Theorems · Theorem · order theory

GaloisConnection.u_sInf

∀ {α : Type u} {β : Type v} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] {u : α → β} {l : β → α},
  GaloisConnection l u → ∀ {s : Set α}, u (sInf s) = ⨅ a ∈ s, u a

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

11 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CompleteLatticeCompleteLattice