Theorems · Theorem · ring theory
Polynomial.coeff_opRingEquiv
∀ {R : Type u_1} [inst : Semiring R] (p : (Polynomial R)ᵐᵒᵖ) (n : ℕ),
((Polynomial.opRingEquiv R) p).coeff n = MulOpposite.op ((MulOpposite.unop p).coeff n)- Defined in
- Mathlib.RingTheory.Polynomial.Opposites
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 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.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- RingEquivstatement · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- Polynomial.coeffstatement · cited by 1,045
- RingEquiv.symmproof · cited by 567
- AddEquiv.symmproof · cited by 530
- MulOpposite.opstatement and proof · cited by 520
- AddOppositeproof · cited by 452
- AddMonoidAlgebra.coeffproof · cited by 365
- MulOpposite.unopstatement and proof · cited by 268
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.support_opRingEquivproof · cited by 1
- Polynomial.leadingCoeff_opRingEquivproof · cited by 0