Theorems · Theorem · order theory
InitialSeg.toOrderEmbedding_apply
∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder α] [inst_1 : PartialOrder β] (f : α ≤i β) (x : α),
f.toOrderEmbedding x = f x- Defined in
- Mathlib.Order.InitialSeg
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPartialOrder
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- OrderEmbeddingstatement · cited by 619
- InitialSegstatement and proof · cited by 70
- InitialSeg.toOrderEmbeddingstatement · cited by 8
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