Theorems · Theorem · ring theory
Polynomial.opRingEquiv_symm_monomial
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (r : Rᵐᵒᵖ),
(Polynomial.opRingEquiv R).symm ((Polynomial.monomial n) r) =
MulOpposite.op ((Polynomial.monomial n) (MulOpposite.unop r))- Defined in
- Mathlib.RingTheory.Polynomial.Opposites
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 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.
Cites15
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- RingEquivstatement · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- RingEquiv.symmstatement and proof · cited by 567
- MulOpposite.opstatement and proof · cited by 520
- MulOpposite.unopstatement and proof · cited by 268
- Polynomial.monomialstatement and proof · cited by 256
- RingEquiv.apply_symm_applyproof · cited by 53
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.opRingEquiv_symm_C_mul_X_powproof · cited by 0
- Polynomial.opRingEquiv_symm_Xproof · cited by 0
- Polynomial.opRingEquiv_symm_Cproof · cited by 0