theorem Th11:
  (m1 + m2) + m3 = m1 + (m2 + m3)
proof
  let p be object;
  assume
A1: p in P;
  then
A2: ((m1 + m2) + m3).p = (m1 + m2).p + m3.p by Def4
    .= m1.p + m2.p + m3.p by A1,Def4;
  (m1 + (m2 + m3)).p = m1.p + (m2 + m3).p by A1,Def4
    .= m1.p + (m2.p + m3.p) by A1,Def4
    .= m1.p + m2.p + m3.p;
  hence thesis by A2;
end;
