module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 15
} | {
"line": 84,
"column": 16
} | [
{
"pp": "case inl\nR : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd ↑n\n⊢ ∃ r, x = r ^ ↑n",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"congrArg",
"DivInvMonoid.toZPow",
"Exists",
"Field.toDivisionR... | [
"case inl\nR : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd ↑n\n⊢ ∃ r, x = r ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 84,
"column": 43
} | {
"line": 84,
"column": 54
} | {
"line": 84,
"column": 55
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd ↑n\n⊢ Odd n",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd ↑n\n⊢ Odd n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 85,
"column": 38
} | {
"line": 85,
"column": 49
} | {
"line": 85,
"column": 50
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd (-↑n)\n⊢ Odd ?m.72",
"ppTerm": "?m.73",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd (-↑n)\n⊢ Odd ?m.72"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 86,
"column": 19
} | {
"line": 86,
"column": 30
} | {
"line": 86,
"column": 31
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd (-↑n)\nr : R\nhr : x = r ^ n\n⊢ x = r⁻¹ ^ (-↑n)",
"ppTerm": "?m.97",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.to... | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd (-↑n)\nr : R\nhr : x = r ^ n\n⊢ x = r ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 15
} | {
"line": 103,
"column": 16
} | [
{
"pp": "case inl\nR : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : ↑n ≠ 0\n⊢ ∃ r, x = r ^ ↑n",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"congrArg",
"DivInvMonoid.toZPow",
"Exists",
"... | [
"case inl\nR : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : ↑n ≠ 0\n⊢ ∃ r, x = r ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 103,
"column": 49
} | {
"line": 103,
"column": 60
} | {
"line": 103,
"column": 61
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : ↑n ≠ 0\n⊢ n ≠ 0",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
],
"usedFVars": [
"n"
],
"... | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : ↑n ≠ 0\n⊢ ¬n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 143,
"column": 6
} | {
"line": 143,
"column": 81
} | {
"line": 143,
"column": 82
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (Finset.image... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 104,
"column": 44
} | {
"line": 104,
"column": 55
} | {
"line": 104,
"column": 56
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : -↑n ≠ 0\n⊢ ?m.78 ≠ 0",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
],
"usedFVars": [],
"usedGoals"... | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : -↑n ≠ 0\n⊢ ¬?m.78 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 105,
"column": 19
} | {
"line": 105,
"column": 30
} | {
"line": 105,
"column": 31
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : -↑n ≠ 0\nr : R\nhr : x = r ^ n\n⊢ x = r⁻¹ ^ (-↑n)",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"Di... | [
"R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : -↑n ≠ 0\nr : R\nhr : x = r ^ n\n⊢ x = r ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 149,
"column": 8
} | {
"line": 149,
"column": 19
} | {
"line": 149,
"column": 20
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (Finset.image... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 154,
"column": 8
} | {
"line": 154,
"column": 85
} | {
"line": 154,
"column": 86
} | [
{
"pp": "case refine_2\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n ... | [
"case refine_2\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 172,
"column": 48
} | {
"line": 172,
"column": 59
} | {
"line": 172,
"column": 60
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq (Subgroup G)\nn : ℕ\nih :\n ∀ m < n,\n ∀ {ι : Type u_2} {H : ι → Subgroup G} {g : ι → G} {s : Finset ι},\n ⋃ i ∈ s, g i • ↑(H i) = Set.univ →\n ∀ j ∈ s,\n ⋃ i ∈ {x ∈ s | H x = H j}, g i • ↑(H i) ≠ Set.univ →\n m = (Finset.image... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.JacobsonNoether | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 41
} | {
"line": 125,
"column": 42
} | [
{
"pp": "case h\nD : Type u_1\ninst✝¹ : DivisionRing D\ninst✝ : Algebra.IsAlgebraic (↥k) D\nH : k ≠ ⊤\np : ℕ\nhp : ExpChar D p\ninsep : ∀ (x : D), IsSeparable (↥k) x → x ∈ k\na : D\nha : ∃ x, ¬x * a = a * x\nha₀ : a ≠ 0\n⊢ a * ha.choose - ha.choose * a ≠ 0",
"ppTerm": "?h",
"assigned": true,
"usedCo... | [
"case h\nD : Type u_1\ninst✝¹ : DivisionRing D\ninst✝ : Algebra.IsAlgebraic (↥k) D\nH : k ≠ ⊤\np : ℕ\nhp : ExpChar D p\ninsep : ∀ (x : D), IsSeparable (↥k) x → x ∈ k\na : D\nha : ∃ x, ¬x * a = a * x\nha₀ : a ≠ 0\n⊢ ¬a * ha.choose = ha.choose * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Laurent | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 31
} | {
"line": 107,
"column": 32
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\nr : R\ninst✝ : IsDomain R\nx✝¹ x✝ : R⟮X⟯\nh : (laurent r) x✝¹ = (laurent r) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝¹ : CommRing R\nr : R\ninst✝ : IsDomain R\nx✝¹ x✝ : R⟮X⟯\nh : (laurent r) x✝¹ = (laurent r) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 51
} | {
"line": 50,
"column": 52
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁵ : CommRing F\ninst✝⁴ : Nontrivial F\ninst✝³ : CommRing E\ninst✝² : IsDomain E\ninst✝¹ : Algebra F E\nι : Type w\nx : ι → E\ninst✝ : Nonempty ι\nhx : IsTranscendenceBasis F x\nK : Subalgebra F E := adjoin F (range x)\nthis✝ : Algebra.IsAlgebraic (↥K) E\nthis : Infinite ↥K\... | [
"F : Type u\nE : Type v\ninst✝⁵ : CommRing F\ninst✝⁴ : Nontrivial F\ninst✝³ : CommRing E\ninst✝² : IsDomain E\ninst✝¹ : Algebra F E\nι : Type w\nx : ι → E\ninst✝ : Nonempty ι\nhx : IsTranscendenceBasis F x\nK : Subalgebra F E := adjoin F (range x)\nthis✝ : Algebra.IsAlgebraic (↥K) E\nthis : Infinite ↥K\n⊢ #E ≤ #↥K"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 48
