Theorems · Theorem · order theory

IsLUB.ciSup_eq

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {a : α} [Nonempty ι] {f : ι → α},
  IsLUB (Set.range f) a → ⨆ i, f i = a

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses no axioms
Assumes: ConditionallyCompleteLattice Nonempty

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Cites6

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
iSupstatement · cited by 2,415
ConditionallyCompleteLatticestatement and proof · cited by 364
IsLUBstatement and proof · cited by 280
Set.range_nonemptyproof · cited by 84
IsLUB.csSup_eqproof · cited by 19

Cited by1

Results whose statement or proof uses this declaration.

iSup_eq_of_forall_le_of_tendstoproof · cited by 1