(* Equations ****************************************************************)
+lemma minus_plus_m_m_commutative: ∀n,m:nat. n = m + n - m.
+// qed-.
+
(* Note: uses minus_minus_comm, minus_plus_m_m, commutative_plus, plus_minus *)
lemma plus_minus_minus_be: ∀x,y,z. y ≤ z → z ≤ x → (x - z) + (z - y) = x - y.
#x #z #y #Hzy #Hyx >plus_minus // >commutative_plus >plus_minus //
(* Inversion & forward lemmas ***********************************************)
+lemma discr_plus_xy_y: ∀x,y. x + y = y → x = 0.
+// qed-.
+
lemma lt_plus_SO_to_le: ∀x,y. x < y + 1 → x ≤ y.
/2 width=1 by monotonic_pred/ qed-.
#H destruct
qed-.
+lemma zero_eq_plus: ∀x,y. 0 = x + y → 0 = x ∧ 0 = y.
+* /2 width=1 by conj/ #x #y normalize #H destruct
+qed-.
+
(* Iterators ****************************************************************)
(* Note: see also: lib/arithemetics/bigops.ma *)