Theorems · Theorem · field theory
Polynomial.natTrailingDegree_mul
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} [NoZeroDivisors R],
p ≠ 0 → q ≠ 0 → (p * q).natTrailingDegree = p.natTrailingDegree + q.natTrailingDegree- Cited by
- 4 results in Mathlib
- Foundations
- Depth 93 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.
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
- NoZeroDivisorsstatement and proof · cited by 545
- mul_ne_zeroproof · cited by 178
- Polynomial.natTrailingDegreestatement · cited by 87
- Polynomial.trailingCoeff_eq_zeroproof · cited by 5
- Polynomial.natTrailingDegree_mul'proof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.natTrailingDegree_mul_mirrorproof · cited by 2
- LinearMap.finrank_maxGenEigenspace_zero_eqproof · cited by 2
- Polynomial.mirror_mul_of_domainproof · cited by 2
- Polynomial.trailingDegree_mulproof · cited by 0