reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

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;
