Theorems · Theorem · field theory
Polynomial.degree_le_mul_left
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {q : Polynomial R} (p : Polynomial R),
q ≠ 0 → p.degree ≤ (p * q).degree- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
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.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Bot.botproof · cited by 4,720
- MulZeroClass.zero_mulproof · cited by 1,625
- WithBotstatement and proof · cited by 1,498
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- WithBot.coe_le_coeproof · cited by 76
- Polynomial.degree_eq_natDegreeproof · cited by 69
- Polynomial.degree_mulproof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.degree_le_of_dvdproof · cited by 5
- Polynomial.degree_add_divproof · cited by 0