∈ A := fun r' i hi ↦ by
refine AddSubgroup.closure_induction (fun x hx => ?base) ?zero (fun x y _ _ hx hy ↦ ?add)
(fun x _ hx ↦ ?neg) hi
case base => exact AddSubgroup.subset_closure <| hR'S <| Set.smul_mem_smul trivial hx
case zero => simp_rw [smul_zero]; exact ... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.PowerSeries.Trunc | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 18
} | {
"line": 199,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nf : R⟦X⟧\nn a : ℕ\n⊢ (trunc n) (↑((trunc n) f) ^ a) = (trunc n) (f ^ a)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Nat.recAux",
"Semiring.toModule",
"HMul.hMul",
"Monoid.toMul... | [] | induction a with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 34
} | {
"line": 241,
"column": 2
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\nn : ℕ\na : R\ninst✝ : Decidable (a = 0)\nh : a = 0\n⊢ ((monomial n) a).order = ⊤",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"Semiring.toModule",
"SemilinearMapClass.distri... | [
"case neg\nR : Type u_1\ninst✝¹ : Semiring R\nn : ℕ\na : R\ninst✝ : Decidable (a = 0)\nh : ¬a = 0\n⊢ ((monomial n) a).order = ↑n"
] | · rw [h, order_eq_top, map_zero] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 268,
"column": 62
} | {
"line": 269,
"column": 41
} | {
"line": 271,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝ : Ring R\nφ ψ : R⟦X⟧\nn : ℕ\nh : ↑n < ψ.order\n⊢ (coeff n) (φ * (1 - ψ)) = (coeff n) φ",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_mul_of_lt_order",
"Semiring.toModule",
"HMul.hMul",
"map_sub",
"SemilinearMap... | [] | by
simp [coeff_mul_of_lt_order h, mul_sub] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 63,
"column": 6
} | {
"line": 63,
"column": 19
} | {
"line": 64,
"column": 6
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJd : TwoSidedIdeal R × (σ →₀ ℕ)\nf g : MvPowerSeries σ R\nhg : g ∈ {f | ∀ e ≤ Jd.2, (coeff e) f ∈ Jd.1}\ne : σ →₀ ℕ\nhe : e ≤ Jd.2\n⊢ ∀ c ∈ Finset.antidiagonal e, (coeff c.1) f * (coeff c.2) g ∈ Jd.1",
"ppTerm": "?m.91",
"assigned": true,
"usedCon... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJd : TwoSidedIdeal R × (σ →₀ ℕ)\nf g : MvPowerSeries σ R\nhg : g ∈ {f | ∀ e ≤ Jd.2, (coeff e) f ∈ Jd.1}\ne : σ →₀ ℕ\nhe : e ≤ Jd.2\nuv : (σ →₀ ℕ) × (σ →₀ ℕ)\nhuv : uv ∈ Finset.antidiagonal e\n⊢ (coeff uv.1) f * (coeff uv.2) g ∈ Jd.1"
] | rintro uv huv | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 19
} | {
"line": 71,
"column": 6
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJd : TwoSidedIdeal R × (σ →₀ ℕ)\nf g : MvPowerSeries σ R\nhf : f ∈ {f | ∀ e ≤ Jd.2, (coeff e) f ∈ Jd.1}\ne : σ →₀ ℕ\nhe : e ≤ Jd.2\n⊢ ∀ c ∈ Finset.antidiagonal e, (coeff c.1) f * (coeff c.2) g ∈ Jd.1",
"ppTerm": "?m.133",
"assigned": true,
"usedCo... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJd : TwoSidedIdeal R × (σ →₀ ℕ)\nf g : MvPowerSeries σ R\nhf : f ∈ {f | ∀ e ≤ Jd.2, (coeff e) f ∈ Jd.1}\ne : σ →₀ ℕ\nhe : e ≤ Jd.2\nuv : (σ →₀ ℕ) × (σ →₀ ℕ)\nhuv : uv ∈ Finset.antidiagonal e\n⊢ (coeff uv.1) f * (coeff uv.2) g ∈ Jd.1"
] | rintro uv huv | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.RingTheory.PowerSeries.Evaluation | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 72
} | {
"line": 139,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommRing R\nS : Type u_2\ninst✝² : CommRing S\nφ : R →+* S\na : S\ninst✝¹ : UniformSpace R\ninst✝ : UniformSpace S\nf : Polynomial R\n⊢ eval₂ φ a ↑((MvPolynomial.uniqueAlgEquiv R Unit) ((MvPolynomial.uniqueAlgEquiv R Unit).symm f)) =\n Polynomial.eval₂ φ a ((MvPolynomial.uniqu... | [
