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

theorem Th7:
  lcmlat.(p,lcmlat.(q,r)) = lcmlat.(lcmlat.(p,q),r)
proof
  set s=q"\/"r;
  thus lcmlat.(p,lcmlat.(q,r))=p"\/"s .=(p"\/"q)"\/"r by NEWTON:43
    .=lcmlat.(lcmlat.(p,q),r);
end;
