Theorems · Theorem · field theory
Polynomial.degree_multiset_prod_of_monic
∀ {R : Type u} [inst : CommSemiring R] (t : Multiset (Polynomial R)) [Nontrivial R],
(∀ f ∈ t, f.Monic) → t.prod.degree = (Multiset.map Polynomial.degree t).sum- Defined in
- Mathlib.Algebra.Polynomial.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Multiset.mapstatement and proof · cited by 876
- Polynomial.degreestatement and proof · cited by 643
- Multiset.prodstatement and proof · cited by 528
- Polynomial.Monicstatement and proof · cited by 461
- Multiset.sumstatement and proof · cited by 388
- Multiset.map_congrproof · cited by 232
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.degree_prod_of_monicproof · cited by 0