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 Th23:
  u "/\" pseudo_compl(A).u = Bottom NormForm A
proof
  reconsider zero = {} as Element of Normal_forms_on A by NORMFORM:31;
A1: @(pseudo_compl(A).u) = mi(-@u) by Def8;
  thus u "/\" pseudo_compl(A).u = M(A).(u, pseudo_compl(A).u) by LATTICES:def 2
    .= mi(@u ^ mi(-@u)) by A1,NORMFORM:def 12
    .= mi(@u ^ -@u) by NORMFORM:51
    .= mi(zero) by Th21
    .= {} by NORMFORM:40,XBOOLE_1:3
    .= Bottom NormForm A by NORMFORM:57;
end;
