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 Th26:
  u "/\" pseudo_compl(V, C).u = Bottom SubstLatt (V, C)
proof
  reconsider u9 = u as Element of SubstitutionSet (V, C) by SUBSTLAT:def 4;
  thus u "/\" pseudo_compl(V, C).u = M(V, C).(u, pseudo_compl(V, C).u) by
LATTICES:def 2
    .= M(V, C).(u, mi(-u9)) by Def4
    .= mi(u9 ^ mi(-u9)) by SUBSTLAT:def 4
    .= mi(u9 ^ -u9) by SUBSTLAT:20
    .= Bottom SubstLatt (V, C) by Th12;
end;
