Theorems · Theorem · order theory

ciInf_lt_iff

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

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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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
iInfstatement · cited by 1,690
InfSet.sInfproof · cited by 935
ConditionallyCompleteLinearOrderstatement and proof · cited by 542
BddBelowstatement and proof · cited by 401
Set.range_nonemptyproof · cited by 84
csInf_lt_iffproof · cited by 4

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