Theorems · Theorem · field theory
Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : CommRing S] [IsDomain S] (φ : R →+* S) {f : Polynomial R},
IsUnit f.leadingCoeff → IsUnit (Polynomial.map φ f) → IsUnit f- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Monoidproof · cited by 3,887
- IsDomainstatement and proof · cited by 2,196
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Monic.irreducible_of_irreducible_mapproof · cited by 1