Theorems · Theorem · commutative algebra
MonomialOrder.coeff_sPolynomial_sup_eq_zero
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommRing R] (f g : MvPolynomial σ R),
MvPolynomial.coeff (m.degree f ⊔ m.degree g) (m.sPolynomial f g) = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Nat.cast_zeroproof · cited by 1,870
- MvPolynomial.coeffstatement and proof · cited by 315
- le_sup_leftproof · cited by 265
- MvPolynomial.monomialproof · cited by 253
- le_sup_rightproof · cited by 242
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement and proof · cited by 132
- tsub_add_cancel_of_leproof · cited by 112
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_sPolynomialproof · cited by 1