Theorems · Theorem · commutative algebra
MvPolynomial.degrees_add_of_disjoint
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p q : MvPolynomial σ R} [inst_1 : DecidableEq σ],
Disjoint p.degrees q.degrees → (p + q).degrees = p.degrees ∪ q.degrees- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finsuppstatement · cited by 5,255
- Multisetstatement · cited by 2,627
- Disjointstatement and proof · cited by 2,201
- MvPolynomialstatement and proof · cited by 2,140
- LE.le.antisymmproof · cited by 507
- MvPolynomial.degreesstatement and proof · cited by 51
- Multiset.union_leproof · cited by 4
- MvPolynomial.degrees_add_leproof · cited by 2
- MvPolynomial.le_degrees_add_leftproof · cited by 2
- MvPolynomial.le_degrees_add_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.vars_add_of_disjointproof · cited by 2