Theorems · Theorem · field theory
Polynomial.degree_map_le
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {f : R →+* S} {p : Polynomial R},
(Polynomial.map f p).degree ≤ p.degree- Defined in
- Mathlib.Algebra.Polynomial.Eval.Degree
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- map_zeroproof · cited by 1,614
- le_rflproof · cited by 1,558
- WithBotstatement · cited by 1,498
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.degree_le_iff_coeff_zeroproof · cited by 7
- Polynomial.degree_lt_iff_coeff_zeroproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_map_leproof · cited by 13
- Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroproof · cited by 9
- Polynomial.map_mod_divByMonicproof · cited by 2
- Polynomial.degree_map_ltproof · cited by 1
- Polynomial.SplittingFieldAux.splitsproof · cited by 0
- Polynomial.degree_sum_eq_of_linearIndepOnproof · cited by 0
- Polynomial.card_roots_map_le_degreeproof · cited by 0