theorem Th19:
  p '&' q = r '&' s implies p = r & s = q
proof
  assume p '&' q = r '&' s;
  then <*2*>^(p^q) = r '&' s by FINSEQ_1:32
    .= <*2*>^(r^s) by FINSEQ_1:32;
  then p^q = r^s by Th2;
  hence thesis by Th18;
end;
