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Theorems · Theorem · order theory

exists_lt_of_ciInf_lt

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] {a : α} [Nonempty ι] {f : ι → α},
  iInf f < a → ∃ i, f i < a

Indexed version of exists_lt_of_csInf_lt. When iInf f < a, there is an element i such that f i < a.

Defined in
Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLinearOrderNonempty
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

exists_norm_eq_iInf_of_complete_convex · cited by 1exists_norm_eq_iInf_of_co…iInf · cited by 1690iInfConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…exists_lt_of_lt_ciSup · cited by 4exists_lt_of_lt_ciSupexists_lt_of_ciInf_ltCITED BYCITES

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Cited by1

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