- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / mr2_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_plus.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_plus.ma
index bedc3dae21c030f3df8497343e90e8950c967954..455b669bef01513895a68259af88405cec4e98b4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_plus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/mr2_plus.ma
@@ -12,29 +12,36 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/ynat/ynat_plus.ma".
 include "basic_2/multiple/mr2.ma".
 
 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
 
-let rec pluss (des:list2 nat nat) (i:nat) on des ≝ match des with
+let rec pluss (cs:list2 ynat nat) (i:nat) on cs ≝ match cs with
 [ nil2          ⇒ ◊
-| cons2 l m des ⇒ {l + i, m} @ pluss des i
+| cons2 l m cs ⇒ {l + i, m} @ pluss cs i
 ].
 
 interpretation "plus (multiple relocation with pairs)"
    'plus x y = (pluss x y).
 
+(* Basic properties *********************************************************)
+
+lemma pluss_SO2: ∀l,m,cs. ({l, m} @ cs) + 1 = {⫯l, m} @ cs + 1.
+// qed.
+
 (* Basic inversion lemmas ***************************************************)
 
-lemma pluss_inv_nil2: ∀i,des. des + i = ◊ → des = ◊.
+lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
 #i * // normalize
-#l #m #des #H destruct
+#l #m #cs #H destruct
 qed.
 
-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
-| #l1 #m1 #des1 #H destruct /2 width=3/
+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
+| #l1 #m1 #cs1 whd in ⊢ (??%?→?); #H destruct
+  >yplus_minus_inj /2 width=3 by ex2_intro/
 ]
 qed-.