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Theorems · Theorem · order theory

ConditionallyCompleteLinearOrder.csInf_of_not_bddBelow

∀ {α : Type u_5} [self : ConditionallyCompleteLinearOrder α] (s : Set α), ¬BddBelow s → sInf s = sInf ∅

If a set is not bounded below, its infimum is by convention sInf ∅.

Defined in
Mathlib.Order.ConditionallyCompleteLattice.Defs
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLinearOrder
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csInf_of_not_bddBelow · cited by 8csInf_of_not_bddBelowSet · cited by 53352SetInfSet.sInf · cited by 935InfSet.sInfConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…BddBelow · cited by 401BddBelowConditionallyCompleteLinearOr…CITED BYCITES

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