Theorems · Theorem · field theory
Polynomial.IsMonicOfDegree.of_mul_left
∀ {R : Type u_1} [inst : Semiring R] {p q : Polynomial R} {m n : ℕ},
p.IsMonicOfDegree m → (p * q).IsMonicOfDegree (m + n) → q.IsMonicOfDegree n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 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.
Cites16
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
- one_mulproof · cited by 2,841
- Nontrivialproof · cited by 2,416
- Polynomial.natDegreeproof · cited by 1,105
- one_ne_zeroproof · cited by 885
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicproof · cited by 461
- subsingleton_or_nontrivialproof · cited by 161
- Polynomial.Monic.leadingCoeffproof · cited by 101
- Polynomial.IsMonicOfDegreestatement and proof · cited by 39
- Polynomial.natDegree_mul'proof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_mul_isMonicOfDegreeproof · cited by 0
- Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_two_mul_isMonicOfDegreeproof · cited by 0