reserve x,y for Real;
reserve a,b,c for Element of Real_Lattice;
reserve p,q,r for Element of Real_Lattice;

theorem Th7:
  minreal.(q,maxreal.(p,r))=maxreal.(minreal.(q,p),minreal.(q,r))
proof
  set s=p"\/"r;
  thus minreal.(q,maxreal.(p,r)) =q"/\"s .=(q"/\"p)"\/"(q"/\"r) by XXREAL_0:38
    .=maxreal.(minreal.(q,p),minreal.(q,r));
end;
