Theorems · Theorem · order theory
GaloisInsertion.l_sSup_u_image
∀ {α : Type u} {β : Type v} {l : α → β} {u : β → α} [inst : CompleteLattice α] [inst_1 : CompleteLattice β]
(gi : GaloisInsertion l u) (s : Set β), l (sSup (u '' s)) = sSup s- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- iSupproof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- sSup_eq_iSupproof · cited by 42
- sSup_imageproof · cited by 36
- GaloisInsertionstatement and proof · cited by 35
- GaloisInsertion.l_biSup_uproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- RingCon.sSup_defproof · cited by 1
- AddCon.sSup_defproof · cited by 1
- Con.sSup_defproof · cited by 1
- Submodule.span_biUnionproof · cited by 0