Theorems · Theorem · field theory
Polynomial.natDegree_lt_natDegree
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {p : Polynomial R} {q : Polynomial S},
p ≠ 0 → p.degree < q.degree → p.natDegree < q.natDegree- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- Nat.cast_ltproof · cited by 80
- Polynomial.degree_eq_natDegreeproof · cited by 69
- not_lt_botproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- PowerBasis.constr_pow_aevalproof · cited by 4
- Polynomial.natDegree_modByMonic_ltproof · cited by 4
- Polynomial.Monic.not_dvd_of_degree_ltproof · cited by 2
- Polynomial.natDegree_map_ltproof · cited by 1
- Polynomial.isLittleO_cobounded_of_degree_ltproof · cited by 1