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
  (minfuncreal(A)).(q,(maxfuncreal(A)).(q,p))=q & (minfuncreal(A)).((
maxfuncreal(A)).(p,q),q)=q & (minfuncreal(A)).(q,(maxfuncreal(A)).(p,q))=q & (
  minfuncreal(A)).((maxfuncreal(A)).(q,p),q)=q
proof
  thus
A1: (minfuncreal(A)).(q,(maxfuncreal(A)).(q,p)) =q by Th16;
  thus
A2: (minfuncreal(A)).((maxfuncreal(A)).(p,q),q) =(minfuncreal(A)).(p "\/"q,q)
    .=q"/\"(q"\/"p) by LATTICES:def 2
    .=q by Th16;
  thus (minfuncreal(A)).(q,(maxfuncreal(A)).(p,q))=q by A1,Th21;
  thus thesis by A2,Th21;
end;
