reserve a,b,c for set;

theorem Th30:
  for D being non empty set,f,CR being File of D holds len addcr(f
  ,CR) >= len f & len addcr(f,CR) >= len CR
proof
  let D be non empty set,f,CR be File of D;
A1: addcr(f,CR)=ovlcon(f,CR) by FINSEQ_8:def 11;
  len ovlcon(f,CR)=len f+(len CR -'len ovlpart(f,CR)) by FINSEQ_8:15;
  hence len addcr(f,CR) >= len f by A1,NAT_1:12;
  ovlcon(f,CR)=(f|(len f-'len ovlpart(f,CR)))^CR by FINSEQ_8:11;
  then len ovlcon(f,CR)= len (f|(len f-'len ovlpart(f,CR))) + len CR by
FINSEQ_1:22;
  hence thesis by A1,NAT_1:12;
end;
