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Theorems · Definition · group theory

AddSubmonoid.negOrderIso

{G : Type u_2} → [inst : AddGroup G] → AddSubmonoid G ≃o AddSubmonoid G

Pointwise negation of additive submonoids as an order isomorphism

Defined in
Mathlib.Algebra.Group.Submonoid.Pointwise
Cited by
5 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

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

AddSubmonoid.neg_iInf · cited by 0AddSubmonoid.neg_iInfAddSubmonoid.neg_iSup · cited by 0AddSubmonoid.neg_iSupAddSubmonoid.coe_negOrderIso_apply · cited by 0AddSubmonoid.coe_negOrder…AddSubmonoid.coe_negOrderIso_symm_apply · cited by 0AddSubmonoid.coe_negOrder…AddSubmonoid.neg_sup · cited by 0AddSubmonoid.neg_supEquiv · cited by 8337EquivAddGroup · cited by 4410AddGroupAddSubmonoid · cited by 1178AddSubmonoidOrderIso · cited by 874OrderIsoEquiv.neg · cited by 53Equiv.negAddSubmonoid.neg_le_neg · cited by 0AddSubmonoid.neg_le_negAddSubmonoid.negOrderIsoCITED BYCITES

Cites6

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

Cited by5

Results whose statement or proof uses this declaration.