Theorems · Theorem · field theory
Polynomial.mirror_mul_of_domain
∀ {R : Type u_1} [inst : Semiring R] (p q : Polynomial R) [NoZeroDivisors R], (p * q).mirror = p.mirror * q.mirror- Defined in
- Mathlib.Algebra.Polynomial.Mirror
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- NoZeroDivisorsstatement and proof · cited by 545
- pow_addproof · cited by 315
- Polynomial.natTrailingDegreeproof · cited by 87
- Polynomial.reverseproof · cited by 38
- Polynomial.mirrorstatement and proof · cited by 32
- Polynomial.X_pow_mulproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.irreducible_of_mirrorproof · cited by 1
- Polynomial.mirror_smulproof · cited by 0