theorem eq_minus_minus_minus_plus: \forall n,m,p:nat. (n-m)-p = n-(m+p).
intros.
-cut m+p \le n \or \lnot m+p \le n.
+cut m+p \le n \or m+p \nleq n.
elim Hcut.
symmetry.apply plus_to_minus.assumption.
rewrite > assoc_plus.rewrite > sym_plus p.rewrite < plus_minus_m_m.