theorem
  [:X1,X2,X3:]<>{} & [:X1,X2,X3:] = [:Y1,Y2,Y3:] implies X1=Y1 & X2=Y2 &
  X3=Y3
proof
  assume
A1: [:X1,X2,X3:]<>{};
  then
A2: X3<>{} by Th21;
  X1<>{} & X2<>{} by A1,Th21;
  hence thesis by A2,Th22;
end;
