reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;
reserve T for non empty TopSpace;
reserve T for non empty TopSpace;

theorem Th94:
  for a, b being Element of Closed_Domains_Lattice T for A, B
being Element of Closed_Domains_of T st a = A & b = B holds a "\/" b = A \/ B &
  a "/\" b = Cl(Int(A /\ B))
proof
  let a, b be Element of Closed_Domains_Lattice T;
  let A, B be Element of Closed_Domains_of T;
  assume that
A1: a = A and
A2: b = B;
A3: Closed_Domains_Lattice T = LattStr(#Closed_Domains_of T,CLD-Union T,
    CLD-Meet T#) by TDLAT_1:def 8;
  hence a "\/" b = (CLD-Union T).(A,B) by A1,A2,LATTICES:def 1
    .= A \/ B by TDLAT_1:def 6;
  thus a "/\" b = (CLD-Meet T).(A,B) by A3,A1,A2,LATTICES:def 2
    .= Cl(Int(A /\ B)) by TDLAT_1:def 7;
end;
