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 Th15:
  len p < len(p '&' q) & len q < len(p '&' q)
proof
  len(p '&' q) = len(<*2*>^p) + len q by FINSEQ_1:22
    .= len<*2*> + len p + len q by FINSEQ_1:22
    .= 1 + len p + len q by FINSEQ_1:39
    .= 1 + (len p + len q);
  then
A1: len p + len q < len(p '&' q) by XREAL_1:29;
  len p <= len p + len q & len q <= len p + len q by NAT_1:11;
  hence thesis by A1,XXREAL_0:2;
end;
