Theorems · Theorem · field theory
Polynomial.degree_map_lt
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {f : R →+* S} {p : Polynomial R},
f p.leadingCoeff = 0 → p ≠ 0 → (Polynomial.map f p).degree < p.degree- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Bot.botproof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- LE.le.lt_of_neproof · cited by 116
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_map_ltproof · cited by 1