reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

theorem
  for p,q being FinSequence, i being Nat st
  1 <= i & i <= len q holds (p ^ q).(len p + i) = q.i
proof
  let p,q be FinSequence, i be Nat;
  assume 1 <= i & i <= len q;
  then
  len p + 1 <= len p + i & len p + i <= len p + len q by XREAL_1:6;
  hence (p ^ q).(len p + i) = q.(len p + i - len p) by Th23
    .= q.i;
end;
