update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpms.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
index d1817d6ff7479f56220a26507a47fc36024f41e8..d422aaf2221049b8fa841af761031b403f003408 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
@@ -144,7 +144,7 @@ lemma cprs_refl: ∀h,G,L. reflexive … (cpms h G L 0).
 lemma cpms_sort (h) (G) (L) (n):
                 ∀s. ⦃G,L⦄ ⊢ ⋆s ➡*[n,h] ⋆((next h)^n s).
 #h #G #L #n elim n -n [ // ]
-#n #IH #s <plus_SO
+#n #IH #s <plus_SO_dx
 /3 width=3 by cpms_step_dx, cpm_sort/
 qed.
 
@@ -156,6 +156,36 @@ lemma cpms_inv_sort1 (n) (h) (G) (L): ∀X2,s. ⦃G,L⦄ ⊢ ⋆s ➡*[n,h] X2 
 elim (cpm_inv_sort1 … HX2) -HX2 #H #_ destruct //
 qed-.
 
+lemma cpms_inv_lref1_ctop (n) (h) (G):
+      ∀X2,i. ⦃G,⋆⦄ ⊢ #i ➡*[n,h] X2 → ∧∧ X2 = #i & n = 0.
+#n #h #G #X2 #i #H @(cpms_ind_dx … H) -X2
+[ /2 width=1 by conj/
+| #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
+  elim (cpm_inv_lref1_ctop … HX2) -HX2 #H1 #H2 destruct
+  /2 width=1 by conj/
+]
+qed-.
+
+lemma cpms_inv_zero1_unit (n) (h) (I) (K) (G):
+      ∀X2. ⦃G,K.ⓤ{I}⦄ ⊢ #0 ➡*[n,h] X2 → ∧∧ X2 = #0 & n = 0.
+#n #h #I #G #K #X2 #H @(cpms_ind_dx … H) -X2
+[ /2 width=1 by conj/
+| #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
+  elim (cpm_inv_zero1_unit … HX2) -HX2 #H1 #H2 destruct
+  /2 width=1 by conj/
+]
+qed-.
+
+lemma cpms_inv_gref1 (n) (h) (G) (L):
+      ∀X2,l. ⦃G,L⦄ ⊢ §l ➡*[n,h] X2 → ∧∧ X2 = §l & n = 0.
+#n #h #G #L #X2 #l #H @(cpms_ind_dx … H) -X2
+[ /2 width=1 by conj/
+| #n1 #n2 #X #X2 #_ * #HX #Hn1 #HX2 destruct
+  elim (cpm_inv_gref1 … HX2) -HX2 #H1 #H2 destruct
+  /2 width=1 by conj/
+]
+qed-.
+
 lemma cpms_inv_cast1 (h) (n) (G) (L):
       ∀W1,T1,X2. ⦃G,L⦄ ⊢ ⓝW1.T1 ➡*[n,h] X2 →
       ∨∨ ∃∃W2,T2. ⦃G,L⦄ ⊢ W1 ➡*[n,h] W2 & ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & X2 = ⓝW2.T2