Theorems · Theorem · field theory
Polynomial.natDegree_mul_X
∀ {R : Type u} [inst : Semiring R] [Nontrivial R] {p : Polynomial R},
p ≠ 0 → (p * Polynomial.X).natDegree = p.natDegree + 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNontrivial
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
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement · cited by 1,639
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monic.leadingCoeffproof · cited by 101
- Polynomial.natDegree_Xproof · cited by 43
- Polynomial.natDegree_mul'proof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.reverse_mul_Xproof · cited by 3
- LaurentPolynomial.toLaurent_reverseproof · cited by 1
- Polynomial.natDegree_X_mulproof · cited by 0