exists_lt_of_csInf_lt

∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] {s : Set α} {b : α},
  s.Nonempty → sInf s < b → ∃ a ∈ s, a < b

When sInf s < b, there is an element a in s with a < b, if s is nonempty and the order is a linear order.

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by: 10 results in Mathlib
Foundations: Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLinearOrder

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