
theorem Th2:
  for X be non empty non-empty FinSequence,
      x be Element of product X,
    i,j be Element of dom X,
      r be object
    st r in X.i & i <> j
  holds
    ( reproj (i,x).r ).j = x.j
  proof
    let X be non empty non-empty FinSequence,
        x be Element of product X,
      i,j be Element of dom X,
        r be object;
    assume
    A1: r in X.i & i<> j; then
    reproj (i,x).r = x +* (i,r) by Def1;
    hence thesis by A1,FUNCT_7:32;
  end;
