reserve a,b,c for set;

theorem
  for D being non empty set,f,CR being FinSequence of D st not CR
  is_substring_of f,1 & CR separates_uniquely holds f^CR is_terminated_by CR
proof
  let D be non empty set,f,CR be FinSequence of D;
A1: len (f^CR) + 1 -'len CR=len f+len CR +1-'len CR by FINSEQ_1:22
    .=len CR+(len f+1)-'len CR
    .=len f+1 by NAT_D:34;
  len CR<=len f+len CR by NAT_1:12;
  then
A2: len CR <=len (f^CR) by FINSEQ_1:22;
  assume ( not CR is_substring_of f,1)& CR separates_uniquely;
  then instr(1,f^CR,CR)=len (f^CR) + 1 -'len CR by A1,Th19;
  hence thesis by A2,FINSEQ_8:def 12;
end;
