reserve X for set,
  x,y,z for Element of BooleLatt X,
  s for set;
reserve y for Element of BooleLatt X;
reserve L for Lattice,
  p,q for Element of L;
reserve A for RelStr,
  a,b,c for Element of A;
reserve A for non empty RelStr,
  a,b,c,c9 for Element of A;
reserve V for with_suprema antisymmetric RelStr,
  u1,u2,u3,u4 for Element of V;
reserve N for with_infima antisymmetric RelStr,
  n1,n2,n3,n4 for Element of N;
reserve K for with_suprema with_infima reflexive antisymmetric RelStr,
  k1,k2,k3 for Element of K;

theorem Th15:
  n1 "/\" n2 = n2 "/\" n1
proof
A1: n1"/\"n2 <= n1 by Lm2;
A2: n1"/\"n2 <= n2 by Lm2;
  for n3 st n3 <= n2 & n3 <= n1 holds n3 <= n1"/\"n2 by Lm2;
  hence thesis by A1,A2,Def14;
end;
