Theorems · Theorem · field theory
Polynomial.leadingCoeff_mul_monic
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, q.Monic → (p * q).leadingCoeff = p.leadingCoeff- Cited by
- 6 results in Mathlib
- Foundations
- Depth 92 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.
Cites10
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
- mul_oneproof · cited by 3,885
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.leadingCoeffproof · cited by 101
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.leadingCoeff_mul'proof · cited by 11
- Polynomial.leadingCoeff_zeroproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.splits_iff_exists_multiset'proof · cited by 4
- minpoly.unique'proof · cited by 4
- IsLocalization.exists_isIntegral_smul_of_isIntegral_mapproof · cited by 2
- Polynomial.leadingCoeff_mul_Xproof · cited by 2
- Polynomial.leadingCoeff_mul_X_powproof · cited by 2
- Polynomial.Monic.of_mul_monic_rightproof · cited by 1