Theorems · Definition · order theory
nucleusIsoSublocale
{X : Type u_1} → [inst : Order.Frame X] → (Nucleus X)ᵒᵈ ≃o Sublocale XThe nuclei on a frame corresponds exactly to the sublocales on this frame. The sublocales are ordered dually to the nuclei.
- Defined in
- Mathlib.Order.Sublocale
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualproof · cited by 400
- Order.Framestatement and proof · cited by 88
- Nucleusstatement and proof · cited by 41
- Sublocalestatement and proof · cited by 30
- Nucleus.toSublocaleproof · cited by 5
- Sublocale.toNucleusproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- nucleusIsoSublocale.eq_toSublocalestatement · cited by 0
- nucleusIsoSublocale.symm_eq_toNucleusstatement · cited by 0