Theorems · Theorem · field theory
Polynomial.Sequence.basis_degree_strictMono
∀ {R : Type u_1} [inst : Ring R] (S : Polynomial.Sequence R) [inst_1 : IsDomain R]
(hCoeff : ∀ (i : ℕ), IsUnit (↑S i).leadingCoeff), StrictMono (Polynomial.degree ∘ ⇑(S.basis hCoeff))Basis elements have strictly monotone degree.
- Defined in
- Mathlib.Algebra.Polynomial.Sequence
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- IsUnitstatement and proof · cited by 1,602
- WithBotstatement · cited by 1,498
- Module.Basisstatement · cited by 1,477
- StrictMonostatement · cited by 706
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.Sequencestatement and proof · cited by 19
- Polynomial.Sequence.elems'statement and proof · cited by 15
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