"R : Type u_1\ninst✝³ : CommRing R\nS : Type u_2\ninst✝² : CommRing S\nφ : R →+* S\na : S\ninst✝¹ : UniformSpace R\ninst✝ : UniformSpace S\nf : Polynomial R\n⊢ MvPowerSeries.eval₂ φ (fun x ↦ a)\n ↑((MvPolynomial.uniqueAlgEquiv R Unit) ((MvPolynomial.uniqueAlgEquiv R Unit).symm f)) =\n MvPolynomial.eval₂ φ (... | simp only [PowerSeries.eval₂, MvPolynomial.eval₂_const_uniqueAlgEquiv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 271,
"column": 35
} | {
"line": 276,
"column": 51
} | {
"line": 278,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹⁰ : CommRing R\ninst✝⁹ : UniformSpace R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝⁶ : IsTopologicalSemiring R\ninst✝⁵ : IsUniformAddGroup R\ninst✝⁴ : IsUniformAddGroup S\ninst✝³ : CompleteSpace S\ninst✝² : T2Space S\ninst... | [] | by
rw [← coe_eval₂Hom hφ ha, eval₂Hom_eq_extend hφ ha]
convert! (hasSum_of_monomials_self f).map (eval₂Hom hφ ha) (?_) with d
· simp only [Function.comp_apply, coe_eval₂Hom, ← MvPolynomial.coe_monomial,
eval₂_coe, eval₂_monomial]
· rw [coe_eval₂Hom]; exact continuous_eval₂ hφ ha | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 151,
"column": 2
} | {
"line": 160,
"column": 86
} | {
"line": 162,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsLinearTopology R R\nf : MvPowerSeries σ R\nhf : IsTopologicallyNilpotent (constantCoeff f)\n⊢ IsTopologicallyNilpotent f",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Filter.instMember... | [] | simp_rw [IsTopologicallyNilpotent, tendsto_iff_coeff_tendsto, coeff_zero,
IsLinearTopology.hasBasis_ideal.tendsto_right_iff]
intro d I hI
replace hf := hf.eventually_mem hI
simp_rw [eventually_atTop, SetLike.mem_coe, ← Ideal.Quotient.eq_zero_iff_mem,
map_pow, ← coeff_map, ← constantCoeff_map] at hf ⊢
ob... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 151,
"column": 2
} | {
"line": 160,
"column": 86
} | {
"line": 162,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsLinearTopology R R\nf : MvPowerSeries σ R\nhf : IsTopologicallyNilpotent (constantCoeff f)\n⊢ IsTopologicallyNilpotent f",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Filter.instMember... | [] | simp_rw [IsTopologicallyNilpotent, tendsto_iff_coeff_tendsto, coeff_zero,
IsLinearTopology.hasBasis_ideal.tendsto_right_iff]
intro d I hI
replace hf := hf.eventually_mem hI
simp_rw [eventually_atTop, SetLike.mem_coe, ← Ideal.Quotient.eq_zero_iff_mem,
map_pow, ← coeff_map, ← constantCoeff_map] at hf ⊢
ob... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 465,
"column": 2
} | {
"line": 465,
"column": 80
} | {
"line": 466,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : Ha... | [
"σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : HasSubst a\nhb... | apply comp_aeval (R := R) (ε := (substAlgHom hb).restrictScalars R) ha.hasEval | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 661,
"column": 6
} | {
"line": 661,
"column": 29
} | {
"line": 662,
"column": 6
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝²¹ : CommSemiring A\nR✝ : Type u_3\ninst✝²⁰ : CommRing R✝\ninst✝¹⁹ : Algebra A R✝\nτ : Type u_4\nS : Type u_5\ninst✝¹⁸ : CommRing S\ninst✝¹⁷ : Algebra A S\ninst✝¹⁶ : Algebra R✝ S\ninst✝¹⁵ : IsScalarTower A R✝ S\na✝¹ a✝ : σ → MvPowerSeries τ S\nT✝ : Type u_6\ninst✝¹⁴ : C... | [
"σ : Type u_1\nA : Type u_2\ninst✝²¹ : CommSemiring A\nR✝ : Type u_3\ninst✝²⁰ : CommRing R✝\ninst✝¹⁹ : Algebra A R✝\nτ : Type u_4\nS : Type u_5\ninst✝¹⁸ : CommRing S\ninst✝¹⁷ : Algebra A S\ninst✝¹⁶ : Algebra R✝ S\ninst✝¹⁵ : IsScalarTower A R✝ S\na✝¹ a✝ : σ → MvPowerSeries τ S\nT✝ : Type u_6\ninst✝¹⁴ : CommRing T✝\n... | simp only [← mul_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 341,
"column": 87
} | {
"line": 341,
"column": 92
} | {
"line": 341,
"column": 92
} | [
{
