Theorems · Theorem · commutative algebra
MvPolynomial.monomial_dvd_monomial
∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] {r s : R} {i j : σ →₀ ℕ},
(MvPolynomial.monomial i) r ∣ (MvPolynomial.monomial j) s ↔ (s = 0 ∨ i ≤ j) ∧ r ∣ s- Defined in
- Mathlib.Algebra.MvPolynomial.Division
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.monomialstatement and proof · cited by 253
- add_tsub_cancel_of_leproof · cited by 79
- dvd_zeroproof · cited by 63
- MvPolynomial.coeff_monomialproof · cited by 32
- MvPolynomial.monomial_zeroproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.monomial_one_dvd_monomial_oneproof · cited by 1
- MvPolynomial.X_dvd_monomialproof · cited by 0