Theorems · Theorem · field theory
Polynomial.degree_smul_of_isRightRegular_leadingCoeff
∀ {R : Type u} {a : R} [inst : Semiring R] {p : Polynomial R},
a ≠ 0 → IsRightRegular p.leadingCoeff → (a • p).degree = p.degree- Cited by
- 2 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.
Cites15
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
- le_antisymmproof · cited by 2,068
- WithBotstatement · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- smul_eq_mulproof · cited by 357
- IsRightRegularstatement and proof · cited by 93
- Iff.neproof · cited by 52
- Polynomial.coeff_smulproof · cited by 31
- Polynomial.coeff_natDegreeproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- Polynomial.Sequence.linearIndependentproof · cited by 1