reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem
  (p '&' q) '&' s => p '&' (q '&' s) in HP_TAUT
proof
A1: p '&' (s '&' q) => p '&' (q '&' s) in HP_TAUT by Lm15;
  (p '&' q) '&' s => p '&' (s '&' q) in HP_TAUT by Lm14;
  hence thesis by A1,Th23;
end;
