theorem
  p^<*a*> = q^<*b*> implies p = q & a = b
proof
  assume
A1: p^<*a*> = q^<*b*>;
A2: (p^<*a*>).(len p + 1) = a & (q^<*b*>).(len q + 1) = b by FINSEQ_1:42;
  len(p^<*a*>) = len p + 1 & len(q^<*b*>) = len q + 1 by Th14;
  hence thesis by A1,A2,FINSEQ_1:33;
end;
