Theorems · Theorem · field theory
Polynomial.natDegree_iterate_comp
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} [NoZeroDivisors R] (k : ℕ),
(p.comp^[k] q).natDegree = p.natDegree ^ k * q.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Nat.iteratestatement and proof · cited by 740
- NoZeroDivisorsstatement and proof · cited by 545
- pow_succ'proof · cited by 228
- Polynomial.compstatement and proof · cited by 193
- Function.iterate_succ_apply'proof · cited by 72
- Polynomial.natDegree_compproof · cited by 13
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