Theorems · Theorem · ring theory
AddMonoidAlgebra.opRingEquiv_single
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : Add M] (r : R) (x : M),
AddMonoidAlgebra.opRingEquiv (MulOpposite.op (AddMonoidAlgebra.single x r)) =
AddMonoidAlgebra.single (AddOpposite.op x) (MulOpposite.op r)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Opposite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites22
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 · cited by 1,135
- Finsupp.singleproof · cited by 943
- AddMonoidAlgebrastatement · cited by 649
- MulOpposite.opstatement and proof · cited by 520
- AddOppositestatement and proof · cited by 452
- Finsupp.extproof · cited by 399
- AddMonoidAlgebra.coeffproof · cited by 365
- AddMonoidAlgebra.singlestatement and proof · cited by 250
- AddOpposite.opstatement and proof · cited by 192
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