Theorems · Theorem · field theory
Polynomial.degree_monomial
∀ {R : Type u} {a : R} [inst : Semiring R] (n : ℕ), a ≠ 0 → ((Polynomial.monomial n) a).degree = ↑n- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 99 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.
Cites14
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.degreestatement · cited by 643
- WithBot.someproof · cited by 541
- Polynomial.monomialstatement and proof · cited by 256
- Finset.maxproof · cited by 50
- Nat.cast_withBotproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.degree_X_powproof · cited by 15
- Polynomial.degree_Xproof · cited by 9
- Polynomial.degree_C_mul_X_powproof · cited by 7
- Polynomial.degree_monomial_leproof · cited by 4
- LinearRecurrence.charPoly_degree_eq_orderproof · cited by 1
- Polynomial.monomial_mem_lifts_and_degree_eqproof · cited by 0