} | {
"line": 69,
"column": 49
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\ninst✝ : Algebra.Transcendental F E\nι : Type v\nx : ι → E\nhx : IsTranscendenceBasis F x\nthis : Nonempty ι\n⊢ Module.rank F E = #E",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\ninst✝ : Algebra.Transcendental F E\nι : Type v\nx : ι → E\nhx : IsTranscendenceBasis F x\nthis : Nonempty ι\n⊢ Module.rank F E = #E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 93,
"column": 2
} | {
"line": 95,
"column": 9
} | {
"line": 95,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nζ : R\nhζ : IsPrimitiveRoot ζ n\nα a : R\nhn : 0 < n\ne : α ^ n = a\nK : Type u_1 := FractionRing R\ni : R →+* K := algebraMap R K\nh : Function.Injective ⇑(algebraMap R K)\n⊢ Polynomial.map i (X ^ n - C a) = Polynomial.map i (∏ i ∈ Finset.r... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nζ : R\nhζ : IsPrimitiveRoot ζ n\nα a : R\nhn : 0 < n\ne : α ^ n = a\nK : Type u_1 := FractionRing R\ni : R →+* K := algebraMap R K\nh : Function.Injective ⇑(algebraMap R K)\n⊢ X ^ n - C (i a) = ∏ x ∈ Finset.range n, (X - C (i ζ) ^ x * C (i α))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 23
} | {
"line": 110,
"column": 24
} | [
{
"pp": "K : Type u\ninst✝ : Field K\nn m : ℕ\na : K\nhm : Irreducible (X ^ m - C a)\nhn :\n ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x : E),\n minpoly K x = X ^ m - C a → Irreducible (X ^ n - C (AdjoinSimple.gen K x))\nhm' : m ≠ 0\n⊢ Irreducible (X ^ (n * m) - C a)",
"ppTerm": "?m.99",
... | [
"K : Type u\ninst✝ : Field K\nn m : ℕ\na : K\nhm : Irreducible (X ^ m - C a)\nhn :\n ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x : E),\n minpoly K x = X ^ m - C a → Irreducible (X ^ n - C (AdjoinSimple.gen K x))\nhm' : m ≠ 0\n⊢ Irreducible ((X ^ n) ^ m - C a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 111,
"column": 8
} | {
"line": 111,
"column": 52
} | {
"line": 111,
"column": 53
} | [
{
"pp": "K : Type u\ninst✝ : Field K\nn m : ℕ\na : K\nhm : Irreducible (X ^ m - C a)\nhn :\n ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x : E),\n minpoly K x = X ^ m - C a → Irreducible (X ^ n - C (AdjoinSimple.gen K x))\nhm' : m ≠ 0\n⊢ ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x ... | [
"K : Type u\ninst✝ : Field K\nn m : ℕ\na : K\nhm : Irreducible (X ^ m - C a)\nhn :\n ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x : E),\n minpoly K x = X ^ m - C a → Irreducible (X ^ n - C (AdjoinSimple.gen K x))\nhm' : m ≠ 0\n⊢ ∀ (E : Type u) [inst : Field E] [inst_1 : Algebra K E] (x : E),\n m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 119,
"column": 11
} | {
"line": 119,
"column": 22
} | {
"line": 119,
"column": 23
} | [
{
"pp": "case one\nK : Type u\ninst✝ : Field K\nhn : Odd 1\na : K\nha : ∀ (p : ℕ), Nat.Prime p → p ∣ 1 → ∀ (b : K), b ^ p ≠ a\n⊢ Irreducible (X ^ 1 - C a)",
"ppTerm": "?one",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.C",
"congrArg",
"HSub.hSub",
"RingHo... | [
"case one\nK : Type u\ninst✝ : Field K\nhn : Odd 1\na : K\nha : ∀ (p : ℕ), Nat.Prime p → p ∣ 1 → ∀ (b : K), b ^ p ≠ a\n⊢ Irreducible (X - C a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 126,
"column": 6
} | {
"line": 127,
"column": 37
} | {
"line": 127,
"column": 38
} | [
{
"pp": "p n : ℕ\nhp : Nat.Prime p\nIH :\n ∀ {K : Type u} [inst : Field K],\n Odd n → ∀ {a : K}, (∀ (p : ℕ), Nat.Prime p → p ∣ n → ∀ (b : K), b ^ p ≠ a) → Irreducible (X ^ n - C a)\nK : Type u\ninst✝² : Field K\nhn : Odd (p * n)\na : K\nha : ∀ (p_1 : ℕ), Nat.Prime p_1 → p_1 ∣ p * n → ∀ (b : K), b ^ p_1 ≠ a\... | [
"p n : ℕ\nhp : Nat.Prime p\nIH :\n ∀ {K : Type u} [inst : Field K],\n Odd n → ∀ {a : K}, (∀ (p : ℕ), Nat.Prime p → p ∣ n → ∀ (b : K), b ^ p ≠ a) → Irreducible (X ^ n - C a)\nK : Type u\ninst✝² : Field K\nhn : Odd (p * n)\na : K\nha : ∀ (p_1 : ℕ), Nat.Prime p_1 → p_1 ∣ p * n → ∀ (b : K), b ^ p_1 ≠ a\nE : Type u\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 77
} | {
"line": 151,
"column": 78
} | [
{
"pp": "K : Type u\ninst✝ : Field K\np : ℕ\nhp : Nat.Prime p\nhp' : p ≠ 2\nn : ℕ\na : K\nha : ∀ (b : K), b ^ p ≠ a\nq : ℕ\nhq : Nat.Prime q\nhq' : q ∣ p ^ n\n⊢ ∀ (b : K), b ^ q ≠ a",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"Na... | [
"K : Type u\ninst✝ : Field K\np : ℕ\nhp : Nat.Prime p\nhp' : p ≠ 2\nn : ℕ\na : K\nha : ∀ (b : K), b ^ p ≠ a\nq : ℕ\nhq : Nat.Prime q\nhq' : q ∣ p ^ n\n⊢ ∀ (b : K), ¬b ^ p = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 346,
"column": 2
} | {
"line": 346,
"column": 13
} | {
"line": 347,
"column": 2
} | [
{
"pp": "case inr\nG : Type u_1\ninst✝ : Group G\nι : Type u_2\nH : ι → Subgroup G\ng : ι → G\ns : Finset ι\nhcovers : ⋃ i ∈ s, g i • ↑(H i) = Set.univ\nh : ∀ i ∈ s, (H i).FiniteIndex → s.card < (H i).index\nhs : s.Nonempty\n⊢ ∑ i ∈ s, (↑(H i).index)⁻¹ < 1",
"ppTerm": "?inr",
"assigned": true,
"used... | [] | | inr hs => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 375,
"column": 10
} | {
"line": 375,
"column": 45
} | {
"line": 375,
"column": 46
} | [
{
"pp": "K : Type u\ninst✝⁶ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na✝ : K\nH : Irreducible (X ^ n - C a✝)\nL✝ : Type u_1\ninst✝⁵ : Field L✝\ninst✝⁴ : Algebra K L✝\ninst✝³ : IsSplittingField K L✝ (X ^ n - C a✝)\nα : L✝\nhα : α ^ n = (algebraMap K L✝) a✝\nhn : 0 < n\na : K\nL : Type ?u.56\ninst✝² :... | [
"K : Type u\ninst✝⁶ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na✝ : K\nH : Irreducible (X ^ n - C a✝)\nL✝ : Type u_1\ninst✝⁵ : Field L✝\ninst✝⁴ : Algebra K L✝\ninst✝³ : IsSplittingField K L✝ (X ^ n - C a✝)\nα : L✝\nhα : α ^ n = (algebraMap K L✝) a✝\nhn : 0 < n\na : K\nL : Type ?u.56\ninst✝² : Field L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 381,
