Theorems · Definition · order theory
OrderIso.toGaloisCoinsertion
{α : Type u} → {β : Type v} → [inst : Preorder α] → [inst_1 : Preorder β] → (e : α ≃o β) → GaloisCoinsertion ⇑e ⇑e.symmMakes a Galois coinsertion from an order-preserving bijection.
- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- OrderIsostatement and proof · cited by 874
- OrderIso.symmstatement and proof · cited by 475
- GaloisCoinsertionstatement · cited by 35
- OrderIso.to_galoisConnectionproof · cited by 32
Cited by2
Results whose statement or proof uses this declaration.
- OrderIso.isAtom_iffproof · cited by 5
- IsGalois.galoisCoinsertionIntermediateFieldSubgroupproof · cited by 0