reserve X,x for set;
reserve k,m,n for Element of NAT,
  p,q,r,s,r9,s9 for Element of HP-WFF,
  T1,T2 for Tree;
reserve T1,T2 for DecoratedTree;
reserve t,t1 for FinSequence;

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;
