reserve x, X, Y for set;
reserve L for complete LATTICE,
  a for Element of L;

theorem Th25: ::Proposition 2.2 (i)  (variant 2)   cf variant 3
  for L being non empty RelStr holds (for X holds ex_inf_of X,L)
  implies L is complete
proof
  let L be non empty RelStr;
  assume for X holds ex_inf_of X,L;
  then for X holds ex_sup_of X,L by Th23;
  hence thesis by Th24;
end;