"pp": "case e'_2\nR : Type u_2\ninst✝² : CommRing R\nτ : Type u_3\nS : Type u_4\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : MvPowerSeries τ S\nw : τ → ℕ\nha : HasSubst a\nf : R⟦X⟧\ni : Unit →₀ ℕ\nhi : ¬(MvPowerSeries.coeff i) f = 0\n⊢ Finsupp.single () (i ()) = i",
"ppTerm": "?e'_2",
"assigned": tr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Convex.EGauge | {
"line": 261,
"column": 77
} | {
"line": 279,
"column": 23
} | {
"line": 280,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\nI : Set ι\nhI : I.Finite\nU : (i : ι) → Set (E i)\nhU : ∀ i ∈ I, Balanced 𝕜 (U i)\nx : (i : ι) → E i\nhI₀ : I = univ ∨ (∃ i ∈ I, x i ≠ 0) ∨ (𝓝[≠] 0)... | [] | by
have hr₀ : 0 < r := hr.bot_lt
rcases I.eq_empty_or_nonempty with rfl | hIne
· obtain hι | hbot : IsEmpty ι ∨ (𝓝[≠] (0 : 𝕜)).NeBot := by simpa [@eq_comm _ ∅] using hI₀
· use 0
simp [@eq_comm _ ∅, hι, hr₀]
· rcases exists_enorm_lt 𝕜 hr₀.ne' with ⟨c₀, hc₀, hc₀r⟩
exact ⟨c₀, .in... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.TangentCone.Real | {
"line": 64,
"column": 6
} | {
"line": 64,
"column": 31
} | {
"line": 64,
"column": 31
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul ℝ E\ns : Set E\nx : E\ninst✝ : IsTopologicalAddGroup E\nconv : Convex ℝ s\nhx : x ∈ closure[inst✝²] s\ny : E\nhy : y ∈ interior s\n⊢ y - x ∈ interior (tangentConeAt ℝ s x)",
"ppTerm": "?... | [
"E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul ℝ E\ns : Set E\nx : E\ninst✝ : IsTopologicalAddGroup E\nconv : Convex ℝ s\nhx : x ∈ closure[inst✝²] s\ny : E\nhy : y ∈ interior s\n⊢ tangentConeAt ℝ s x ∈ 𝓝 (y - x)"
] | mem_interior_iff_mem_nhds | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.FDeriv.Const | {
"line": 345,
"column": 2
} | {
"line": 345,
"column": 72
} | {
"line": 346,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\nF : Type u_3\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 F\ninst✝ : TopologicalSpace F\nf : E → F\nx : E\nhf : Injective ⇑(fderiv 𝕜 f x)\n⊢ DifferentiableAt 𝕜... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\nF : Type u_3\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 F\ninst✝ : TopologicalSpace F\nf : E → F\nx : E\nhf : Injective ⇑(fderivWithin 𝕜 f univ x)\n⊢ DifferentiableWithin... | simp only [← differentiableWithinAt_univ, ← fderivWithin_univ] at hf ⊢ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 928,
"column": 2
} | {
"line": 928,
"column": 33
} | {
"line": 929,
"column": 2
} | [
{
"pp": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝³ : RingHomIsometric σ\ninst✝² : RingHomInvPair σ σ'\nF' : Type u_1\ninst✝¹ : NormedAddCommGroup F'\ninst✝ : NormedSpace 𝕜 F'\nL : ... | [
"𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx : 𝕜\nσ σ' : 𝕜 →+* 𝕜\ninst✝³ : RingHomIsometric σ\ninst✝² : RingHomInvPair σ σ'\nF' : Type u_1\ninst✝¹ : NormedAddCommGroup F'\ninst✝ : NormedSpace 𝕜 F'\nL : F →SL[σ] F'\... | rw [hasDerivAt_iff_hasFDerivAt] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 354,
"column": 76
} | {
"line": 356,
"column": 17
} | {
"line": 358,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\nF : Type u_3\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 F\ninst✝ : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns t : Set E\nhs : HasFDerivWithinAt f... | [] | by
simp only [hasFDerivWithinAt_iff_isLittleOTVS, nhdsWithin_union] at *
exact hs.sup ht | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.ConvergenceRadius | {
"line": 122,
"column": 4
} | {
"line": 122,
"column": 20
} | {
"line": 124,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0\nh : Summable fun n ↦ ↑‖p n‖₊ * ↑r ^ n\n⊢ Summable fun n ↦ ‖p n‖... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 914,
"column": 2
} | {
"line": 915,
"column": 78
} | {
