module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 377,
"column": 7
} | {
"line": 377,
"column": 56
} | [
{
"pp": "case h\nG : Type u_1\nK : Type u_3\nL : Type u_4\ninst✝⁴ : Group G\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : MulSemiringAction G L\nhGKL : IsGaloisGroup G K L\nthis : FaithfulSMul G L\nx✝ : G\n⊢ x✝ ∈ fixingSubgroup G ↑⊤ ↔ x✝ ∈ ⊥",
"usedConstants": [
"Eq.mpr",
"N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 510,
"column": 4
} | {
"line": 510,
"column": 44
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝⁸ : Group G\ninst✝⁷ : Group G'\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Algebra K L\ninst✝³ : MulSemiringAction G L\ninst✝² : MulSemiringAction G' L\nH H' : Subgroup G\nF F' : IntermediateField K L\nN : Subgroup G\ninst✝¹ : N.Normal\nhF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 514,
"column": 6
} | {
"line": 514,
"column": 37
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝⁸ : Group G\ninst✝⁷ : Group G'\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Algebra K L\ninst✝³ : MulSemiringAction G L\ninst✝² : MulSemiringAction G' L\nH H' : Subgroup G\nF F' : IntermediateField K L\nN : Subgroup G\ninst✝¹ : N.Normal\nhF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 514,
"column": 6
} | {
"line": 514,
"column": 65
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝⁸ : Group G\ninst✝⁷ : Group G'\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Algebra K L\ninst✝³ : MulSemiringAction G L\ninst✝² : MulSemiringAction G' L\nH H' : Subgroup G\nF F' : IntermediateField K L\nN : Subgroup G\ninst✝¹ : N.Normal\nhF... | simpa [coe_quotient_smul] using congr_arg Subtype.val (h g) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 514,
"column": 6
} | {
"line": 514,
"column": 65
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝⁸ : Group G\ninst✝⁷ : Group G'\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Algebra K L\ninst✝³ : MulSemiringAction G L\ninst✝² : MulSemiringAction G' L\nH H' : Subgroup G\nF F' : IntermediateField K L\nN : Subgroup G\ninst✝¹ : N.Normal\nhF... | simpa [coe_quotient_smul] using congr_arg Subtype.val (h g) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.Galois.IsGaloisGroup | {
"line": 514,
"column": 6
} | {
"line": 514,
"column": 65
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝⁸ : Group G\ninst✝⁷ : Group G'\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Algebra K L\ninst✝³ : MulSemiringAction G L\ninst✝² : MulSemiringAction G' L\nH H' : Subgroup G\nF F' : IntermediateField K L\nN : Subgroup G\ninst✝¹ : N.Normal\nhF... | simpa [coe_quotient_smul] using congr_arg Subtype.val (h g) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Invariant.Basic | {
"line": 463,
"column": 4
} | {
"line": 463,
"column": 82
} | [
{
"pp": "A : Type u_1\nB : Type u_2\nk : Type u_3\ninst✝¹³ : CommRing A\ninst✝¹² : CommRing B\ninst✝¹¹ : Algebra A B\nG : Type u_4\ninst✝¹⁰ : Finite G\ninst✝⁹ : Group G\ninst✝⁸ : MulSemiringAction G B\ninst✝⁷ : Algebra.IsInvariant A B G\nP✝ : Ideal A\nQ : Ideal B\ninst✝⁶ : Q.LiesOver P✝\ninst✝⁵ : CommRing k\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Galois.Profinite | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 13
} | [
{
"pp": "case h\nk : Type u_3\nK : Type u_4\ninst✝³ : Field k\ninst✝² : Field K\ninst✝¹ : Algebra k K\ninst✝ : IsGalois k K\nL : FiniteGaloisIntermediateField k K\nfix1 : Set\n ((L : (FiniteGaloisIntermediateField k K)ᵒᵖ) → ↑((asProfiniteGaloisGroupFunctor k K).obj L).toProfinite.toTop) :=\n {f | f (op L) = 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Galois.Profinite | {
"line": 318,
"column": 2
} | {
"line": 318,
"column": 23
} | [
{
"pp": "case h\nk : Type u_3\nK : Type u_4\ninst✝³ : Field k\ninst✝² : Field K\ninst✝¹ : Algebra k K\ninst✝ : IsGalois k K\nH : Set Gal(K/k)\nL : FiniteGaloisIntermediateField k K\nle : ↑L.fixingSubgroup ⊆ H\n⊢ (fun a ↦ (mulEquivToLimit k K) a) '' ↑L.fixingSubgroup ⊆ (fun a ↦ (mulEquivToLimit k K).toEquiv a) '... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | {
"line": 362,
"column": 4
} | {
"line": 362,
"column": 15