"column": 2
} | {
"line": 381,
"column": 75
} | {
"line": 381,
"column": 76
} | [
{
"pp": "K : Type u\ninst✝⁴ : Field K\nn : ℕ\na : K\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\ninst✝ : NeZero n\nthis : eval (rootOfSplits ⋯ ⋯) (Polynomial.map (algebraMap K L) (X ^ n - C a)) = 0\n⊢ rootOfSplitsXPowSubC ⋯ a L ^ n = (algebraMap K L) a",
... | [
"K : Type u\ninst✝⁴ : Field K\nn : ℕ\na : K\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\ninst✝ : NeZero n\nthis : eval (rootOfSplits ⋯ ⋯) (Polynomial.map (algebraMap K L) (X ^ n - C a)) = 0\n⊢ rootOfSplitsXPowSubC ⋯ a L ^ n = (algebraMap K L) a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 56
} | {
"line": 414,
"column": 2
} | [
{
"pp": "K : Type u\ninst✝⁴ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na : K\nH : Irreducible (X ^ n - C a)\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\nα : L\ninst✝ : NeZero n\nσ : Gal(L/K)\nζ : K\nhα : α ∈ Multiset.map (fun x ↦ (algebraMap K L)... | [
"K : Type u\ninst✝⁴ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na : K\nH : Irreducible (X ^ n - C a)\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\nα : L\ninst✝ : NeZero n\nσ : Gal(L/K)\nζ : K\nhζ'✝ : ζ ∈ primitiveRoots n K\nhζ' : IsPrimitiveRoot ζ n\nh... | simp only [Multiset.mem_map, Multiset.mem_range] at hα | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.FieldTheory.KummerExtension | {
"line": 417,
"column": 2
} | {
"line": 417,
"column": 23
} | {
"line": 419,
"column": 0
} | [
{
"pp": "K : Type u\ninst✝⁴ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na : K\nH : Irreducible (X ^ n - C a)\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\ninst✝ : NeZero n\nσ : Gal(L/K)\nζ : K\nhζ'✝ : ζ ∈ primitiveRoots n K\nhζ' : IsPrimitiveRoot ζ... | [] | exact smul_comm _ _ _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.FieldTheory.KummerExtension | {
"line": 439,
"column": 2
} | {
"line": 439,
"column": 51
} | {
"line": 439,
"column": 52
} | [
{
"pp": "K : Type u\ninst✝⁴ : Field K\nn : ℕ\na : K\nH : Irreducible (X ^ n - C a)\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\nα : L\nhα : α ^ n = (algebraMap K L) a\ninst✝ : NeZero n\nζ : K\nhζ : IsPrimitiveRoot ζ n\nm : ℕ\n⊢ ((autEquivZmod H L hζ).symm (... | [
"K : Type u\ninst✝⁴ : Field K\nn : ℕ\na : K\nH : Irreducible (X ^ n - C a)\nL : Type u_1\ninst✝³ : Field L\ninst✝² : Algebra K L\ninst✝¹ : IsSplittingField K L (X ^ n - C a)\nα : L\nhα : α ^ n = (algebraMap K L) a\ninst✝ : NeZero n\nζ : K\nhζ : IsPrimitiveRoot ζ n\nm : ℕ\n⊢ ((autEquivZmod H L hζ).symm (Multiplicati... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 486,
"column": 4
} | {
"line": 487,
"column": 24
} | {
"line": 487,
"column": 25
} | [
{
"pp": "K : Type u\ninst✝⁵ : Field K\nL : Type u_1\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : FiniteDimensional K L\nhK : (primitiveRoots (finrank K L) K).Nonempty\ninst✝¹ : IsGalois K L\ninst✝ : IsCyclic Gal(L/K)\nζ : K\nhζ : IsPrimitiveRoot ζ (finrank K L)\nσ : Gal(L/K)\nhσ : Function.Surjective fun x... | [
"K : Type u\ninst✝⁵ : Field K\nL : Type u_1\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : FiniteDimensional K L\nhK : (primitiveRoots (finrank K L) K).Nonempty\ninst✝¹ : IsGalois K L\ninst✝ : IsCyclic Gal(L/K)\nζ : K\nhζ : IsPrimitiveRoot ζ (finrank K L)\nσ : Gal(L/K)\nhσ : Function.Surjective fun x ↦ σ ^ x\nhσ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 71,
"column": 24
} | {
"line": 71,
"column": 39
} | {
"line": 71,
"column": 40
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nx✝ : L\n⊢ mk K x✝ = 0 ↔ x✝ ∈ {0}",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Set.instSingletonSet",
"id",
"ConjRoot... | [
"K : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nx✝ : L\n⊢ x✝ = 0 ↔ x✝ ∈ {0}"
] | mk_eq_zero_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 30
} | {
"line": 99,
"column": 4
} | [
{
"pp": "case mp\nK : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nx y : ConjRootClass K L\n⊢ (∃ a, mk K a = x ∧ ∃ b, mk K b = y ∧ a + b = 0) → x = -y",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Exists",
"ConjRootClass.instNeg",
"Dis... | [
"case mp\nK : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\na b : L\nh : a + b = 0\n⊢ mk K a = -mk K b"
] | rintro ⟨a, rfl, b, rfl, h⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 153,
"column": 2
} | {
"line": 155,
"column": 61
} | {
"line": 157,
"column": 0
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : Algebra.IsAlgebraic K L\nc : ConjRootClass K L\n⊢ Irreducible c.minpoly",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIntegral",
"congr... | [] | induction c
rw [minpoly_mk]
exact minpoly.irreducible (Algebra.IsIntegral.isIntegral _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 153,
"column": 2
} | {
"line": 155,
"column": 61
} | {
"line": 157,
"column": 0
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : Algebra.IsAlgebraic K L\nc : ConjRootClass K L\n⊢ Irreducible c.minpoly",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIntegral",
"congr... | [] | induction c
rw [minpoly_mk]
exact minpoly.irreducible (Algebra.IsIntegral.isIntegral _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 80
} | {
"line": 160,
"column": 81
} | [
{
"pp": "case h\nK : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : Algebra.IsAlgebraic K L\nx x✝ : L\n⊢ (aeval x) (mk K x✝).minpoly = 0 ↔ mk K x = mk K x✝",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIn... | [
"case h\nK : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : Algebra.IsAlgebraic K L\nx x✝ : L\n⊢ IsConjRoot K x✝ x ↔ IsConjRoot K x x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.LinearDisjoint | {
"line": 360,
"column": 32
} | {
"line": 360,
"column": 61
} | {
"line": 360,
"column": 61
