Theorems · Theorem · field theory
Polynomial.zero_le_degree_iff
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, 0 ≤ p.degree ↔ p ≠ 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 88 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.
Cites7
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 · cited by 1,498
- Polynomial.degreestatement · cited by 643
- not_ltproof · cited by 306
- Polynomial.degree_eq_botproof · cited by 34
- Nat.WithBot.lt_zero_iffproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.degree_eq_zero_of_isUnitproof · cited by 14
- Polynomial.degree_divX_ltproof · cited by 1
- Polynomial.ne_zero_of_coe_le_degreeproof · cited by 1
- AdjoinRoot.of.injective_of_degree_ne_zeroproof · cited by 1