reserve n,m for Nat;
reserve p,q,r for Element of Nat_Lattice;
reserve p,q,r for Element of Nat_Lattice;

theorem Th9:
  hcflat.(p,hcflat.(q,r)) = hcflat.(hcflat.(p,q),r)
proof
  set s=q"/\"r;
  thus hcflat.(p,hcflat.(q,r))=p"/\"s .=(p"/\"q)"/\"r by NEWTON:48
    .=hcflat.(hcflat.(p,q),r);
end;
