Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le
∀ (R : Type u) (S₁ : Type v) [inst : CommSemiring R] (p : MvPolynomial (Option S₁) R), ∀ i ≤ p.totalDegree, (((MvPolynomial.optionEquivLeft R S₁) p).coeff i).totalDegree + i ≤ p.totalDegree
- Defined in
- Mathlib.Algebra.MvPolynomial.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 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.
Cites34
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
- Polynomialstatement · cited by 5,681
- Finsuppstatement and proof · cited by 5,255
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- MvPolynomialstatement and proof · cited by 2,140
- AlgEquivstatement · cited by 1,681
- add_commproof · cited by 1,535
- Polynomial.coeffstatement and proof · cited by 1,045
- le_transproof · cited by 985
- Finsupp.singleproof · cited by 943
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zeroproof · cited by 2