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
  (maxfuncreal(A)).(f,(minfuncreal(A)).(g,f))=f
proof
  thus (maxfuncreal(A)).(f,(minfuncreal(A)).(g,f)) =(maxfuncreal(A)).(f,(
  minfuncreal(A)).(f,g)) by Th9
    .=f by Th12;
end;
