Theorems · Theorem · field theory
Polynomial.Monic.degree_mul
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, q.Monic → (p * q).degree = p.degree + q.degree- Cited by
- 7 results in Mathlib
- Foundations
- Depth 90 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.
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
- mul_oneproof · cited by 3,885
- MulZeroClass.zero_mulproof · cited by 1,625
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.leadingCoeffproof · cited by 101
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.degree_mul'proof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.degree_mul_Xproof · cited by 4
- Polynomial.div_wf_lemmaproof · cited by 3
- Polynomial.Monic.mul_left_ne_zeroproof · cited by 2
- Polynomial.Monic.degree_mul_commproof · cited by 2
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- Polynomial.Monic.mul_right_ne_zeroproof · cited by 1
- Polynomial.degree_mul_X_powproof · cited by 0