Theorems · Theorem · order theory
gc_sSup_Iic
∀ {α : Type u} [inst : CompleteSemilatticeSup α], GaloisConnection sSup Set.IicsSup and Iic form a Galois connection.
- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteSemilatticeSup
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.
- Setstatement and proof · cited by 53,352
- Set.Iicstatement · cited by 1,111
- SupSet.sSupstatement · cited by 954
- GaloisConnectionstatement · cited by 253
- CompleteSemilatticeSupstatement and proof · cited by 18
- sSup_le_iffproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Set.sUnion_powerset_gcproof · cited by 0
- giSSupIicproof · cited by 0