reserve a,b,c for set;

theorem Th31:
  for D being non empty set,f,g being FinSequence of D holds g =
  ovlpart(f,g)^ovlrdiff(f,g)
proof
  let D be non empty set,f,g be FinSequence of D;
  ovlpart(f,g)=smid(g,1,len ovlpart(f,g)) by FINSEQ_8:def 2
    .=g|len ovlpart(f,g) by FINSEQ_8:5;
  then
  ovlpart(f,g)^ovlrdiff(f,g)=(g|len ovlpart(f,g))^(g/^(len ovlpart(f,g)))
  by FINSEQ_8:def 5
    .=g by RFINSEQ:8;
  hence thesis;
end;
