Theorems · Theorem · order theory

csSup_lowerBounds_range

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] [Nonempty β] {f : β → α},
  BddBelow (Set.range f) → sSup (lowerBounds (Set.range f)) = ⨅ i, f i

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 11 from the axioms · uses no axioms
Assumes: ConditionallyCompleteLattice 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
SupSet.sSupstatement · cited by 954
BddBelowstatement and proof · cited by 401
ConditionallyCompleteLatticestatement and proof · cited by 364
lowerBoundsstatement · cited by 212
Set.range_nonemptyproof · cited by 84
csSup_lowerBounds_eq_csInfproof · cited by 1

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