Theorems · Theorem · field theory
IsRealClosed.exists_isRoot_of_odd_natDegree
∀ {R : Type u_1} {inst : Field R} [self : IsRealClosed R] {f : Polynomial R}, Odd f.natDegree → ∃ x, f.IsRoot x- Defined in
- Mathlib.FieldTheory.IsRealClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsRealClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Oddstatement · cited by 364
- Polynomial.IsRootstatement · cited by 152
- IsRealClosedstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- IsRealClosed.exists_eq_pow_of_oddproof · cited by 2