Mathlib Map

Theorems · Theorem · field theory

Polynomial.leadingCoeff_dvd_leadingCoeff

∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {a p : Polynomial R}, a ∣ p → a.leadingCoeff ∣ p.leadingCoeff
Defined in
Mathlib.Algebra.Polynomial.Degree.Operations
Cited by
1 results in Mathlib
Foundations
Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringNoZeroDivisors
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.Monic.isUnit_leadingCoeff_of_dvd · cited by 1Monic.isUnit_leadingCoeff…Semiring · cited by 13802SemiringPolynomial · cited by 5681PolynomialNoZeroDivisors · cited by 545NoZeroDivisorsPolynomial.leadingCoeff · cited by 498Polynomial.leadingCoeffmap_dvd · cited by 44map_dvdPolynomial.leadingCoeffHom · cited by 6Polynomial.leadingCoeffHomPolynomial.leadingCoeff_dvd_l…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.