reserve MS for non empty MidStr;
reserve a, b for Element of MS;
reserve M for MidSp;
reserve a,b,c,d,a9,b9,c9,d9,x,y,x9 for Element of M;
reserve p,q,r,p9,q9 for Element of [:the carrier of M,the carrier of M:];
reserve u,v,w,u9,w9 for Vector of M;

theorem Th41:
  [a,a@b] ## [a@b,b]
proof
  a@b = (a@b)@(a@b) by Def3;
  then a,a@b @@ a@b,b;
  hence thesis;
end;
