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 Th17:
  (k1 "/\" k2) "\/" k2 = k2
proof
A1: k1"/\"k2 <= k2 by Lm2;
A2: k2 <= k2;
  for k3 st k1"/\" k2 <= k3 & k2 <= k3 holds k2 <= k3;
  hence thesis by A1,A2,Def13;
end;
