Mathlib Map

Theorems · Definition · group theory

AddSubsemigroup.op

{M : Type u_2} → [inst : Add M] → AddSubsemigroup M → AddSubsemigroup Mᵃᵒᵖ

Pull an additive subsemigroup back to an opposite subsemigroup along AddOpposite.unop

Defined in
Mathlib.Algebra.Group.Subsemigroup.MulOpposite
Cited by
28 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
Add
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubsemigroup.opEquiv · cited by 18AddSubsemigroup.opEquivAddSubsemigroup.equivOp · cited by 2AddSubsemigroup.equivOpAddSubsemigroup.op_injective · cited by 2AddSubsemigroup.op_inject…AddSubsemigroup.op_bot · cited by 1AddSubsemigroup.op_botAddSubsemigroup.op_closure · cited by 1AddSubsemigroup.op_closureAddSubsemigroup.op_inj · cited by 1AddSubsemigroup.op_injAddSubsemigroup.op_sInf · cited by 1AddSubsemigroup.op_sInfAddSubsemigroup.op_top · cited by 1AddSubsemigroup.op_topAddSubsemigroup.op_unop · cited by 1AddSubsemigroup.op_unopAddSubsemigroup.equivOp_apply_coe · cited by 0AddSubsemigroup.equivOp_a…AddSubmonoid.op_toSubsemigroup · cited by 0AddSubmonoid.op_toSubsemi…AddSubsemigroup.equivOp_symm_apply_coe · cited by 0AddSubsemigroup.equivOp_s…AddSubsemigroup.mem_op · cited by 0AddSubsemigroup.mem_opAddSubsemigroup.unop_closure · cited by 0AddSubsemigroup.unop_clos…AddSubsemigroup.coe_op · cited by 0AddSubsemigroup.coe_opSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageAddOpposite · cited by 452AddOppositeAddSubsemigroup · cited by 262AddSubsemigroupAddOpposite.unop · cited by 125AddOpposite.unopAddSubsemigroup.opCITED BYCITES

Cites5

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

Cited by30

Results whose statement or proof uses this declaration.