Theorems · Definition · order theory
OrderIso.setCongr
{α : Type u_1} → [inst : Preorder α] → (s t : Set α) → s = t → ↑s ≃o ↑tOrder isomorphism between two equal sets.
- Defined in
- Mathlib.Order.Hom.Set
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by22
Results whose statement or proof uses this declaration.
- Real.tanOrderIsoproof · cited by 10
- Real.sinOrderIsoproof · cited by 9
- StrictMono.orderIsoOfSurjectiveproof · cited by 8
- Finset.orderIsoOfFinproof · cited by 7
- OrderIso.sumLexIicIoiproof · cited by 6
- OrderIso.sumLexIioIciproof · cited by 6
- IsLocalization.AtPrime.orderIsoOfPrimeproof · cited by 4
- monoEquivOfFinproof · cited by 2
- IsCompl.IicOrderIsoIciproof · cited by 2
- infIccOrderIsoIccSup'proof · cited by 2
- infIooOrderIsoIooSup'proof · cited by 2
- FirstOrder.Language.dlo_isExtensionPairproof · cited by 1