(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
-let rec pluss (des:list2 nat nat) (i:nat) on des ≝ match des with
-[ nil2 â\87\92 â\9f
-| cons2 d e des ⇒ {d + i, e} @ pluss des i
+let rec pluss (cs:list2 nat nat) (i:nat) on cs ≝ match cs with
+[ nil2 â\87\92 â\97\8a
+| cons2 l m cs ⇒ {l + i, m} @ pluss cs i
].
interpretation "plus (multiple relocation with pairs)"
(* Basic inversion lemmas ***************************************************)
-lemma pluss_inv_nil2: ∀i,des. des + i = ⟠ → des = ⟠.
+lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
#i * // normalize
-#d #e #des #H destruct
+#l #m #cs #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,cs2,cs. cs + i = {l, m} @ cs2 →
+ ∃∃cs1. cs1 + i = cs2 & cs = {l - i, m} @ cs1.
+#i #l #m #cs2 * normalize
[ #H destruct
-| #d1 #e1 #des1 #H destruct /2 width=3/
+| #l1 #m1 #cs1 #H destruct /2 width=3 by ex2_intro/
]
qed-.