
theorem
  for D being non empty set,f,g being FinSequence of D holds ovlcon(f,g)
  =ovlldiff(f,g)^ovlpart(f,g)^ovlrdiff(f,g) & ovlcon(f,g)
  =ovlldiff(f,g)^(ovlpart(f,g)^ovlrdiff(f,g))
proof
  let D be non empty set,f,g be FinSequence of D;
  ovlpart(f,g)^(g/^(len ovlpart(f,g)))
  = smid(g,1,len ovlpart(f,g))^(g/^(len ovlpart(f,g))) by Def2
    .= g|(len ovlpart(f,g))^(g/^(len ovlpart(f,g))) by Th5
    .= g by RFINSEQ:8;
  hence ovlcon(f,g)
  =(f|(len f-'len ovlpart(f,g)))^(ovlpart(f,g)^(g/^(len ovlpart(f,g))))
  by Th11
    .=ovlldiff(f,g)^ovlpart(f,g)^ovlrdiff(f,g) by FINSEQ_1:32;
  hence thesis by FINSEQ_1:32;
end;
