Theorems · Definition · order theory
Nucleus.giRestrict
{X : Type u_1} → [inst : Order.Frame X] → (n : Nucleus X) → GaloisInsertion (⇑n.restrict) Subtype.valThe restriction of a nucleus to its range forms a Galois insertion with the forgetful map from the range to the original frame.
- Defined in
- Mathlib.Order.Nucleus
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Frame
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Order.Framestatement and proof · cited by 88
- FrameHomstatement · cited by 70
- Nucleusstatement and proof · cited by 41
- GaloisInsertionstatement · cited by 35
- Nucleus.restrictstatement · cited by 1
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