Mathlib Map

Theorems · Definition · order theory

OrderHom.id

{α : Type u_2} → [inst : Preorder α] → α →o α

The identity function as bundled monotone function.

Defined in
Mathlib.Order.Hom.Basic
Cited by
37 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderHom.id_coe · cited by 14OrderHom.id_coeOrderRingHom.id · cited by 11OrderRingHom.idBoundedOrderHom.id · cited by 8BoundedOrderHom.idOrderAddMonoidHom.id · cited by 7OrderAddMonoidHom.idOrderMonoidHom.id · cited by 6OrderMonoidHom.idPseudoEpimorphism.id · cited by 6PseudoEpimorphism.idContinuousOrderHom.id · cited by 5ContinuousOrderHom.idOrderMonoidWithZeroHom.id · cited by 5OrderMonoidWithZeroHom.idPositiveLinearMap.id · cited by 5PositiveLinearMap.idAugmentedSimplexCategory.inl'_eval · cited by 3AugmentedSimplexCategory.…OmegaCompletePartialOrder.ContinuousHom.id · cited by 3ContinuousHom.idOrderIso.ofHomInv · cited by 3OrderIso.ofHomInvOrderIso.ofHomInv_apply · cited by 3OrderIso.ofHomInv_applyClosureOperator.id · cited by 2ClosureOperator.idSSet.boundary_lt_top · cited by 2SSet.boundary_lt_topPreorder · cited by 7952PreorderOrderHom · cited by 934OrderHommonotone_id · cited by 31monotone_idOrderHom.idCITED BYCITES

Cites3

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

Cited by51

Results whose statement or proof uses this declaration.