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring S\ninst✝ : Algebra R S\nA B : Subalgebra R S\nι : Type u_1\na : ι → ↥A\ni : (ι →₀ ↥B) →ₗ[R] S := Submodule.mulLeftMap (toSubmodule B) a\nj : (ι →₀ ↥B) →ₗ[R] S :=\n ↑(MulOpposite.opLinearEquiv R).symm ∘ₗ\n ↑R (Finsupp.linearCombination (↥B.o... | [] | LinearMap.coe_restrictScalars | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.LinearDisjoint | {
"line": 362,
"column": 2
} | {
"line": 366,
"column": 53
} | {
"line": 367,
"column": 2
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring S\ninst✝ : Algebra R S\nA B : Subalgebra R S\nι : Type u_1\na : ι → ↥A\ni : (ι →₀ ↥B) →ₗ[R] S := Submodule.mulLeftMap (toSubmodule B) a\nj : (ι →₀ ↥B) →ₗ[R] S :=\n ↑(MulOpposite.opLinearEquiv R).symm ∘ₗ\n ↑R (Finsupp.linearCombination (↥B.o... | [
"R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring S\ninst✝ : Algebra R S\nA B : Subalgebra R S\nι : Type u_1\na : ι → ↥A\ni : (ι →₀ ↥B) →ₗ[R] S := Submodule.mulLeftMap (toSubmodule B) a\nj : (ι →₀ ↥B) →ₗ[R] S :=\n ↑(MulOpposite.opLinearEquiv R).symm ∘ₗ\n ↑R (Finsupp.linearCombination (↥B.op) (MulOppos... | simp only [LinearMap.coe_comp, Function.comp_apply, Finsupp.lsingle_apply, coe_val,
Finsupp.mapRange.linearEquiv_toLinearMap, LinearEquiv.coe_coe,
MulOpposite.coe_opLinearEquiv_symm, LinearMap.coe_restrictScalars,
Finsupp.mapRange.linearMap_apply, Finsupp.mapRange_single, Finsupp.linearCombination_single,
... | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 59
} | {
"line": 373,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝¹³ : Field F\ninst✝¹² : Field E\ninst✝¹¹ : Algebra F E\nA : IntermediateField F E\nL : Type w\ninst✝¹⁰ : Field L\ninst✝⁹ : Algebra F L\ninst✝⁸ : Algebra L E\ninst✝⁷ : IsScalarTower F L E\nH : A.LinearDisjoint L\nL' : Type u_1\ninst✝⁶ : Field L'\ninst✝⁵ : Algebra F L'\ninst✝... | [
"F : Type u\nE : Type v\ninst✝¹³ : Field F\ninst✝¹² : Field E\ninst✝¹¹ : Algebra F E\nA : IntermediateField F E\nL : Type w\ninst✝¹⁰ : Field L\ninst✝⁹ : Algebra F L\ninst✝⁸ : Algebra L E\ninst✝⁷ : IsScalarTower F L E\nH : A.LinearDisjoint L\nL' : Type u_1\ninst✝⁶ : Field L'\ninst✝⁵ : Algebra F L'\ninst✝⁴ : Algebra ... | refine Subalgebra.LinearDisjoint.of_le_right_of_flat H ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 45
} | {
"line": 145,
"column": 46
} | [
{
"pp": "case refine_2\nF : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nK : Type w\ninst✝¹ : Field K\ninst✝ : Algebra F K\ni : E →ₐ[F] K\nx : E\nx✝ : ∃ n, x ^ ringExpChar F ^ n ∈ (algebraMap F E).range\nn : ℕ\ny : F\nh : (algebraMap F E) y = x ^ ringExpChar F ^ n\n⊢ (algebraMap... | [
"case refine_2\nF : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nK : Type w\ninst✝¹ : Field K\ninst✝ : Algebra F K\ni : E →ₐ[F] K\nx : E\nx✝ : ∃ n, x ^ ringExpChar F ^ n ∈ (algebraMap F E).range\nn : ℕ\ny : F\nh : (algebraMap F E) y = x ^ ringExpChar F ^ n\n⊢ (algebraMap F K) y = i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.LinearDisjoint | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 42
} | {
"line": 590,
"column": 43
} | [
{
"pp": "R : Type u\ninst✝⁷ : CommRing R\nA : Type v\ninst✝⁶ : CommRing A\nB : Type w\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : Flat R A\ninst✝¹ : Flat R B\ninst✝ : IsDomain (A ⊗[R] B)\nha : Function.Injective ⇑(algebraMap R A)\nhb : Function.Injective ⇑(algebraMap R B)\nK : Typ... | [
"R : Type u\ninst✝⁷ : CommRing R\nA : Type v\ninst✝⁶ : CommRing A\nB : Type w\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : Flat R A\ninst✝¹ : Flat R B\ninst✝ : IsDomain (A ⊗[R] B)\nha : Function.Injective ⇑(algebraMap R A)\nhb : Function.Injective ⇑(algebraMap R B)\nK : Type (max w v) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 34
} | {
"line": 244,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nS : Set E\nq : ℕ\ninst✝¹ : ExpChar F q\nn : ℕ\nL : IntermediateField F E := adjoin F S\ninst✝ : Algebra.IsSeparable F ↥L\nM : IntermediateField F E := adjoin F ((fun x ↦ x ^ q ^ n) '' S)\nhi : M ≤ L\n⊢ L = M",
"ppTerm... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nS : Set E\nq : ℕ\ninst✝¹ : ExpChar F q\nn : ℕ\nL : IntermediateField F E := adjoin F S\ninst✝ : Algebra.IsSeparable F ↥L\nM : IntermediateField F E := adjoin F ((fun x ↦ x ^ q ^ n) '' S)\nhi : M ≤ L\nthis : Algebra ↥M ↥L := (inclusio... | letI := (inclusion hi).toAlgebra | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLetI___1 | Lean.Parser.Tactic.tacticLetI__ |
Mathlib.LinearAlgebra.TensorProduct.Subalgebra | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 80
} | {
"line": 149,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring S\ninst✝² : Algebra R S\ninst✝¹ : Semiring T\ninst✝ : Algebra R T\nx : S\ny : T\n⊢ (includeLeft.toLinearMap.range.mulMap includeRight.toLinearMap.range ∘ₗ\n _root_.TensorProduct.map includeLeft.toLinearMap.range... | [
"R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring S\ninst✝² : Algebra R S\ninst✝¹ : Semiring T\ninst✝ : Algebra R T\nx : S\ny : T\n⊢ (includeLeft.toLinearMap.range.mulMap includeRight.toLinearMap.range)\n (includeLeft.toLinearMap.rangeRestrict x ⊗ₜ[R] includeRight.toLinearMa... | rw [LinearMap.comp_apply, LinearMap.id_apply, _root_.TensorProduct.map_tmul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 249,
"column": 2
} | {
"line": 249,
"column": 79
} | {
"line": 249,
"column": 80
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nS : Set E\nq : ℕ\ninst✝¹ : ExpChar F q\nn : ℕ\nL : IntermediateField F E := adjoin F S\ninst✝ : Algebra.IsSeparable F ↥L\nM : IntermediateField F E := adjoin F ((fun x ↦ x ^ q ^ n) '' S)\nhi : M ≤ L\nthis✝¹ : Algebra ↥M ↥... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nS : Set E\nq : ℕ\ninst✝¹ : ExpChar F q\nn : ℕ\nL : IntermediateField F E := adjoin F S\ninst✝ : Algebra.IsSeparable F ↥L\nM : IntermediateField F E := adjoin F ((fun x ↦ x ^ q ^ n) '' S)\nhi : M ≤ L\nthis✝¹ : Algebra ↥M ↥L := (inclus... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 279,
