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Theorems · Theorem · order theory

ConditionallyCompleteLattice.isGLB_csInf

∀ {α : Type u_5} [self : ConditionallyCompleteLattice α] (s : Set α), s.Nonempty → BddBelow s → IsGLB s (sInf s)

Every nonempty subset which is bounded below has a greatest lower bound.

Defined in
Mathlib.Order.ConditionallyCompleteLattice.Defs
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isGLB_csInf · cited by 24isGLB_csInfconditionallyCompleteLatticeOfLatticeOfsInf · cited by 0conditionallyCompleteLatt…conditionallyCompleteLatticeOfLatticeOfsSup · cited by 0conditionallyCompleteLatt…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptyInfSet.sInf · cited by 935InfSet.sInfBddBelow · cited by 401BddBelowConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…IsGLB · cited by 213IsGLBConditionallyCompleteLattice.…CITED BYCITES

Cites6

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Cited by3

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