Theorems · Theorem · order theory
sSup_compact_le_eq
∀ {α : Type u_2} [inst : CompleteLattice α] [IsCompactlyGenerated α] (b : α), sSup {c | IsCompactElement c ∧ c ≤ b} = b- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredstatement and proof · cited by 6,101
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- le_sSupproof · cited by 79
- IsCompactlyGeneratedstatement and proof · cited by 37
- sSup_leproof · cited by 35
- IsCompactElementstatement and proof · cited by 34
- sSup_le_sSupproof · cited by 24
- IsCompactlyGenerated.exists_sSup_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- le_iff_compact_le_impproof · cited by 2
- sSup_compact_eq_topproof · cited by 0