Theorems · Theorem · field theory
Polynomial.natTrailingDegree_le_natDegree
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R), p.natTrailingDegree ≤ p.natDegree- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 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.
Cites9
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
- le_reflproof · cited by 2,061
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.natTrailingDegreestatement and proof · cited by 87
- Polynomial.natDegree_zeroproof · cited by 24
- Polynomial.le_natDegree_of_ne_zeroproof · cited by 14
- Polynomial.trailingCoeff_eq_zeroproof · cited by 5
- Polynomial.natTrailingDegree_zeroproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.reverse_leadingCoeffproof · cited by 5
- Polynomial.mirror_natDegreeproof · cited by 4
- Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegreeproof · cited by 1
- Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegreeproof · cited by 1