Theorems · Theorem · ring theory
AddMonoidAlgebra.opRingEquiv_symm_apply
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : Add M] (a : AddMonoidAlgebra Rᵐᵒᵖ Mᵃᵒᵖ),
AddMonoidAlgebra.opRingEquiv.symm a =
MulOpposite.op
((AddMonoidAlgebra.mapDomainAddEquiv R AddOpposite.opEquiv.symm)
((AddMonoidAlgebra.mapAddEquiv Mᵃᵒᵖ MulOpposite.opAddEquiv.symm) 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.
Cites16
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
- Equiv.symmstatement · cited by 3,681
- RingEquivstatement · cited by 1,147
- MulOppositestatement and proof · cited by 1,135
- AddEquivstatement · cited by 1,087
- AddMonoidAlgebrastatement and proof · cited by 649
- RingEquiv.symmstatement and proof · cited by 567
- AddEquiv.symmstatement · cited by 530
- MulOpposite.opstatement · cited by 520
- AddOppositestatement and proof · cited by 452
- MulOpposite.opAddEquivstatement · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.opRingEquiv_symm_singleproof · cited by 0