Theorems · Theorem · order theory

GaloisConnection.u_ciInf

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α]
  [inst_1 : ConditionallyCompleteLattice β] [Nonempty ι] {l : α → β} {u : β → α},
  GaloisConnection l u → ∀ {f : ι → β}, BddBelow (Set.range f) → u (⨅ i, f i) = ⨅ i, u (f i)

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by: 0 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Quot.sound
Assumes: ConditionallyCompleteLattice ConditionallyCompleteLattice Nonempty

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Set.rangestatement and proof · cited by 4,705
iInfstatement · cited by 1,690
BddBelowstatement and proof · cited by 401
ConditionallyCompleteLatticestatement and proof · cited by 364
GaloisConnectionstatement and proof · cited by 253
GaloisConnection.dualproof · cited by 4
GaloisConnection.l_ciSupproof · cited by 3

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