reserve V, C, x, a, b for set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve C for finite set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve u, v for Element of SubstLatt (V, C);
reserve s, t, a, b for Element of PFuncs (V,C);
reserve K, L for Element of SubstitutionSet (V, C);

theorem
  u => v = FinJoin(SUB u, (the L_meet of SubstLatt (V, C)).:(
  pseudo_compl(V, C), StrongImpl(V, C)[:](diff u, v)))
proof
  deffunc IMPL(Element of SubstLatt (V, C), Element of SubstLatt (V, C)) =
FinJoin(SUB $1,M(V, C).:(pseudo_compl(V, C), StrongImpl(V, C)[:](diff $1, $2)))
  ;
A1: for w be Element of SubstLatt (V, C) st u "/\" w [= v holds w [= IMPL(u,
  v) by Lm10;
  u "/\" IMPL(u,v) [= v by Lm10;
  hence thesis by A1,FILTER_0:def 7;
end;
