Mathlib Map

Theorems · Definition · group theory

Submonoid.invOrderIso

{G : Type u_2} → [inst : Group G] → Submonoid G ≃o Submonoid G

Pointwise inversion of 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
Group
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Submonoid.coe_invOrderIso_apply · cited by 0Submonoid.coe_invOrderIso…Submonoid.coe_invOrderIso_symm_apply · cited by 0Submonoid.coe_invOrderIso…Submonoid.inv_sup · cited by 0Submonoid.inv_supSubmonoid.inv_iInf · cited by 0Submonoid.inv_iInfSubmonoid.inv_iSup · cited by 0Submonoid.inv_iSupEquiv · cited by 8337EquivGroup · cited by 6238GroupSubmonoid · cited by 3086SubmonoidOrderIso · cited by 874OrderIsoEquiv.inv · cited by 23Equiv.invSubmonoid.inv_le_inv · cited by 0Submonoid.inv_le_invSubmonoid.invOrderIsoCITED 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.