let rec pluss (des:list2 nat nat) (i:nat) on des ≝ match des with
[ nil2 ⇒ ◊
-| cons2 d e des ⇒ {d + i, e} @ pluss des i
+| cons2 l m des ⇒ {l + i, m} @ pluss des i
].
interpretation "plus (multiple relocation with pairs)"
lemma pluss_inv_nil2: ∀i,des. des + i = ◊ → des = ◊.
#i * // normalize
-#d #e #des #H destruct
+#l #m #des #H destruct
qed.
-lemma pluss_inv_cons2: ∀i,d,e,des2,des. des + i = {d, e} @ des2 →
- ∃∃des1. des1 + i = des2 & des = {d - i, e} @ des1.
-#i #d #e #des2 * normalize
+lemma pluss_inv_cons2: ∀i,l,m,des2,des. des + i = {l, m} @ des2 →
+ ∃∃des1. des1 + i = des2 & des = {l - i, m} @ des1.
+#i #l #m #des2 * normalize
[ #H destruct
-| #d1 #e1 #des1 #H destruct /2 width=3/
+| #l1 #m1 #des1 #H destruct /2 width=3/
]
qed-.