} | [
{
"pp": "case a\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ ProfiniteGrp.{max v u}\ncone : Limits.Cone F\nm : cone.pt ⟶ (limitCone F).pt\nh : ∀ (j : J), m ≫ (limitCone F).π.app j = cone.π.app j\n⊢ (forget₂ ProfiniteGrp.{max u v} Profinite).map m =\n (forget₂ ProfiniteGrp.{max u v} Profinite).map\n (of... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Invariant.Basic | {
"line": 550,
"column": 40
} | {
"line": 550,
"column": 51
} | [
{
"pp": "G : Type u_1\nA : Type u_2\nB : Type u_3\nK : Type u_4\nL : Type u_5\ninst✝¹⁸ : Group G\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : CommRing B\ninst✝¹⁵ : MulSemiringAction G B\ninst✝¹⁴ : Algebra A B\ninst✝¹³ : Field K\ninst✝¹² : Field L\ninst✝¹¹ : Algebra K L\ninst✝¹⁰ : Algebra A K\ninst✝⁹ : Algebra B L\ninst✝⁸ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Invariant.Basic | {
"line": 558,
"column": 8
} | {
"line": 558,
"column": 65
} | [
{
"pp": "G : Type u_1\nA : Type u_2\nB : Type u_3\nK : Type u_4\nL : Type u_5\ninst✝¹⁸ : Group G\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : CommRing B\ninst✝¹⁵ : MulSemiringAction G B\ninst✝¹⁴ : Algebra A B\ninst✝¹³ : Field K\ninst✝¹² : Field L\ninst✝¹¹ : Algebra K L\ninst✝¹⁰ : Algebra A K\ninst✝⁹ : Algebra B L\ninst✝⁸ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsPerfectClosure | {
"line": 165,
"column": 15
} | {
"line": 165,
"column": 51
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝² : CommSemiring K\ninst✝¹ : CommSemiring L\ni : K →+* L\np : ℕ\ninst✝ : IsPRadical i p\nx : K\nn : ℕ\nh : x ^ p ^ n = 0\n⊢ i x ^ p ^ n = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsPerfectClosure | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 59
} | [
{
"pp": "K : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁴ : CommSemiring K\ninst✝³ : CommSemiring L\ninst✝² : CommSemiring M\ni : K →+* L\nf : L →+* M\np : ℕ\ninst✝¹ : IsPRadical i p\ninst✝ : IsPRadical f p\nx : K\nh : i x ∈ RingHom.ker f\n⊢ x ∈ pNilradical K p",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IntegralClosure.IntegralRestrict | {
"line": 94,
"column": 4
} | {
"line": 96,
"column": 45
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝³¹ : CommRing A\ninst✝³⁰ : CommRing B\ninst✝²⁹ : CommRing B₂\ninst✝²⁸ : CommRing B₃\ninst✝²⁷ : Algebra A B\ninst✝²⁶ : Algebra A B₂\ninst✝²⁵ : Algebra A B₃\ninst✝²⁴ : Field K\ninst✝²³... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsPerfectClosure | {
"line": 264,
"column": 2
} | {
"line": 264,
"column": 36
} | [
{
"pp": "case a\nK : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁴ : CommRing K\ninst✝³ : CommRing L\ninst✝² : CommRing M\ni : K →+* L\np : ℕ\ninst✝¹ : ExpChar M p\ninst✝ : IsPRadical i p\nh : pNilradical M p = ⊥\nf g : L →+* M\nheq : (fun f ↦ f.comp i) f = (fun f ↦ f.comp i) g\nx : L\nn : ℕ\ny : K\nhx : i y = x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PerfectClosure | {
"line": 352,
"column": 17
} | {
"line": 353,
"column": 38
} | [
{
"pp": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx : ℕ × K\nn : ℕ\nih : mk K p x ^ n = mk K p (x.1, x.2 ^ n)\n⊢ (⇑(frobenius K p))^[(x.1, x.2 ^ n * x.2).1 + 0]\n ((x.1, x.2 ^ n).1 + x.1,\n (⇑(frobenius K p))^[x.1] (x.1, x.2 ^ n).2 * (⇑(frobenius K p)... | simp_rw [iterate_frobenius, add_zero, mul_pow, ← pow_mul,
← pow_add, mul_assoc, ← pow_add] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.FieldTheory.PerfectClosure | {
"line": 352,
"column": 17
} | {
"line": 353,
"column": 38
} | [
{
"pp": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx : ℕ × K\nn : ℕ\nih : mk K p x ^ n = mk K p (x.1, x.2 ^ n)\n⊢ (⇑(frobenius K p))^[(x.1, x.2 ^ n * x.2).1 + 0]\n ((x.1, x.2 ^ n).1 + x.1,\n (⇑(frobenius K p))^[x.1] (x.1, x.2 ^ n).2 * (⇑(frobenius K p)... | simp_rw [iterate_frobenius, add_zero, mul_pow, ← pow_mul,
← pow_add, mul_assoc, ← pow_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.PerfectClosure | {
"line": 352,
"column": 17
} | {
"line": 353,
"column": 38
} | [
{
