Theorems · Theorem · field theory
Polynomial.natDegree_add_coeff_mul
∀ {R : Type u} [inst : Semiring R] (f g : Polynomial R),
(f * g).coeff (f.natDegree + g.natDegree) = f.coeff f.natDegree * g.coeff g.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites6
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
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.coeff_mul_degree_add_degreeproof · cited by 5
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