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, k being Nat st 1<=k holds mid(f,1,k)=f|k
proof
  let f be FinSequence,k be Nat;
  1-'1=0 by XREAL_1:232;
  then
A1: f/^(1-'1)=f;
  assume
A2: 1<=k;
  then mid(f,1,k)=(f/^(1-'1))|(k-'1+1) by Def3;
  hence thesis by A2,A1,XREAL_1:235;
end;
