Theorems · Definition · order theory
OrderMonoidHom.id
(α : Type u_2) → [inst : Preorder α] → [inst_1 : MulOneClass α] → α →*o α
The identity map as an ordered monoid homomorphism.
- Defined in
- Mathlib.Algebra.Order.Hom.Monoid
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PreorderMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MonoidHomproof · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- OrderHomproof · cited by 934
- MonoidHom.idproof · cited by 323
- OrderMonoidHomstatement · cited by 67
- OrderHom.idproof · cited by 37
- OrderHom.monotone'proof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- OrderMonoidHom.fst_comp_inlstatement · cited by 0
- OrderMonoidHom.fstₗ_comp_inlₗstatement · cited by 0
- OrderMonoidHom.comp_idstatement · cited by 0
- OrderMonoidHom.id_compstatement · cited by 0
- OrderMonoidHom.snd_comp_inrstatement · cited by 0
- OrderMonoidHom.coe_idstatement · cited by 0