"pp": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx : ℕ × K\nn : ℕ\nih : mk K p x ^ n = mk K p (x.1, x.2 ^ n)\n⊢ (⇑(frobenius K p))^[(x.1, x.2 ^ n * x.2).1 + 0]\n ((x.1, x.2 ^ n).1 + x.1,\n (⇑(frobenius K p))^[x.1] (x.1, x.2 ^ n).2 * (⇑(frobenius K p)... | simp_rw [iterate_frobenius, add_zero, mul_pow, ← pow_mul,
← pow_add, mul_assoc, ← pow_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.PerfectClosure | {
"line": 374,
"column": 4
} | {
"line": 374,
"column": 64
} | [
{
"pp": "case mp\nK : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx y z : ℕ\nH : (⇑(frobenius K p))^[(0, ↑y).1 + z] (0, ↑x).2 = (⇑(frobenius K p))^[(0, ↑x).1 + z] (0, ↑y).2\n⊢ ↑x = ↑y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PerfectClosure | {
"line": 405,
"column": 21
} | {
"line": 405,
"column": 78
} | [
{
"pp": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx✝¹ : PerfectClosure K p\nx : ℕ × K\nx✝ : IsNilpotent (mk K p x)\nn m : ℕ\nh : (iterateFrobenius K p m) (x.2 ^ p ^ n) = 0\n⊢ (iterateFrobenius K p (n + m)) x.2 = 0",
"usedConstants": [
"Eq.mpr",
"Non... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PerfectClosure | {
"line": 462,
"column": 55
} | {
"line": 462,
"column": 95
} | [
{
"pp": "K : Type u\ninst✝³ : CommRing K\ninst✝² : IsReduced K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx y : ℕ × K\nx✝ : ∃ z, (⇑(frobenius K p))^[y.1 + z] x.2 = (⇑(frobenius K p))^[x.1 + z] y.2\nz : ℕ\nH : (⇑(frobenius K p))^[y.1 + z] x.2 = (⇑(frobenius K p))^[x.1 + z] y.2\n⊢ (⇑(frobenius K p))^... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 80,
"column": 40
} | {
"line": 80,
"column": 51
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhn : Odd n\nr : R\nhr : (X ^ n - C x).IsRoot r\n⊢ r ^ n - x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 15
} | [
{
"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",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"congrArg",
"DivInvMonoid.toZPow",
"Exists",
"Field.toDivisionRing",
"DivisionRing.toDivInvMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 84,
"column": 43
} | {
"line": 84,
"column": 54
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd ↑n\n⊢ Odd n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 85,
"column": 38
} | {
"line": 85,
"column": 49
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nn : ℕ\nhk : Odd (-↑n)\n⊢ Odd ?m.72",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 86,
"column": 19
} | {
"line": 86,
"column": 30
} | [
{
"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)",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DivInv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 15
} | [
{
"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",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"congrArg",
"DivInvMonoid.toZPow",
"Exists",
"Field.toDivisionRing",
"DivisionRing.t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 103,
"column": 49
} | {
"line": 103,
"column": 60
} | [
{
"pp": "R : Type u\ninst✝¹ : Field R\ninst✝ : IsRealClosed R\nx : R\nhx : IsSquare x\nn : ℕ\nhk : ↑n ≠ 0\n⊢ n ≠ 0",
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 104,
"column": 44
} | {
"line": 104,
"column": 55
} | [
{
"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",
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.IsRealClosed.Basic | {
"line": 105,
"column": 19
} | {
"line": 105,
"column": 30
} | [
{
"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)",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IntegralClosure.IntegralRestrict | {
"line": 384,
"column": 27
} | {
"line": 384,
"column": 38
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝⁴² : CommRing A\ninst✝⁴¹ : CommRing B\ninst✝⁴⁰ : CommRing B₂\ninst✝³⁹ : CommRing B₃\ninst✝³⁸ : Algebra A B\ninst✝³⁷ : Algebra A B₂\ninst✝³⁶ : Algebra A B₃\ninst✝³⁵ : Field K\ninst✝³⁴... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Laurent | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 31
} | [
{
"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✝",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.JacobsonNoether | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 41
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"HMul.hM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 69,
