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 Th25:
  for p holds { q : q ## p } is non empty Subset of [:the carrier
  of M,the carrier of M:]
proof
  let p;
  set pp = { q : q ## p };
A1: for x be object holds x in pp implies x in [:the carrier of M,the carrier
  of M:]
  proof
    let x be object;
    assume x in pp;
    then ex q st x = q & q ## p;
    hence thesis;
  end;
  p in pp;
  hence thesis by A1,TARSKI:def 3;
end;
