 reserve n,s for Nat;

theorem Th78:
  Triangle n is triangular square implies
    Triangle (4 * n * (n + 1)) is triangular square
  proof
    assume Triangle n is triangular square; then
    n * (n + 1) / 2 is triangular square by Th19; then
    consider k being Nat such that
A1: n * (n + 1) / 2 = k ^2 by PYTHTRIP:def 3;
    Triangle (4 * n * (n + 1)) = (8 * k ^2) * (8 * k^2 + 1) / 2 by Th19,A1
                .= (4 * k ^2) * (4 * n * (n + 1) + 1) by A1
                .= ((2 * k) * (2 * n + 1)) ^2;
    hence thesis;
  end;
