
theorem Th5:
  for S being non empty RelStr, a, b being Element of S,
  i being Element of Net-Str (a, b) holds
  Net-Str (a, b).i = a or Net-Str (a, b).i = b
proof
  let S be non empty RelStr;
  let a, b be Element of S, i be Element of Net-Str (a, b);
  set N = Net-Str (a,b);
  reconsider I = i as Element of NAT by Def3;
A1: N.i = (a,b),....i by Def3;
  defpred C[Element of NAT] means ex k be Element of NAT st $1 = 2*k;
  per cases;
  suppose C[I];
    hence thesis by A1,Def1;
  end;
  suppose not C[I];
    hence thesis by A1,Def1;
  end;
end;