"line": 917,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nf' : E →L[𝕜] F\nx₀ : E\nhf : HasFDerivAt f f' x₀\ns : Set E\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : Lip... | [] | refine hf.le_of_lip' C.coe_nonneg ?_
filter_upwards [hs] with x hx using hlip.norm_sub_le hx (mem_of_mem_nhds hs) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 914,
"column": 2
} | {
"line": 915,
"column": 78
} | {
"line": 917,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nf' : E →L[𝕜] F\nx₀ : E\nhf : HasFDerivAt f f' x₀\ns : Set E\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : Lip... | [] | refine hf.le_of_lip' C.coe_nonneg ?_
filter_upwards [hs] with x hx using hlip.norm_sub_le hx (mem_of_mem_nhds hs) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Module.Multilinear.Curry | {
"line": 243,
"column": 44
} | {
"line": 243,
"column": 58
} | {
"line": 243,
"column": 58
} | [
{
"pp": "𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : ... | [
"𝕜 : Type u\nn : ℕ\nEi : Fin n.succ → Type wEi\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : Fin n.succ) → NormedAddCommGroup (Ei i)\ninst✝² : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : (i : Fin n.s... | snoc_init_self | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.CPolynomialDef | {
"line": 198,
"column": 4
} | {
"line": 199,
"column": 25
} | {
"line": 199,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\np : FormalMultilinearSeri... | [] | rw [compFormalMultilinearSeries_apply, h.finite m hm]
ext; exact map_zero g | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.CPolynomialDef | {
"line": 198,
"column": 4
} | {
"line": 199,
"column": 25
} | {
"line": 199,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\np : FormalMultilinearSeri... | [] | rw [compFormalMultilinearSeries_apply, h.finite m hm]
ext; exact map_zero g | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 348,
"column": 2
} | {
"line": 351,
"column": 29
} | {
"line": 353,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx y : E\nr : ℝ≥0∞\nhf : ... | [] | have : (‖y - x‖₊ : ℝ≥0∞) < r := by simpa [edist_eq_enorm_sub] using! h.2
have := hf.changeOrigin this (by simpa using! h.1)
rw [add_sub_cancel] at this
exact this.analyticWithinAt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.ChangeOrigin | {
"line": 348,
"column": 2
} | {
"line": 351,
"column": 29
} | {
"line": 353,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx y : E\nr : ℝ≥0∞\nhf : ... | [] | have : (‖y - x‖₊ : ℝ≥0∞) < r := by simpa [edist_eq_enorm_sub] using! h.2
have := hf.changeOrigin this (by simpa using! h.1)
rw [add_sub_cancel] at this
exact this.analyticWithinAt | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Linear | {
"line": 44,
"column": 12
} | {
"line": 48,
"column": 34
} | {
"line": 50,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E →L[𝕜] F\nx : E\n⊢ ∀ (m : ℕ), 2 ≤ m → f.fpowerSeries x m = 0",
"ppTerm": "?m.70",
"assigned": ... | [] | by
intro m hm
match m with
| 0 | 1 => linarith
| n + 2 => simp [fpowerSeries] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 233,
"column": 41
} | {
"line": 233,
"column": 46
} | {
"line": 233,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nr : ℝ≥0\nhr : r ≠ 0\nhc : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop (𝓝 ↑r)\nr' : ℝ≥0\nhr' : ↑r' < (ofScalars E c).radius\nthis : 1 < r' * r\n⊢ r' ≠... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 233,
"column": 41
} | {
"line": 233,
"column": 46
} | {
"line": 233,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nr : ℝ≥0\nhr : r ≠ 0\nhc : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop (𝓝 ↑r)\nr' : ℝ≥0\nhr' : ↑r' < (ofScalars E c).radius\nthis : 1 < r' * r\n⊢ r' ≠... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 233,
