Theorems · Theorem · field theory
Field.isAlgebraic_of_adjoin_eq_adjoin
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {α : E} {m n : ℕ},
m ≠ n → F⟮α ^ m⟯ = F⟮α ^ n⟯ → IsAlgebraic F α- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- Polynomial.natDegreeproof · cited by 1,105
Cited by1
Results whose statement or proof uses this declaration.
- Field.isAlgebraic_of_finite_intermediateFieldproof · cited by 2