reserve F for Field;

theorem Th1:
  MPS(F) is ParSp
proof
  for a,b,c,d,p,q,r,s being Element of MPS(F) holds a,b '||' b,a & a,b
  '||' c,c & (a,b '||' p,q & a,b '||' r,s implies p,q '||' r,s or a=b) & (a,b
'||' a,c implies b,a '||' b,c) & ex x being Element of MPS(F) st a,b '||' c,x &
  a,c '||' b,x by PARSP_1:13,14,15,16,17;
  hence thesis by PARSP_1:def 12;
end;
