Theorems · Theorem · field theory
Polynomial.natTrailingDegree_mul_X_pow
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R},
p ≠ 0 → ∀ (n : ℕ), (p * Polynomial.X ^ n).natTrailingDegree = p.natTrailingDegree + n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 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.
Cites18
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_antisymmproof · cited by 2,068
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.coeffproof · cited by 1,045
- Polynomial.supportproof · cited by 237
- Polynomial.natTrailingDegreestatement and proof · cited by 87
- by_contraproof · cited by 60
- Polynomial.mem_support_iffproof · cited by 30
- Polynomial.natTrailingDegree_le_of_ne_zeroproof · cited by 10
- Polynomial.coeff_mul_X_powproof · cited by 9
- Polynomial.nonempty_support_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.mirror_natTrailingDegreeproof · cited by 5