Theorems · Theorem · commutative algebra
MonomialOrder.degree_mul_le
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] {f g : MvPolynomial σ R},
m.toSyn (m.degree (f * g)) ≤ m.toSyn (m.degree f + m.degree g)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 87 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.
Cites26
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
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_reflproof · cited by 2,061
- MulZeroClass.zero_mulproof · cited by 1,625
- AddEquivstatement · cited by 1,087
- map_addproof · cited by 964
- add_le_addproof · cited by 666
- MvPolynomial.coeffproof · cited by 315
- not_ltproof · cited by 306
Cited by10
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zeroproof · cited by 5
- MonomialOrder.degree_prod_leproof · cited by 4
- MonomialOrder.divproof · cited by 2
- MonomialOrder.degree_pow_leproof · cited by 2
- MonomialOrder.toSyn_degree_mul_leproof · cited by 1
- MonomialOrder.degree_reduce_ltproof · cited by 1
- MonomialOrder.degree_sPolynomial_leproof · cited by 1
- MonomialOrder.degree_smul_leproof · cited by 1
- MonomialOrder.degree_lt_of_left_ne_zero_of_degree_mul_ltproof · cited by 1
- MonomialOrder.withBotDegree_mul_leproof · cited by 0