reserve G for non empty addLoopStr;
reserve x for Element of G;
reserve M for non empty MidStr;
reserve p,q,r for Point of M;
reserve w for Function of [:the carrier of M,the carrier of M:], the carrier
  of G;

theorem Th1:
  w is associating implies p@p = p
proof
A1: w.(p,p) = w.(p,p);
  assume w is associating;
  hence thesis by A1;
end;
