lambda_delta: partial commit ...

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / grammar / cl_shift.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/cl_shift.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/cl_shift.ma
index ea82bde3cfc1616dad076e1a671b4c8b1b33a157..837b1c670c65cc6726e129056cbccc0e87d51925 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/cl_shift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/grammar/cl_shift.ma
@@ -12,13 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/lenv.ma".
+include "basic_2/grammar/lenv_append.ma".
 
 (* SHIFT OF A CLOSURE *******************************************************)
 
 let rec shift L T on L ≝ match L with
 [ LAtom       ⇒ T
-| LPair L I V ⇒ shift L (ⓑ{I} V. T)
+| LPair L I V ⇒ shift L (-ⓑ{I} V. T)
 ].
 
 interpretation "shift (closure)" 'Append L T = (shift L T).
+
+(* Basic properties *********************************************************)
+
+lemma shift_append_assoc: ∀L,K. ∀T:term. (L @@ K) @@ T = L @@ K @@ T.
+#L #K elim K -K normalize //
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma shift_inj: ∀L1,L2. ∀T1,T2:term. L1 @@ T1 = L2 @@ T2 → |L1| = |L2| →
+                 L1 = L2 ∧ T1 = T2.
+#L1 elim L1 -L1
+[ * normalize /2 width=1/
+  #L2 #I2 #V2 #T1 #T2 #_ <plus_n_Sm #H destruct
+| #L1 #H1 #V1 #IH * normalize
+  [ #T1 #T2 #_ <plus_n_Sm #H destruct
+  | #L2 #I2 #V2 #T1 #T2 #H1 #H2
+    elim (IH … H1 ?) -IH -H1 /2 width=1/ -H2 #H1 #H2 destruct /2 width=1/
+  ]
+]
+qed-.
+  
\ No newline at end of file