Theorems · Theorem · order theory
StrictMono.orderIsoOfSurjective_self_symm_apply
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : Preorder β] (f : α → β) (h_mono : StrictMono f)
(h_surj : Function.Surjective f) (b : β), f ((StrictMono.orderIsoOfSurjective f h_mono h_surj).symm b) = b- Defined in
- Mathlib.Order.Hom.Set
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderPreorder
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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 · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- OrderIsostatement · cited by 874
- StrictMonostatement and proof · cited by 706
- OrderIso.symmstatement · cited by 475
- OrderIso.apply_symm_applyproof · cited by 45
- StrictMono.orderIsoOfSurjectivestatement and proof · cited by 8
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