reserve A for non empty set,
  a for Element of A;
reserve A for set;
reserve B,C for Element of Fin DISJOINT_PAIRS A,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t,s9,t9,t1,t2,s1,s2 for Element of DISJOINT_PAIRS A,
  u,v,w for Element of NormForm A;
reserve K,L for Element of Normal_forms_on A;
reserve f,f9 for (Element of Funcs(DISJOINT_PAIRS A, [:Fin A,Fin A:])),
  g,h for Element of Funcs(DISJOINT_PAIRS A, [A]);

theorem Th27:
  u => v = FinJoin(SUB u, (the L_meet of NormForm A).:(
  pseudo_compl(A), StrongImpl(A)[:](diff u, v)))
proof
  deffunc IMPL(Element of NormForm A, Element of NormForm A) = FinJoin(SUB $1,
  M(A).: (pseudo_compl(A), StrongImpl(A)[:](diff $1, $2)));
  u "/\" IMPL(u,v) [= v & for w st u "/\" w [= v holds w [= IMPL(u,v) by Lm9;
  hence thesis by FILTER_0:def 7;
end;
