Theorems · Theorem · order theory

lt_ciSup_iff

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] {a : α} [Nonempty ι] {f : ι → α},
  BddAbove (Set.range f) → (a < iSup f ↔ ∃ i, a < f i)

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 0 results in Mathlib
Foundations: Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLinearOrder Nonempty

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Set.rangestatement and proof · cited by 4,705
iSupstatement · cited by 2,415
SupSet.sSupproof · cited by 954
BddAbovestatement and proof · cited by 620
ConditionallyCompleteLinearOrderstatement and proof · cited by 542
Set.range_nonemptyproof · cited by 84
lt_csSup_iffproof · cited by 4

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