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:];

theorem Th26:
  for p holds r in p~ iff r ## p
proof
  let p;
  thus r in p~ implies r ## p
  proof
    assume r in p~;
    then ex q st r = q & q ## p;
    hence thesis;
  end;
  thus thesis;
end;
