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Theorems · Definition · group theory

Subsemigroup.unop

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

Pull an opposite subsemigroup back to a subsemigroup along MulOpposite.op

Defined in
Mathlib.Algebra.Group.Subsemigroup.MulOpposite
Cited by
25 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

Subsemigroup.opEquiv · cited by 18Subsemigroup.opEquivSubsemigroup.unop_injective · cited by 2Subsemigroup.unop_injecti…Subsemigroup.unop_top · cited by 1Subsemigroup.unop_topSubsemigroup.unop_bot · cited by 1Subsemigroup.unop_botSubsemigroup.op_sInf · cited by 1Subsemigroup.op_sInfSubsemigroup.op_unop · cited by 1Subsemigroup.op_unopSubsemigroup.coe_unop · cited by 1Subsemigroup.coe_unopSubsemigroup.unop_le_unop_iff · cited by 0Subsemigroup.unop_le_unop…Subsemigroup.unop_op · cited by 0Subsemigroup.unop_opSubsemigroup.unop_sInf · cited by 0Subsemigroup.unop_sInfSubsemigroup.unop_sSup · cited by 0Subsemigroup.unop_sSupSubsemigroup.unop_sup · cited by 0Subsemigroup.unop_supSubsemigroup.opEquiv_symm_apply · cited by 0Subsemigroup.opEquiv_symm…Subgroup.unop_toSubsemigroup · cited by 0Subgroup.unop_toSubsemigr…Subsemigroup.op_le_iff · cited by 0Subsemigroup.op_le_iffSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageMulOpposite · cited by 1135MulOppositeMulOpposite.op · cited by 520MulOpposite.opSubsemigroup · cited by 323SubsemigroupSubsemigroup.unopCITED BYCITES

Cites5

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Cited by26

Results whose statement or proof uses this declaration.