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 Th44:
  u+ID(M) = u
proof
  set a = the Element of M;
  consider b such that
A1: u = vect(a,b) by Th35;
  u+ID(M) = vect(a,b)+vect(b,b) by A1,Th32
    .= u by A1,Th40;
  hence thesis;
end;