"column": 2
} | {
"line": 279,
"column": 13
} | {
"line": 279,
"column": 14
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\na : E\nha : IsSeparable F a\nq : ℕ\ninst✝ : ExpChar F q\nn : ℕ\nthis : Algebra.IsSeparable F ↥F⟮a⟯\n⊢ F⟮a⟯ = F⟮a ^ q ^ n⟯",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\na : E\nha : IsSeparable F a\nq : ℕ\ninst✝ : ExpChar F q\nn : ℕ\nthis : Algebra.IsSeparable F ↥F⟮a⟯\n⊢ F⟮a⟯ = F⟮a ^ q ^ n⟯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 285,
"column": 2
} | {
"line": 285,
"column": 13
} | {
"line": 285,
"column": 14
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\ninst✝¹ : Algebra.IsSeparable F E\na : E\nq : ℕ\ninst✝ : ExpChar F q\nn : ℕ\n⊢ F⟮a⟯ = F⟮a ^ q ^ n⟯",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\ninst✝¹ : Algebra.IsSeparable F E\na : E\nq : ℕ\ninst✝ : ExpChar F q\nn : ℕ\n⊢ F⟮a⟯ = F⟮a ^ q ^ n⟯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 340,
"column": 50
} | {
"line": 340,
"column": 88
} | {
"line": 340,
"column": 89
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nq n : ℕ\nhF : ExpChar F q\nι : Type u_1\nv : ι → E\ninst✝¹ : FiniteDimensional F E\ninst✝ : Algebra.IsSeparable F E\nh : LinearIndependent F v\nh' : LinearIndepOn F id (Set.range v)\nι' : Set E := h'.extend ⋯\nb : Basis (... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nq n : ℕ\nhF : ExpChar F q\nι : Type u_1\nv : ι → E\ninst✝¹ : FiniteDimensional F E\ninst✝ : Algebra.IsSeparable F E\nh : LinearIndependent F v\nh' : LinearIndepOn F id (Set.range v)\nι' : Set E := h'.extend ⋯\nb : Basis (↑ι') F E := ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 13
} | {
"line": 406,
"column": 14
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq : ℕ\nhF : ExpChar F q\ninst✝ : ExpChar E q\na : E\nhsep : IsSeparable F a\n⊢ minpoly F ((frobenius E q) a) = Polynomial.map (frobenius F q) (minpoly F a)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstant... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq : ℕ\nhF : ExpChar F q\ninst✝ : ExpChar E q\na : E\nhsep : IsSeparable F a\n⊢ minpoly F ((frobenius E q) a) = Polynomial.map (frobenius F q) (minpoly F a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 37
} | {
"line": 574,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁶ : Field F\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝³ : Field L\ninst✝² : Algebra F L\ninst✝¹ : Algebra L E\ninst✝ : IsScalarTower F L E\nH : A.LinearDisjoint L\nhalg : Algebra.IsAlgebraic F ↥A ∨ Algebra.IsAlgebraic F L\n⊢ Module... | [
"F : Type u\nE : Type v\ninst✝⁶ : Field F\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝³ : Field L\ninst✝² : Algebra F L\ninst✝¹ : Algebra L E\ninst✝ : IsScalarTower F L E\nH : A.LinearDisjoint L\nhalg : Algebra.IsAlgebraic F ↥A ∨ Algebra.IsAlgebraic F L\n⊢ Module.rank ↥A ↥(e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 593,
"column": 2
} | {
"line": 593,
"column": 37
} | {
"line": 593,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁶ : Field F\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝³ : Field L\ninst✝² : Algebra F L\ninst✝¹ : Algebra L E\ninst✝ : IsScalarTower F L E\nH : A.LinearDisjoint L\nhalg : Algebra.IsAlgebraic F ↥A ∨ Algebra.IsAlgebraic F L\n⊢ Module... | [
"F : Type u\nE : Type v\ninst✝⁶ : Field F\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝³ : Field L\ninst✝² : Algebra F L\ninst✝¹ : Algebra L E\ninst✝ : IsScalarTower F L E\nH : A.LinearDisjoint L\nhalg : Algebra.IsAlgebraic F ↥A ∨ Algebra.IsAlgebraic F L\n⊢ Module.rank F L * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 749,
"column": 2
} | {
"line": 749,
"column": 53
} | {
"line": 749,
"column": 54
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nA B : IntermediateField F E\ninst✝ : FiniteDimensional F E\nh₁ : A.LinearDisjoint B.toSubalgebra\nh₂ : A ⊔ B = ⊤\nx : ↥B\n⊢ A.toSubalgebra ⊔ B.toSubalgebra = ⊤",
"ppTerm": "?m.73",
"assigned": false,
"usedCons... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nA B : IntermediateField F E\ninst✝ : FiniteDimensional F E\nh₁ : A.LinearDisjoint B.toSubalgebra\nh₂ : A ⊔ B = ⊤\nx : ↥B\n⊢ A.toSubalgebra ⊔ B.toSubalgebra = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 78,
"column": 14
} | {
"line": 78,
"column": 78
} | {
"line": 78,
"column": 78
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type w\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : IsPurelyInseparable F E\nι : Type u_1\nv : ι → K\nhsep : ∀ (i : ι), IsSeparable F (v i)\nh : LinearIndependen... | [] | by rw [map_zero, Finsupp.notMem_support_iff.1 hs, zero_pow this] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 759,
"column": 2
} | {
"line": 759,
"column": 53
} | {
"line": 759,
"column": 54
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nA B : IntermediateField F E\ninst✝ : FiniteDimensional F E\nh₁ : A.LinearDisjoint B.toSubalgebra\nh₂ : A ⊔ B = ⊤\nx : ↥B\n⊢ A.toSubalgebra ⊔ B.toSubalgebra = ⊤",
"ppTerm": "?m.75",
"assigned": false,
"usedCons... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nA B : IntermediateField F E\ninst✝ : FiniteDimensional F E\nh₁ : A.LinearDisjoint B.toSubalgebra\nh₂ : A ⊔ B = ⊤\nx : ↥B\n⊢ A.toSubalgebra ⊔ B.toSubalgebra = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 37
} | {
"line": 134,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsSeparable F E\n⊢ Module.rank F E * sepDegree E K = sepDegree F K",
"ppTerm": "?m.34",
"assi... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsSeparable F E\n⊢ Module.rank F E * sepDegree E K = sepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 37
} | {
