Theorems · Theorem · order theory
ciSup_le_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] [Nonempty ι] {f : ι → α} {a : α},
BddAbove (Set.range f) → (iSup f ≤ a ↔ ∀ (i : ι), f i ≤ a)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
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.
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.forall_mem_rangeproof · cited by 135
- isLUB_le_iffproof · cited by 24
- isLUB_ciSupproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- ciSup_prodproof · cited by 2
- Matroid.cRk_map_image_liftproof · cited by 1
- Module.le_rank_iff_exists_finsetproof · cited by 1
- Seminorm.closedBall_iSupproof · cited by 1
- Matroid.cRk_comap_liftproof · cited by 1
- NNReal.iSup_eq_zeroproof · cited by 0