update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
index d520aa6c2248116f325c345580413b0396b4d15e..507e0c3effa0153a61415a01301eaf7438839d41 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/notation/relations/predtysnstar_4.ma".
 include "basic_2/relocation/lex.ma".
-include "basic_2/rt_computation/cpxs.ma".
+include "basic_2/rt_computation/cpxs_ext.ma".
 
 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *****************)
 
@@ -24,3 +24,17 @@ definition lpxs: ∀h. relation3 genv lenv lenv ≝
 interpretation
    "uncounted parallel rt-computation (local environment)"
    'PRedTySnStar h G L1 L2 = (lpxs h G L1 L2).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lpxs_inv_bind_sn: ∀h,G,I1,L2,K1. ⦃G, K1.ⓘ{I1}⦄ ⊢⬈*[h] L2 →
+                        ∃∃I2,K2. ⦃G, K1⦄ ⊢⬈*[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈*[h] I2 & L2 = K2.ⓘ{I2}.
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
+lemma lpxs_inv_pair_sn: ∀h,G,I,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢⬈*[h] L2 →
+                        ∃∃K2,V2. ⦃G, K1⦄ ⊢⬈*[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈*[h] V2 & L2 = K2.ⓑ{I}V2.
+#h #G #I #L2 #K1 #V1 #H
+elim (lpxs_inv_bind_sn … H) -H #Y #K2 #HK12 #H0 #H destruct
+elim (ext2_inv_pair_sn … H0) -H0 #V2 #HV12 #H destruct
+/2 width=5 by ex3_2_intro/
+qed-.