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feat(field_theory/splitting_field): add splits_X theorem (#5343)
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This is a handy result and isn't definitionally a special case of splits_X_sub_C
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tb65536 committed Dec 14, 2020
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Expand Up @@ -101,6 +101,9 @@ splits_of_splits_of_dvd i one_ne_zero (splits_one _) $ is_unit_iff_dvd_one.1 hu
theorem splits_X_sub_C {x : α} : (X - C x).splits i :=
splits_of_degree_eq_one _ $ degree_X_sub_C x

theorem splits_X : X.splits i :=
splits_of_degree_eq_one _ $ degree_X

theorem splits_id_iff_splits {f : polynomial α} :
(f.map i).splits (ring_hom.id β) ↔ f.splits i :=
by rw [splits_map_iff, ring_hom.id_comp]
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