Theorems · Theorem · ring theory
MonoidAlgebra.opRingEquiv_apply
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : Mul M] (a : (MonoidAlgebra R M)ᵐᵒᵖ),
MonoidAlgebra.opRingEquiv a =
(MonoidAlgebra.mapAddEquiv Mᵐᵒᵖ MulOpposite.opAddEquiv)
((MonoidAlgebra.mapDomainAddEquiv R MulOpposite.opEquiv) (MulOpposite.unop a))- Defined in
- Mathlib.Algebra.MonoidAlgebra.Opposite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingEquivstatement · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- AddEquivstatement · cited by 1,087
- MonoidAlgebrastatement and proof · cited by 590
- MulOpposite.unopstatement · cited by 268
- MulOpposite.opAddEquivstatement · cited by 25
- MulOpposite.opEquivstatement · cited by 24
- MonoidAlgebra.mapAddEquivstatement · cited by 12
- MonoidAlgebra.mapDomainAddEquivstatement · cited by 8
- MonoidAlgebra.opRingEquivstatement and proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MonoidAlgebra.opRingEquiv_singleproof · cited by 0