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Theorems · Theorem · order theory

biSup_ge_eq_sup

∀ {α : Type u_1} [inst : CompleteLattice α] {ι : Type u_8} [inst_1 : PartialOrder ι] (f : ι → α) (i : ι),
  ⨆ j, ⨆ (_ : j ≥ i), f j = f i ⊔ ⨆ j, ⨆ (_ : j > i), f j
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLatticePartialOrder
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Around this declaration

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Set.biUnion_ge · cited by 0Set.biUnion_gePartialOrder · cited by 6410PartialOrderiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeiSup_congr_Prop · cited by 247iSup_congr_PropiSup_pos · cited by 61iSup_posiSup_and' · cited by 4iSup_and'iSup_split_single · cited by 3iSup_split_singlebiSup_ge_eq_supCITED BYCITES

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Cited by1

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