Theorems · Theorem · field theory
Polynomial.Monic.mul_right_ne_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → ∀ {q : Polynomial R}, q ≠ 0 → p * q ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 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.
Cites15
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
- one_mulproof · cited by 2,841
- WithBotproof · cited by 1,498
- LT.lt.ne'proof · cited by 1,417
- Polynomial.degreeproof · cited by 643
- Polynomial.Monicstatement and proof · cited by 461
- not_leproof · cited by 328
- lt_transproof · cited by 165
- Polynomial.degree_eq_botproof · cited by 34
- Polynomial.Monic.degree_mulproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Monic.mul_right_eq_zero_iffproof · cited by 3