"line": 173,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : IsPurelyInseparable F E\n⊢ Module.rank F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : IsPurelyInseparable F E\n⊢ Module.rank F E * insepDegree E K = insepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 37
} | {
"line": 188,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ sepDegree F E * sepDegree E K = sepDegree F K",
"ppTerm": "?m.34",
"assign... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ sepDegree F E * sepDegree E K = sepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 37
} | {
"line": 203,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 226,
"column": 2
} | {
"line": 228,
"column": 50
} | {
"line": 229,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁸ : Field F\ninst✝⁷ : Field E\ninst✝⁶ : Algebra F E\nK : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Algebra F K\ninst✝³ : Algebra E K\ninst✝² : IsScalarTower F E K\nS : Set K\ninst✝¹ : IsPurelyInseparable F E\nM : IntermediateField F K := adjoin F S\ninst✝ : Algebra.IsAlgebraic F ↥... | [
"F : Type u\nE : Type v\ninst✝⁸ : Field F\ninst✝⁷ : Field E\ninst✝⁶ : Algebra F E\nK : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Algebra F K\ninst✝³ : Algebra E K\ninst✝² : IsScalarTower F E K\nS : Set K\ninst✝¹ : IsPurelyInseparable F E\nM : IntermediateField F K := adjoin F S\ninst✝ : Algebra.IsAlgebraic F ↥M\nL : Inter... | have hi : M ≤ L.restrictScalars F := by
rw [restrictScalars_adjoin_of_algEquiv (E := K) j rfl, restrictScalars_adjoin]
exact adjoin.mono _ _ _ Set.subset_union_right | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 276,
"column": 53
} | {
"line": 276,
"column": 74
} | {
"line": 277,
"column": 4
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type w\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\nx : K\nhsep : IsSeparable F x\ninst✝ : IsPurelyInseparable F E\nhi : IsIntegral F x\nhi' : IsIntegral E x\nhsep' : Is... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type w\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\nx : K\nhsep : IsSeparable F x\ninst✝ : IsPurelyInseparable F E\nhi : IsIntegral F x\nhi' : IsIntegral E x\nhsep' : IsSeparable E ... | ← adjoin.finrank hi', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 71
} | {
"line": 291,
"column": 4
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nf : F[X]\nhsep : f.Separable\nhirr : Irreducible f\ninst✝ : IsPurelyInseparable F E\nK : Type v := AlgebraicClosure E\nx : K\nhx : (aeval x) f = 0\n⊢ Associated f (minpoly F x)",
"ppTerm": "?m.66",
"assigned": tru... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nf : F[X]\nhsep : f.Separable\nhirr : Irreducible f\ninst✝ : IsPurelyInseparable F E\nK : Type v := AlgebraicClosure E\nx : K\nhx : (aeval x) f = 0\nthis : IsUnit (C f.leadingCoeff⁻¹)\n⊢ Associated f (minpoly F x)"
] | have := isUnit_C.2 (leadingCoeff_ne_zero.2 hirr.ne_zero).isUnit.inv | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.FieldTheory.Relrank | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 52
} | {
"line": 129,
"column": 52
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA : Subfield E\nx✝ : AddCommMonoid ↥⊤ := inferInstance\n⊢ Module.rank ↥A ↥⊤ = Module.rank (↥A) E",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Subfield.toAlgebra",
"Semiring.toModule",
... | [
"E : Type v\ninst✝ : Field E\nA : Subfield E\nx✝ : AddCommMonoid ↥⊤ := inferInstance\n⊢ Module.rank (↥A) E = Module.rank (↥A) E"
] | IntermediateField.topEquiv.toLinearEquiv.rank_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Relrank | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 28
} | {
"line": 143,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : E →+* L\n⊢ (map f A).relrank (map f B) = A.relrank B",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : E →+* L\n⊢ (map f A).relrank (map f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 28
} | {
"line": 152,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nB : Subfield L\n⊢ (comap f A).relrank B = A.relrank (map f B)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nB : Subfield L\n⊢ (comap f A).relrank B = A.relrank (map f B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 67
} | {
"line": 160,
"column": 68
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\n⊢ lift.{v, w} (Module.rank (↥(comap f A)) L) = lift.{w, v} (A.relrank f.fieldRange)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\n⊢ lift.{v, w} (Module.rank (↥(comap f A)) L) = lift.{w, v} (A.relrank f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 28
} | {
"line": 164,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 28
} | {
"line": 184,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.IntermediateField | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 27
} | {
"line": 70,
"column": 28
} | [
{
"pp": "case h\nK : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ↑((f.minpolyX ↥K⟮f⟯).coeff f.denom.natDegree) = 0\n⊢ C (f.num.coeff f.denom.natDegree) = f * C f.denom.leadingCoeff",
"ppTerm": "?h",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case h\nK : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ↑((f.minpolyX ↥K⟮f⟯).coeff f.denom.natDegree) = 0\n⊢ C (f.num.coeff f.denom.natDegree) = f * C f.denom.leadingCoeff"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 37
} | {
"line": 193,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ lift.{v, w} ((comap f A).relrank (comap f B)) = lift.{w, v} (A.relrank B)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ lift.{v, w} ((comap f A).relrank (comap f B)) = lift.{w, v} (A.relrank B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 28
} | {
"line": 198,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 13
} | {
"line": 213,
"column": 14
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 20
} | {
"line": 107,
"column": 21
