Theorems · Definition · order theory

orderEmbeddingOfInjective

{F : Type u_1} →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : FunLike F α β] →
        [inst_1 : SemilatticeInf α] →
          [inst_2 : SemilatticeInf β] → (f : F) → [InfHomClass F α β] → Function.Injective ⇑f → α ↪o β

We can regard an injective map preserving binary infima as an order embedding.

Defined in

Mathlib.Order.Hom.Lattice

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLikeSemilatticeInfSemilatticeInfInfHomClass