reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;
reserve D for non empty set;

theorem
  for f being FinSequence st 1<=len f holds mid(f,1,len f)=f
proof
  let f be FinSequence;
  assume
A1: 1<=len f;
  then mid(f,1,len f)=(f/^(1-'1))|(len f-'1+1) by Def3
    .=(f/^0)|(len f-'1+1) by XREAL_1:232
    .=f|(len f-'1+1)
    .=f|len f by A1,XREAL_1:235
    .=f by FINSEQ_1:58;
  hence thesis;
end;