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nF : Set (PointedCone R M)\nh : ∀ f ∈ F, f.IsFaceOf C\nx✝ y✝ : M\na : R\nxc : x✝ ∈ C\nyc : y✝ ∈ C\na0 : 0 < a\na✝ : a • x✝ + y✝ ∈ C\nh' : ... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nF : Set (PointedCone R M)\nh : ∀ f ∈ F, f.IsFaceOf C\nx✝ y✝ : M\na : R\nxc : x✝ ∈ C\nyc : y✝ ∈ C\na0 : 0 < a\na✝ : a • x✝ + y✝ ∈ C\nh' : ∀ p ∈ F, a •... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.IntermediateField | {
"line": 112,
"column": 57
} | {
"line": 112,
"column": 79
} | {
"line": 112,
"column": 80
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ¬∃ c, f = C c\nthis :\n (f.minpolyX ↥K⟮f⟯).natDegree ≤\n max f.num.natDegree\n (Polynomial.C ((algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩) * Polynomial.map (algebraMap K ↥K⟮f⟯) f.denom).natDegree\nH : (algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩ = 0\n⊢ f = C 0",
"ppTer... | [
"K : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ¬∃ c, f = C c\nthis :\n (f.minpolyX ↥K⟮f⟯).natDegree ≤\n max f.num.natDegree\n (Polynomial.C ((algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩) * Polynomial.map (algebraMap K ↥K⟮f⟯) f.denom).natDegree\nH : (algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩ = 0\n⊢ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 19
} | {
"line": 112,
"column": 20
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nhF : F.IsFaceOf C\nx y : M\nhx : x ∈ C\nhy : y ∈ C\nhxy : x + y ∈ F\na✝ : Nontrivial R\n⊢ x ∈ F",
"ppTerm": "?m.63",
"assigned"... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nhF : F.IsFaceOf C\nx y : M\nhx : x ∈ C\nhy : y ∈ C\nhxy : x + y ∈ F\na✝ : Nontrivial R\n⊢ x ∈ F"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 37
} | {
"line": 255,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 37
} | {
"line": 265,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 15
} | {
"line": 74,
"column": 16
} | [
{
"pp": "case refine_2\nK : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nf : K[X]\nhf : Polynomial.map (algebraMap K ↥E) f = φ E\n⊢ (aeval X) f = 0",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Algebra.algebraMap",
"AddGroupWithOne.... | [
"case refine_2\nK : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nf : K[X]\nhf : Polynomial.map (algebraMap K ↥E) f = φ E\n⊢ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 28
} | {
"line": 357,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 368,
"column": 2
} | {
"line": 368,
"column": 28
} | {
"line": 368,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nB : IntermediateField F L\n⊢ (comap f A).relrank B = A.relrank (map f B)",
"ppTerm": "?m.51",
"assigned": false,
"us... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nB : IntermediateField F L\n⊢ (comap f A).relrank B = A.relrank (map f B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 105,
"column": 41
} | {
"line": 105,
"column": 52
} | {
"line": 105,
"column": 53
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nx✝ : ∃ c, generator E = C c\nc : K\nhc : generator E = C c\n⊢ (algebraMap K K⟮X⟯) c = generator E",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nx✝ : ∃ c, generator E = C c\nc : K\nhc : generator E = C c\n⊢ C c = generator E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 28
} | {
"line": 380,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : E →ₐ[F] L\n⊢ (map f A).relrank (map f B) = A.relrank B",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"used... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : E →ₐ[F] L\n⊢ (map f A).relrank (map f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 394,
"column": 2
} | {
"line": 394,
"column": 28
} | {
"line": 394,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)",
"ppTerm": "?m.58",
"assigned": false,
"usedCons... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 37
} | {
"line": 402,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nL : Type w\ninst✝¹ : Field L\ninst✝ : Algebra F L\nA B : IntermediateField F E\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ Cardinal.lift.{v, w} ((comap f A).relrank (comap f B)) = Cardinal.lift.{w, v} (A.relrank B)",
"ppT... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nL : Type w\ninst✝¹ : Field L\ninst✝ : Algebra F L\nA B : IntermediateField F E\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ Cardinal.lift.{v, w} ((comap f A).relrank (comap f B)) = Cardinal.lift.{w, v} (A.relrank B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 28
} | {
"line": 407,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.58",
"assigned": false,
"use... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 421,
"column": 2
} | {
"line": 421,
"column": 13
} | {
"line": 421,
"column": 14
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.51",
"assigned": false,
... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 480,
"column": 2
} | {
"line": 480,
"column": 37
} | {
"line": 480,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 490,
"column": 2
} | {
"line": 490,
"column": 37
} | {
"line": 490,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 59
} | {
"line": 223,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nh₁ : F ≤ C\nh₂ : ∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → x ∈ F\nx✝ y✝ : M\na✝ : R\nhx : x✝ ∈ C\nhy : y✝ ∈ C\nha : 0 < a✝\nhaxy : a✝... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nh₁ : F ≤ C\nh₂ : ∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → x ∈ F\nx✝ y✝ : M\na✝ : R\nhx : x✝ ∈ C\nhy : y✝ ∈ C\nha : 0 < a✝\nhaxy : a✝ • x✝ + y✝ ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 35
} | {
"line": 231,
"column": 36
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nx✝ y✝ : M\nxc : x✝ ∈ C\nyc : y✝ ∈ C\nxyf : x✝ + y✝ ∈ C ∧ -y✝ + -x✝ ∈ C\n⊢ -x✝ ∈ C",
"ppTerm": "?m.77",
