Theorems · Definition · order theory
Sublocale.giRestrict
{X : Type u_1} → [inst : Order.Frame X] → (S : Sublocale X) → GaloisInsertion (⇑S.restrict) Subtype.valThe restriction corresponding to a sublocale forms a Galois insertion with the forgetful map from the sublocale to the original locale.
- Defined in
- Mathlib.Order.Sublocale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Frame
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
- Order.Framestatement and proof · cited by 88
- FrameHomstatement · cited by 70
- GaloisInsertionstatement · cited by 35
- Sublocalestatement and proof · cited by 30
- Sublocale.restrictstatement · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Sublocale.restrict_of_memproof · cited by 1