reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;
reserve t,s,r1 for Real;
reserve n for Element of NAT;
reserve X,Y,B1,B2 for Subset of TOP-REAL n;
reserve x,y for Point of TOP-REAL n;

theorem
  t<>0 implies t(.)(X (o) Y) = t(.)X (o) t(.)Y
proof
  assume t<>0;
  then t(.)(X (o) Y) =t(.)(X (+) Y) (-) t(.)Y by Th64
    .=t(.)X (+) t(.)Y (-) t(.)Y by Th63;
  hence thesis;
end;