"assigned": false,
... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nx✝ y✝ : M\nxc : x✝ ∈ C\nyc : y✝ ∈ C\nxyf : x✝ + y✝ ∈ C ∧ -y✝ + -x✝ ∈ C\n⊢ -x✝ ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 251,
"column": 24
} | {
"line": 251,
"column": 46
} | {
"line": 251,
"column": 47
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁶ : DivisionRing R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : IsOrderedRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nC₁ F₁ : PointedCone R M\nC₂ F₂ : PointedCone R N\nhF₁ : F₁.IsFaceOf C₁\nhF₂ : F₂.IsFaceOf C₂\nx... | [
"R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁶ : DivisionRing R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : IsOrderedRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nC₁ F₁ : PointedCone R M\nC₂ F₂ : PointedCone R N\nhF₁ : F₁.IsFaceOf C₁\nhF₂ : F₂.IsFaceOf C₂\nx : M × N\nhx... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 348,
"column": 4
} | {
"line": 348,
"column": 76
} | {
"line": 348,
"column": 77
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis :\n Polynomial.C ((algebraMap K[X] K⟮X⟯) (g E)) * Polynomial.map (algebraMap (↥E) K⟮X⟯) (q E) *\n Polynomial.map (algebraMap (↥E) K⟮X⟯) (φ E) =\n Polynomial.map (algebraMap K[X] K⟮X⟯) (θ E)\n⊢ Polynomial.C ((algebraMa... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis :\n Polynomial.C ((algebraMap K[X] K⟮X⟯) (g E)) * Polynomial.map (algebraMap (↥E) K⟮X⟯) (q E) *\n Polynomial.map (algebraMap (↥E) K⟮X⟯) (φ E) =\n Polynomial.map (algebraMap K[X] K⟮X⟯) (θ E)\n⊢ Polynomial.C ((algebraMap K[X] K⟮X⟯)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Diffeology.Basic | {
"line": 326,
"column": 4
} | {
"line": 326,
"column": 53
} | {
"line": 327,
"column": 4
} | [
{
"pp": "X : Type u_1\nd : CorePlotsOn X\nn : ℕ\np : EuclideanSpace ℝ (Fin n) → X\nh :\n ∀ (x : EuclideanSpace ℝ (Fin n)),\n ∃ u,\n IsOpen u ∧\n x ∈ u ∧\n ∀ {m : ℕ} {f : EuclideanSpace ℝ (Fin m) → EuclideanSpace ℝ (Fin n)},\n (∀ (x : EuclideanSpace ℝ (Fin m)), f x ∈ u) → Cont... | [
"X : Type u_1\nd : CorePlotsOn X\nn : ℕ\np : EuclideanSpace ℝ (Fin n) → X\nh :\n ∀ (x : EuclideanSpace ℝ (Fin n)),\n ∃ u,\n IsOpen u ∧\n x ∈ u ∧\n ∀ {m : ℕ} {f : EuclideanSpace ℝ (Fin m) → EuclideanSpace ℝ (Fin n)},\n (∀ (x : EuclideanSpace ℝ (Fin m)), f x ∈ u) → ContDiff ℝ ∞ f →... | let ⟨ε, hε, hε'⟩ := Metric.isOpen_iff.mp hu x hxu | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 452,
"column": 12
} | {
"line": 452,
"column": 23
} | {
"line": 452,
"column": 24
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynom... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynomial.mapRingH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 453,
"column": 7
} | {
"line": 453,
"column": 18
} | {
"line": 453,
"column": 19
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynom... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynomial.mapRingH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 167,
"column": 6
} | {
"line": 167,
"column": 17
} | {
"line": 167,
"column": 18
} | [
{
"pp": "case mpr.refine_1\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢... | [
"case mpr.refine_1\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ p -ᵥ s.poin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 170,
"column": 31
} | {
"line": 170,
"column": 42
} | {
"line": 170,
"column": 43
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ id (p -ᵥ s.points ... | [
"V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ ¬p = s.points i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 34
} | {
"line": 207,
"column": 0
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\n⊢ s.altitudeFoot i ∈ affineSpan ℝ (Set.range (s.faceOpposite i).points)",
"ppTerm": "?m.66",
... | [] | exact orthogonalProjection_mem _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 49,
"column": 6
} | {
"line": 53,
"column": 42
} | {
"line": 54,
"column": 6
} | [
{
"pp": "V : Type u_1\nV' : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : NormedAddCommGroup V'\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : InnerProductSpace ℝ V'\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Fact (finrank ℝ V' = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nx y : V\n⊢ ⟪(θ.cos • LinearMap.id +... | [
"V : Type u_1\nV' : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : NormedAddCommGroup V'\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : InnerProductSpace ℝ V'\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Fact (finrank ℝ V' = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nx y : V\n⊢ θ.cos * (θ.cos * ⟪x, y⟫ + θ.sin * (o... | simp only [RCLike.conj_to_real, id, LinearMap.smul_apply, LinearMap.add_apply,
LinearMap.id_coe, LinearEquiv.coe_coe, LinearIsometryEquiv.coe_toLinearEquiv,
Orientation.areaForm_rightAngleRotation_left, Orientation.inner_rightAngleRotation_left,
Orientation.inner_rightAngleRotation_right, inner_... | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 18
} | {
"line": 111,
"column": 19
} | [
{
"pp": "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ LinearMap.det\n ((Matrix.toLin (o.basisRightAngleRotation x hx) (o.basisRightAngleRotation x hx))\n ... | [
"V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ θ.cos * θ.cos + θ.sin * θ.sin = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 57
} | {
"line": 118,
"column": 58
} | [
{
"pp": "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\n⊢ ↑(LinearEquiv.det (o.rotation θ).toLinearEquiv) = ↑1",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"LinearEquiv.det",... | [
"V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\n⊢ LinearMap.det ↑(o.rotation θ).toLinearEquiv = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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