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Theorems · Theorem · order theory

csInf_upperBounds_range

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] [Nonempty β] {f : β → α},
  BddAbove (Set.range f) → sInf (upperBounds (Set.range f)) = ⨆ i, f i
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLatticeNonempty
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Around this declaration

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

Monotone.ciSup_comp_tendsto_atTop · cited by 4Monotone.ciSup_comp_tends…Set.range · cited by 4705Set.rangeiSup · cited by 2415iSupInfSet.sInf · cited by 935InfSet.sInfBddAbove · cited by 620BddAboveConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…upperBounds · cited by 263upperBoundsSet.range_nonempty · cited by 84Set.range_nonemptycsInf_upperBounds_eq_csSup · cited by 2csInf_upperBounds_eq_csSupcsInf_upperBounds_rangeCITED BYCITES

Cites8

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Cited by1

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