
theorem Th10:
  for D being non empty set,f,g being FinSequence of D
  holds len ovlpart(f,g)<=len f
proof
  let D be non empty set,f,g be FinSequence of D;
  now
    assume
A1: len ovlpart(f,g)>len f;
    then len f - len ovlpart(f,g)<0 by XREAL_1:49;
    then len f -' len ovlpart(f,g)=0 by XREAL_0:def 2;
    then smid(f,len f-'len ovlpart(f,g)+1,len f) =f by Th6;
    hence contradiction by A1,Def2;
  end;
  hence thesis;
end;