"column": 41
} | {
"line": 233,
"column": 46
} | {
"line": 233,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nr : ℝ≥0\nhr : r ≠ 0\nhc : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop (𝓝 ↑r)\nr' : ℝ≥0\nhr' : ↑r' < (ofScalars E c).radius\nthis : 1 < r' * r\n⊢ r' ≠... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 279,
"column": 18
} | {
"line": 279,
"column": 23
} | {
"line": 280,
"column": 2
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nr : ℝ≥0\nhr : ↑r < (ofScalars E c).radius\nthis : 0 < r\nhc : ∀ᶠ (x : ℕ) in atTop, ‖‖ofScalars E c x‖ * ↑r ^ x‖ = 0\nn : ℕ\nh✝ : ‖c n‖ = 0\... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 279,
"column": 18
} | {
"line": 279,
"column": 23
} | {
"line": 280,
"column": 2
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nr : ℝ≥0\nhr : ↑r < (ofScalars E c).radius\nthis : 0 < r\nhc : ∀ᶠ (x : ℕ) in atTop, ‖‖ofScalars E c x‖ * ↑r ^ x‖ = 0\nn : ℕ\nh✝ : ‖↑r ^ n‖ =... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.OfScalars | {
"line": 285,
"column": 6
} | {
"line": 285,
"column": 11
} | {
"line": 286,
"column": 4
} | [
{
"pp": "case ha\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedRing E\ninst✝¹ : NormedAlgebra 𝕜 E\nc : ℕ → 𝕜\ninst✝ : NormOneClass E\nhc✝ : Tendsto (fun n ↦ ‖c n.succ‖ / ‖c n‖) atTop atTop\nr : ℝ≥0\nhr : ↑r < (ofScalars E c).radius\nthis : 0 < r\nn : ℕ\nhc : 2 * ↑r⁻¹ ≤ ‖c n... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.Inverse | {
"line": 379,
"column": 64
} | {
"line": 384,
"column": 10
} | {
"line": 385,
"column": 4
} | [
{
"pp": "n : ℕ\np : ℕ → ℝ\nhp : ∀ (k : ℕ), 0 ≤ p k\nr a : ℝ\nhr : 0 ≤ r\nha : 0 ≤ a\n⊢ ∑ k ∈ Ico 2 (n + 1), a ^ k * ∑ c ∈ {c | 1 < c.length}.toFinset, r ^ c.length * ∏ j, p (c.blocksFun j) =\n ∑ k ∈ Ico 2 (n + 1), ∑ c ∈ {c | 1 < c.length}.toFinset, ∏ j, r * (a ^ c.blocksFun j * p (c.blocksFun j))",
"ppTe... | [] | by
simp_rw [mul_sum]
congr! with k _ c
rw [prod_mul_distrib, prod_mul_distrib, prod_pow_eq_pow_sum, Composition.sum_blocksFun,
prod_const, card_fin]
ring | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Composition | {
"line": 1196,
"column": 25
} | {
"line": 1196,
"column": 56
} | {
"line": 1196,
"column": 56
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCom... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : NormedAddCommGroup H\nin... | dsimp only [Composition.length] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Analysis.Analytic.Inverse | {
"line": 621,
"column": 6
} | {
"line": 621,
"column": 49
} | {
"line": 622,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMult... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMultilinearSerie... | apply ContinuousAt.sub _ continuousAt_const | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Analytic.Constructions | {
"line": 547,
"column": 2
} | {
"line": 548,
"column": 38
} | {
"line": 550,
"column": 0
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\ne : E\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nf : (i : ι) → E → Fm i\np : (i ... | [] | simp_rw [← hasFPowerSeriesWithinAt_univ]
exact hasFPowerSeriesWithinAt_pi_iff | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Constructions | {
"line": 547,
"column": 2
} | {
"line": 548,
"column": 38
} | {
"line": 550,
"column": 0
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\ne : E\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nf : (i : ι) → E → Fm i\np : (i ... | [] | simp_rw [← hasFPowerSeriesWithinAt_univ]
exact hasFPowerSeriesWithinAt_pi_iff | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 343,
"column": 2
} | {
"line": 343,
"column": 37
} | {
