reserve x,y for Real;
reserve a,b,c for Element of Real_Lattice;
reserve p,q,r for Element of Real_Lattice;
reserve A,B for non empty set;
reserve f,g,h for Element of Funcs(A,REAL);

theorem
  (minfuncreal(A)).((maxfuncreal(A)).(f,g),f)=f
proof
  thus (minfuncreal(A)).((maxfuncreal(A)).(f,g),f) =(minfuncreal(A)).((
  maxfuncreal(A)).(g,f),f) by Th8
    .=f by Th18;
end;