"column": 52
} | {
"line": 69,
"column": 63
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nD H : Subgroup G\ninst✝ : D.FiniteIndex\nhD_le_H : D ≤ H\nt : Set ↥H\nht : IsComplement t ↑(D.subgroupOf H) ∧ 1 ∈ t\nhf : t.Finite\nx : G\nthis : (∃ y ∈ t, ∃ d ∈ D, ↑y * d = x) ↔ x ∈ H\n⊢ x ∈ ⋃ g ∈ hf.toFinset, ↑g • ↑D ↔ x ∈ ↑H",
"usedConstants": [
"Iff.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 143,
"column": 6
} | {
"line": 143,
"column": 81
} | [
{
"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 = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 149,
"column": 8
} | {
"line": 149,
"column": 19
} | [
{
"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 = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 83,
"column": 2
} | {
"line": 85,
"column": 9
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 51
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 23
} | [
{
"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)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 52
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 109,
"column": 11
} | {
"line": 109,
"column": 22
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"Polynomial.C",
"congrArg",
"HSub.hSub",
"RingHom",
"Field.toDivisionRing",
"Irr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 116,
"column": 6
} | {
"line": 117,
"column": 37
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 48
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 154,
"column": 8
} | {
"line": 154,
"column": 85
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 77
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"Nat.Prime.dvd_of_dvd_pow",
"Nat.prime_dvd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 172,
"column": 48
} | {
"line": 172,
"column": 59
} | [
{
"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 = (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 365,
"column": 10
} | {
"line": 365,
"column": 45
} | [
{
"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.229271\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 75
} | [
{
"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",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 403,
"column": 2
} | {
"line": 403,
"column": 56
} | [
{
"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)... | simp only [Multiset.mem_map, Multiset.mem_range] at hα | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.FieldTheory.KummerExtension | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 23
} | [
{
"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": 429,
"column": 2
} | {
"line": 429,
"column": 51
} | [
{
"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 (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 476,
"column": 4
} | {
"line": 477,
"column": 24
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 270,
"column": 6
} | {
"line": 270,
"column": 26
} | [
{
"pp": "case pos\nG : Type u_1\ninst✝¹ : 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\ninst✝ : DecidablePred FiniteIndex\nD : Subgroup G := ⨅ k ∈ {i ∈ s | (H i).FiniteIndex}, H k\nhD : D.FiniteIndex\nhD_le : ∀ {i : ι}, i ∈ s → (H i).FiniteIndex ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 272,
"column": 6
} | {
"line": 272,
"column": 26
} | [
{
"pp": "case neg\nG : Type u_1\ninst✝¹ : 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\ninst✝ : DecidablePred FiniteIndex\nD : Subgroup G := ⨅ k ∈ {i ∈ s | (H i).FiniteIndex}, H k\nhD : D.FiniteIndex\nhD_le : ∀ {i : ι}, i ∈ s → (H i).FiniteIndex ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 298,
"column": 8
} | {
"line": 298,
"column": 39
} | [
{
"pp": "G : Type u_1\ninst✝¹ : 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\ninst✝ : DecidablePred FiniteIndex\nD : Subgroup G := ⨅ k ∈ {i ∈ s | (H i).FiniteIndex}, H k\nhD : D.FiniteIndex\nhD_le : ∀ {i : ι}, i ∈ s → (H i).FiniteIndex → D ≤ H i\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 299,
"column": 6
} | {
"line": 299,
"column": 77
} | [
{
