Theorems · Theorem · order theory

IsLUB.ciSup_set_eq

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {a : α} {s : Set β} {f : β → α},
  IsLUB (f '' s) a → s.Nonempty → ⨆ i, f ↑i = a

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext, Quot.sound
Assumes: ConditionallyCompleteLattice

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Set.Elemstatement · cited by 7,166
Set.imagestatement and proof · cited by 5,609
Set.Nonemptystatement and proof · cited by 2,627
iSupstatement · cited by 2,415
ConditionallyCompleteLatticestatement and proof · cited by 364
IsLUBstatement and proof · cited by 280
Set.Nonempty.imageproof · cited by 87
Set.image_eq_rangeproof · cited by 57
IsLUB.csSup_eqproof · cited by 19

Cited by1

Results whose statement or proof uses this declaration.

GaloisConnection.l_csSupproof · cited by 4