Theorems · Theorem · field theory
Polynomial.ne_zero_of_degree_ge_degree
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p.degree ≤ q.degree → p ≠ 0 → q ≠ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- lt_of_lt_of_leproof · cited by 438
- bot_lt_iff_ne_botproof · cited by 57
- Polynomial.degree_eq_botproof · cited by 34
- Polynomial.ne_zero_of_degree_gtproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.isBigO_atTop_of_degree_leproof · cited by 2
- Polynomial.isLittleO_atTop_of_degree_ltproof · cited by 1