Theorems · Theorem · field theory
Polynomial.natDegree_one
∀ {R : Type u} [inst : Semiring R], Polynomial.natDegree 1 = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 104 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.
Cites4
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 · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.natDegree_Cproof · cited by 59
Cited by43
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_powproof · cited by 11
- Polynomial.Monic.natDegree_eq_zeroproof · cited by 10
- Polynomial.natDegree_pow_leproof · cited by 6
- Polynomial.lifts_and_natDegree_eq_and_monicproof · cited by 6
- Polynomial.Monic.eq_one_of_isUnitproof · cited by 6
- Polynomial.natDegree_eq_zero_of_isUnitproof · cited by 5
- Polynomial.one_scaleRootsproof · cited by 4
- Polynomial.natDegree_pow'proof · cited by 4
- Polynomial.Monic.natDegree_powproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.natDegree_multiset_prod'proof · cited by 3
- RatFunc.eq_C_iffproof · cited by 2