"pp": "G : Type u_1\ninst✝¹ : 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\ninst✝ : DecidablePred FiniteIndex\nD : Subgroup G := ⨅ k ∈ {i ∈ s | (H i).FiniteIndex}, H k\nhD : D.FiniteIndex\nhD_le : ∀ {i : ι}, i ∈ s → (H i).FiniteIndex → D ≤ H i\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.CosetCover | {
"line": 346,
"column": 2
} | {
"line": 346,
"column": 13
} | [
{
"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",
"usedConstants": [
"Rat.addCommMonoid",
... | | inr hs => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.GroupTheory.CosetCover | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 32
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nι : Type u_3\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : ι → Submodule R M\ns : Finset ι\nhcovers : ⋃ i ∈ s, ↑(p i) = Set.univ\n⊢ ⋃ i ∈ s, 0 +ᵥ ↑(p i).toAddSubgroup = Set.univ",
"usedConstants": [
"Eq.mpr",
"instVAddOfAdd",
"Iff.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 71,
"column": 24
} | {
"line": 71,
"column": 39
} | [
{
"pp": "case h\nK : 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}",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Set.instSingletonSet",
"id",
"ConjRootClass",
"Field.toSemifield",
... | mk_eq_zero_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 30
} | [
{
"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",
"usedConstants": [
"Exists",
"Distrib.toAdd",
"ConjRootClass",
"Field.toSemifield",
"inst... | 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIntegral",
"congrArg",
"Field.toDivisionRing",
"Co... | 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIntegral",
"congrArg",
"Field.toDivisionRing",
"Co... | 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
} | [
{
"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✝",
"usedConstants": [
"Eq.mpr",
"Algebra.IsIntegral.isIntegral",
"IsDomain",
"congrArg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.TensorProduct.Subalgebra | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 80
} | [
{
"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... | 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.RingTheory.LinearDisjoint | {
"line": 360,
"column": 32
} | {
"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
} | [
{
"pp": "case h.h\nR : 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.linearCombina... | 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.RingTheory.LinearDisjoint | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 42
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 59
} | [
{
"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✝... | refine Subalgebra.LinearDisjoint.of_le_right_of_flat H ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 28
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B : IntermediateField F E\nH : A.LinearDisjoint ↥B\n⊢ finrank F ↥(A ⊔ B) = finrank F ↥A * finrank F ↥B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 37
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 593,
"column": 2
} | {
"line": 593,
"column": 37
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.LinearDisjoint | {
"line": 709,
"column": 2
} | {
"line": 709,
"column": 28
} | [
{
"pp": "R : Type u\nS : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nA B : Subalgebra R S\nH : A.LinearDisjoint B\ninst✝¹ : Free R ↥A\ninst✝ : Free R ↥B\n⊢ finrank R ↥(A ⊔ B) = finrank R ↥A * finrank R ↥B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 78,
"column": 14
} | {
"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": 749,
"column": 2
} | {
"line": 749,
"column": 53
} | [
{
"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 = ⊤",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.LinearDisjoint | {
"line": 759,
"column": 2
} | {
"line": 759,
"column": 53
} | [
{
"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 = ⊤",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 48
} | [
{
"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\ninst✝¹ : IsPurelyInseparable F E\nS : IntermediateField F K\ninst✝ : Algebra.IsSeparable F ↥S\nι : Set ↥S\nb : Module... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 37
} | [
{
"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",
