Theorems · Theorem · field theory
Polynomial.natSepDegree_X_pow_char_pow_sub_C
∀ {F : Type u} [inst : Field F] (q : ℕ) [ExpChar F q] (n : ℕ) (y : F),
(Polynomial.X ^ q ^ n - Polynomial.C y).natSepDegree = 1- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- map_subproof · cited by 565
- ExpCharstatement and proof · cited by 276
- Polynomial.expandproof · cited by 90
- Polynomial.natSepDegreestatement and proof · cited by 53
- Polynomial.expand_Cproof · cited by 12
- Polynomial.expand_Xproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- minpoly.natSepDegree_eq_one_iff_pow_memproof · cited by 4
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.Monic.natSepDegree_eq_one_iffproof · cited by 0