"line": 345,
"column": 0
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns : Set E\nc : F\nh : HasFDerivWithinAt f f' s x\nhf' : ∃ C, An... | [] | · exact eventually_ne_nhdsWithin hc | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 308,
"column": 34
} | {
"line": 308,
"column": 48
} | {
"line": 308,
"column": 48
} | [
{
"pp": "case e'_12\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\np : E → FormalMultilinearSeries 𝕜 E F\nn : ℕ\nH : HasFTaylorSeriesUpToOn (↑(n... | [
"case e'_12\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\np : E → FormalMultilinearSeries 𝕜 E F\nn : ℕ\nH : HasFTaylorSeriesUpToOn (↑(n + 1)) f p s... | snoc_init_self | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 45
} | {
"line": 234,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ HasFDerivAt p.sum (p... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nx : E\ninst✝ : CompleteSpace F\nh : ‖x‖ₑ < p.radius\n⊢ HasFDerivAt p.sum (fderiv 𝕜 p.s... | rw [← FormalMultilinearSeries.fderiv_sum h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 347,
"column": 38
} | {
"line": 347,
"column": 52
} | {
"line": 347,
"column": 52
} | [
{
"pp": "case e'_12\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\np : E → FormalMultilinearSeries 𝕜 E F\nn : ℕ\nHzero_eq : ∀ x ∈ s, (p x 0).cur... | [
"case e'_12\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\np : E → FormalMultilinearSeries 𝕜 E F\nn : ℕ\nHzero_eq : ∀ x ∈ s, (p x 0).curry0 = f x\nH... | snoc_init_self | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 250,
"column": 4
} | {
"line": 250,
"column": 67
} | {
"line": 251,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : CompleteSpace F\nh : HasFPow... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : CompleteSpace F\nh : HasFPowerSeriesWith... | · simpa only [edist_eq_enorm_sub, Metric.mem_eball] using! hz.2 | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 644,
"column": 12
} | {
"line": 644,
"column": 77
} | {
"line": 645,
"column": 2
} | [
{
"pp": "case zero\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nh : HasFTaylorSeriesUpToOn n f... | [] | rw [h.zero_eq' hx, iteratedFDerivWithin_zero_eq_comp, comp_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 644,
"column": 12
} | {
"line": 644,
"column": 77
} | {
"line": 645,
"column": 2
} | [
{
"pp": "case zero\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nh : HasFTaylorSeriesUpToOn n f... | [] | rw [h.zero_eq' hx, iteratedFDerivWithin_zero_eq_comp, comp_apply] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | {
"line": 644,
"column": 12
} | {
"line": 644,
"column": 77
} | {
"line": 645,
"column": 2
} | [
{
"pp": "case zero\n𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nf : E → F\nn : ℕ∞ω\np : E → FormalMultilinearSeries 𝕜 E F\nh : HasFTaylorSeriesUpToOn n f... | [] | rw [h.zero_eq' hx, iteratedFDerivWithin_zero_eq_comp, comp_apply] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Analytic | {
"line": 607,
"column": 32
} | {
"line": 607,
"column": 70
} | {
"line": 607,
"column": 71
} | [
{
"pp": "case inl\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝³ : (i : ι) → NormedAddCommGroup (E i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝¹ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E... | [
"case inl\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nι : Type u_2\nE : ι → Type u_3\ninst✝³ : (i : ι) → NormedAddCommGroup (E i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝¹ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E F\nx : (i :... | changeOriginSeries_support _ (this _), | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
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