Theorems · Theorem · order theory
PrincipalSeg.orderIsoIio_apply_coe
∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder α] [inst_1 : PartialOrder β] (f : α <i β) (a : α),
↑(f.orderIsoIio a) = f.toRelEmbedding a- Defined in
- Mathlib.Order.Interval.Set.InitialSeg
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPartialOrder
Around this declaration
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Cites11
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
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- Set.Iiostatement · cited by 1,166
- RelIsostatement · cited by 456
- RelEmbeddingstatement · cited by 281
- PrincipalSeg.toRelEmbeddingstatement · cited by 129
- PrincipalSegstatement and proof · cited by 73
- PrincipalSeg.topstatement · cited by 41
- PrincipalSeg.orderIsoIiostatement and proof · cited by 2
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