Theorems · Theorem · order theory
sSup_mem_upperBounds
∀ {α : Type u_1} [inst : CompleteSemilatticeSup α] {s : Set α}, sSup s ∈ upperBounds s- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteSemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 954
- upperBoundsstatement · cited by 263
- reflproof · cited by 80
- isLUB_le_iffproof · cited by 24
- isLUB_sSupproof · cited by 21
- CompleteSemilatticeSupstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- sSup_lt_iffproof · cited by 1