Theorems · Theorem · field theory
Polynomial.Monic.natDegree_pow
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → ∀ (n : ℕ), (p ^ n).natDegree = n * p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Polynomial.Monicstatement and proof · cited by 461
- pow_succproof · cited by 374
- Polynomial.natDegree_oneproof · cited by 43
- Polynomial.Monic.powproof · cited by 11
- Polynomial.Monic.natDegree_mulproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Monic.geom_sumproof · cited by 2
- Polynomial.quo_mul_prod_pow_add_sum_rem_mul_prod_pow_uniqueproof · cited by 1
- Polynomial.natDegree_pow_X_add_Cproof · cited by 1