Theorems · Theorem · field theory
Polynomial.le_natTrailingDegree_mul
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R},
p * q ≠ 0 → p.natTrailingDegree + q.natTrailingDegree ≤ (p * q).natTrailingDegree- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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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
- ENatproof · cited by 4,985
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.natTrailingDegreestatement and proof · cited by 87
- Polynomial.trailingDegreeproof · cited by 39
- ENat.natCast_le_natCastproof · cited by 19
- ENat.natCast_addproof · cited by 17
- Polynomial.trailingDegree_eq_natTrailingDegreeproof · cited by 8
- Polynomial.le_trailingDegree_mulproof · cited by 2
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