"usedConstants": []
}
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 37
} | [
{
"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",
"usedConstants": []
}
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | [
{
"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",
"usedConstants": [
... | 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
} | [
{
"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",
"usedConstants": [
... | 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
} | [
{
"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",
"usedConstants": [
... | 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": 210,
"column": 2
} | {
"line": 210,
"column": 49
} | [
{
"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✝ : Algebra.IsAlgebraic F E\n⊢ finInsepDegree F E * finInsepDegree E K = finInsepDegree F K",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 209,
"column": 68
} | {
"line": 211,
"column": 87
} | [
{
"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✝ : Algebra.IsAlgebraic F E\n⊢ finInsepDegree F E * finInsepDegree E K = finInsepDegree F K",
"usedConstants"... | by
simpa only [map_mul, Cardinal.toNat_lift] using
congr(Cardinal.toNat $(lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K)) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 226,
"column": 2
} | {
"line": 228,
"column": 50
} | [
{
"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 ↥... | 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.RatFunc.IntermediateField | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 27
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 45
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.IntermediateField | {
"line": 112,
"column": 57
} | {
"line": 112,
"column": 79
} | [
{
"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",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 276,
"column": 53
} | {
"line": 276,
"column": 74
} | [
{
"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... | ← adjoin.finrank hi', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 71
} | [
{
"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)",
"usedConstants": [
"Iff.mpr",
... | 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.PurelyInseparable.PerfectClosure | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 34
} | [
{
"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",
"usedCo... | letI := (inclusion hi).toAlgebra | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLetI___1 | Lean.Parser.Tactic.tacticLetI__ |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 249,
"column": 2
} | {
"line": 249,
"column": 79
} | [
{
"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 ↥... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 279,
"column": 2
} | {
"line": 279,
"column": 13
} | [
{
"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⟯",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 285,
"column": 2
} | {
"line": 285,
"column": 13
} | [
{
"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⟯",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 340,
"column": 50
} | {
"line": 340,
"column": 88
} | [
{
"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 (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B : Subfield E\nh : A ≤ B\n⊢ A.relfinrank B * finrank (↥B) E = finrank (↥A) E",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 129,
"column": 4
} | {
"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",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subfield.toAlgebra",
"Semiring.toM... | IntermediateField.topEquiv.toLinearEquiv.rank_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 395,
"column": 4
} | {
"line": 395,
"column": 15
} | [
{
"pp": "case haeval\nF : 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\nn : ℕ\na : E\nhsep : IsSeparable F a\nhai : IsIntegral F a\nhapi : IsIntegral F ((iterateFrobenius E q n) a)\n⊢ (Polynomial.aeval (a ^ q ^ n)) (Polynomial.map (it... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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