milestone in basic_2 with additions in static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_drops.ma
index c979465c31d3ce4d730f2c36967a96cb7009e057..7bcc3f1fc539b5aab68a86deb14be2ac254b0335 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_drops.ma
@@ -15,13 +15,13 @@
 include "basic_2/rt_computation/cpms_drops.ma".
 include "basic_2/dynamic/cnv.ma".
 
-(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
 (* Advanced dproperties *****************************************************)
 
 (* Basic_2A1: uses: snv_lref *)
 lemma cnv_lref_drops (a) (h) (G): ∀I,K,V,i,L. ⦃G, K⦄ ⊢ V ![a, h] →
-                                  ⬇*[i] L ≘ K.ⓑ{I}V →  ⦃G, L⦄ ⊢ #i ![a, h].
+                                  ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, L⦄ ⊢ #i ![a, h].
 #a #h #G #I #K #V #i elim i -i
 [ #L #HV #H
   lapply (drops_fwd_isid … H ?) -H // #H destruct
@@ -49,6 +49,31 @@ lemma cnv_inv_lref_drops (a) (h) (G):
 ]
 qed-.
 
+lemma cnv_inv_lref_pair (a) (h) (G):
+                        ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
+                        ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ![a, h].
+#a #h #G #i #L #H #I #K #V #HLK
+elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #HX
+lapply (drops_mono … HLY … HLK) -L #H destruct //
+qed-.
+
+lemma cnv_inv_lref_atom (a) (h) (b) (G):
+                        ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
+                        ⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⊥.
+#a #h #b #G #i #L #H #Hi
+elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_
+lapply (drops_gen b … HLY) -HLY #HLY
+lapply (drops_mono … HLY … Hi) -L #H destruct
+qed-.
+
+lemma cnv_inv_lref_unit (a) (h) (G):
+                        ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
+                        ∀I,K. ⬇*[i] L ≘ K.ⓤ{I} → ⊥.
+#a #h #G #i #L #H #I #K #HLK
+elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_
+lapply (drops_mono … HLY … HLK) -L #H destruct
+qed-.
+
 (* Properties with generic slicing for local environments *******************)
 
 (* Basic_2A1: uses: snv_lift *)