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);
reserve L for non empty LattStr,
        p,q,r for Element of L;
reserve p,q,r for Element of RealFunc_Lattice(A);

theorem
  (maxfuncreal(A)).((minfuncreal(A)).(p,q),q)=q & (maxfuncreal(A)).(q,(
  minfuncreal(A)).(p,q))=q & (maxfuncreal(A)).(q,(minfuncreal(A)).(q,p))=q & (
  maxfuncreal(A)).((minfuncreal(A)).(q,p),q)=q
proof
  thus
A1: (maxfuncreal(A)).((minfuncreal(A)).(p,q),q) =q by Th14;
  thus (maxfuncreal(A)).(q,(minfuncreal(A)).(p,q)) =(p"/\"q)"\/"q by
LATTICES:def 1
    .=q by Th14;
  thus (maxfuncreal(A)).(q,(minfuncreal(A)).(q,p)) =(maxfuncreal(A)).(q,q"/\"p
  )
    .=(p"/\"q)"\/"q by LATTICES:def 1
    .=q by Th14;
  thus thesis by A1,Th22;
end;
