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Theorems · Definition · group theory

Subsemigroup.opEquiv

{M : Type u_2} → [inst : Mul M] → Subsemigroup M ≃o Subsemigroup Mᵐᵒᵖ

A subsemigroup H of M determines a subsemigroup H.op of the opposite semigroup Mᵐᵒᵖ.

Defined in
Mathlib.Algebra.Group.Subsemigroup.MulOpposite
Cited by
18 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
Mul
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Around this declaration

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

Subsemigroup.unop_injective · cited by 2Subsemigroup.unop_injecti…Subsemigroup.op_injective · cited by 2Subsemigroup.op_injectiveSubsemigroup.op_bot · cited by 1Subsemigroup.op_botSubsemigroup.op_inj · cited by 1Subsemigroup.op_injSubsemigroup.op_sInf · cited by 1Subsemigroup.op_sInfSubsemigroup.unop_bot · cited by 1Subsemigroup.unop_botSubsemigroup.unop_sInf · cited by 0Subsemigroup.unop_sInfSubsemigroup.unop_sSup · cited by 0Subsemigroup.unop_sSupSubsemigroup.unop_sup · cited by 0Subsemigroup.unop_supSubsemigroup.opEquiv_apply · cited by 0Subsemigroup.opEquiv_applySubsemigroup.opEquiv_symm_apply · cited by 0Subsemigroup.opEquiv_symm…Subsemigroup.op_iInf · cited by 0Subsemigroup.op_iInfSubsemigroup.op_iSup · cited by 0Subsemigroup.op_iSupSubsemigroup.op_sSup · cited by 0Subsemigroup.op_sSupSubsemigroup.op_sup · cited by 0Subsemigroup.op_supMulOpposite · cited by 1135MulOppositeOrderIso · cited by 874OrderIsoSubsemigroup · cited by 323SubsemigroupSubsemigroup.op · cited by 28Subsemigroup.opSubsemigroup.unop · cited by 25Subsemigroup.unopSubsemigroup.op_unop · cited by 1Subsemigroup.op_unopSubsemigroup.unop_op · cited by 0Subsemigroup.unop_opSubsemigroup.op_le_op_iff · cited by 0Subsemigroup.op_le_op_iffSubsemigroup.opEquivCITED BYCITES

Cites8

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

Cited by18

Results whose statement or proof uses this declaration.