reserve a,b,c for set;

theorem Th36:
  for D being non empty set,CR,r1,r2 being File of D st r1
is_terminated_by CR & r2 is_terminated_by CR holds CR^r2 is_substring_of addcr(
  r1^r2,CR),1
proof
  let D be non empty set,CR,r1,r2 be File of D;
  assume that
A1: r1 is_terminated_by CR and
A2: r2 is_terminated_by CR;
  r2 = addcr(r2,CR) by A2,Th28;
  then r2 = ovlcon(r2,CR) by FINSEQ_8:def 11;
  then
A3: r2 = r2^(CR/^len ovlpart(r2,CR)) by FINSEQ_8:def 3;
  r1 = addcr(r1,CR) by A1,Th28;
  then r1 = ovlcon(r1,CR) by FINSEQ_8:def 11;
  then
A4: r1 ^r2=((r1|(len r1-'len ovlpart(r1,CR)))^CR)^(r2^(CR/^len ovlpart(r2,CR
  ))) by A3,FINSEQ_8:11;
  addcr(r1^r2,CR) = ovlcon(r1^r2,CR) by FINSEQ_8:def 11
    .= r1^r2^(CR/^(len ovlpart(r1^r2,CR))) by FINSEQ_8:def 3
    .=(r1|(len r1-'len ovlpart(r1,CR)))^(CR^r2)^(CR/^len ovlpart(r2,CR)) ^(
  CR/^(len ovlpart(r1^r2,CR))) by A4,Th1
    .=(r1|(len r1-'len ovlpart(r1,CR)))^(CR^r2)^ ( (CR/^len ovlpart(r2,CR))^
  (CR/^(len ovlpart(r1^r2,CR))) ) by FINSEQ_1:32;
  hence thesis by Th35;
end;
