Theorems · Theorem · order theory
OrderIso.to_galoisConnection
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] (e : α ≃o β), GaloisConnection ⇑e ⇑e.symmMakes a Galois connection from an order-preserving bijection.
- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 27 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 · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- OrderIsostatement and proof · cited by 874
- OrderIso.symmstatement · cited by 475
- GaloisConnectionstatement · cited by 253
- OrderIso.le_symm_applyproof · cited by 14
Cited by34
Results whose statement or proof uses this declaration.
- OrderIso.map_ciSupproof · cited by 6
- OrderIso.map_csSup'proof · cited by 6
- OrderIso.limsup_applyproof · cited by 5
- Submodule.span_nat_eq_addSubmonoidClosureproof · cited by 5
- NNReal.le_sqrt_iff_sq_leproof · cited by 4
- OrderIso.lift_cof_congrproof · cited by 4
- csSup_addproof · cited by 3
- NNReal.sqrt_le_iff_le_sqproof · cited by 3
- OrderIso.bddAbove_imageproof · cited by 3
- IsLUB.addproof · cited by 2
- OrderIso.map_isCofinalproof · cited by 2
- IsLUB.mulproof · cited by 2