
theorem Th2X:
  for X be non empty non-empty FinSequence,
      x be Element of product X,
      i be Element of dom X
  holds
    reproj (i,x).(x.i) = x
  proof
    let X be non empty non-empty FinSequence,
        x be Element of product X,
        i be Element of dom X;
    reproj (i,x).(x.i) = x +* (i,(x.i)) by Def1;
    hence reproj (i,x).(x.i) = x by FUNCT_7:35;
  end;
