Theorems · Theorem · order theory
RelEmbedding.toOrderHom_injective
∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β]
(f : (fun x1 x2 => x1 < x2) ↪r fun x1 x2 => x1 < x2), Function.Injective ⇑f.toRelHom.toOrderHom- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPreorder
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- PartialOrderstatement and proof · cited by 6,410
- OrderHomstatement · cited by 934
- RelEmbeddingstatement and proof · cited by 281
- RelEmbedding.injectiveproof · cited by 41
- RelEmbedding.toRelHomstatement and proof · cited by 15
- RelHom.toOrderHomstatement and proof · cited by 3
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