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Theorems · Definition · group theory

MulOpposite.opMulEquiv

{M : Type u_1} → [inst : CommMonoid M] → M ≃* Mᵐᵒᵖ

MulOpposite.op on a commutative monoid is an isomorphism.

Defined in
Mathlib.Algebra.Group.Equiv.Opposite
Cited by
4 results in Mathlib
Foundations
Depth 22 from the axioms · uses Quot.sound
Assumes
CommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MulOpposite.opMulEquiv_apply · cited by 0MulOpposite.opMulEquiv_ap…MulOpposite.opMulEquiv_symm_apply · cited by 0MulOpposite.opMulEquiv_sy…MulOpposite.coe_opMulEquiv · cited by 0MulOpposite.coe_opMulEquivMulOpposite.coe_symm_opMulEquiv · cited by 0MulOpposite.coe_symm_opMu…Equiv · cited by 8337EquivCommMonoid · cited by 2264CommMonoidMulEquiv · cited by 1142MulEquivMulOpposite · cited by 1135MulOppositeMulOpposite.opEquiv · cited by 24MulOpposite.opEquivMulOpposite.opMulEquivCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.