Theorems · Theorem · order theory
isLUB_sSup
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] (s : Set α), IsLUB s (sSup s)- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- SupSet.sSupstatement · cited by 954
- IsLUBstatement · cited by 280
- CompleteSemilatticeSupstatement and proof · cited by 18
- CompleteSemilatticeSup.isLUB_sSupproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- le_sSupproof · cited by 79
- GaloisConnection.l_iSupproof · cited by 78
- sSup_leproof · cited by 35
- sSup_le_sSupproof · cited by 24
- sSup_le_iffproof · cited by 8
- isLUB_iSupproof · cited by 6
- sSup_unionproof · cited by 5
- sSup_image2_eq_sSup_sSupproof · cited by 5
- sSup_insertproof · cited by 4
- isLUB_iff_sSup_eqproof · cited by 3
- sInf_upperBounds_eq_sSupproof · cited by 2
- lt_sSup_iffproof · cited by 2