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Proved that L/K is normal #160

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Oct 10, 2024
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Proved that L/K is normal #160

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74b2366
Proved `normal`
4hma4d Oct 4, 2024
0875b28
Apply suggestions from code review
4hma4d Oct 6, 2024
d25de03
Fixed proof
4hma4d Oct 6, 2024
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17 changes: 15 additions & 2 deletions FLT/MathlibExperiments/FrobeniusRiou.lean
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Expand Up @@ -747,8 +747,21 @@ theorem algebraic {A : Type*} [CommRing A] {B : Type*} [Nontrivial B] [CommRing
rw [eval_map, eval₂_hom, F_eval_eq_zero]
exact algebraMap.coe_zero

theorem normal : Normal K L := by
sorry
include G in
theorem normal [DecidableEq L]: Normal K L := by
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rw [normal_iff]
intro l
obtain ⟨f, hf⟩ := @f_exists G _ _ L _ K _ _ _ l
have hnz: f≠0 := by refine Monic.ne_zero_of_ne ?h.left.h ?h.left.hp; exact zero_ne_one' K; exact hf.1
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constructor
rw [← @isAlgebraic_iff_isIntegral]
unfold IsAlgebraic
use f
constructor
exact hnz
exact hf.2.2.1
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refine Polynomial.splits_of_splits_of_dvd (algebraMap K L) hnz hf.2.2.2 ?_
apply minpoly.dvd; exact hf.2.2.1
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open FiniteDimensional

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