X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flpxs_alt.ma;h=8a6b30a577883bc229d0a4071a766d6d85107241;hb=d7ccf1bd91637d3c59a285df6f215ecfde2a2450;hp=e93c88d5c5880b1f6889977975971579dcc71572;hpb=ef49e0e7f5f298c299afdd3cbfdc2404ecb93879;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_alt.ma
index e93c88d5c..8a6b30a57 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_alt.ma
@@ -12,34 +12,36 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/predsnstaralt_5.ma".
 include "basic_2/computation/cpxs_cpxs.ma".
 include "basic_2/computation/lpxs.ma".
 
 (* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************)
 
 (* alternative definition *)
-definition lpxsa: ∀h. sd h → relation lenv ≝ λh,g. lpx_sn … (cpxs h g).
+definition lpxsa: ∀h. sd h → relation3 genv lenv lenv ≝
+                  λh,g,G. lpx_sn … (cpxs h g G).
 
 interpretation "extended parallel computation (local environment, sn variant) alternative"
-   'PRedSnStarAlt h g L1 L2 = (lpxsa h g L1 L2).
+   'PRedSnStarAlt h g G L1 L2 = (lpxsa h g G L1 L2).
 
 (* Main properties on the alternative definition ****************************)
 
-theorem lpxsa_lpxs: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡➡*[g] L2 → ⦃h, L1⦄ ⊢ ➡*[g] L2.
+theorem lpxsa_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
 /2 width=1 by lpx_sn_LTC_TC_lpx_sn/ qed-.
 
 (* Main inversion lemmas on the alternative definition **********************)
 
-theorem lpxs_inv_lpxsa: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡*[g] L2 → ⦃h, L1⦄ ⊢ ➡➡*[g] L2.
+theorem lpxs_inv_lpxsa: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡➡*[h, g] L2.
 /3 width=3 by TC_lpx_sn_inv_lpx_sn_LTC, lpx_cpxs_trans/ qed-.
 
 (* Alternative eliminators **************************************************)
 
-lemma lpxs_ind_alt: ∀h,g. ∀R:relation lenv.
+lemma lpxs_ind_alt: ∀h,g,G. ∀R:relation lenv.
                     R (⋆) (⋆) → (
                        ∀I,K1,K2,V1,V2.
-                       ⦃h, K1⦄ ⊢ ➡*[g] K2 → ⦃h, K1⦄ ⊢ V1 ➡*[g] V2 →
+                       ⦃G, K1⦄ ⊢ ➡*[h, g] K2 → ⦃G, K1⦄ ⊢ V1 ➡*[h, g] V2 →
                        R K1 K2 → R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
                     ) →
-                    ∀L1,L2. ⦃h, L1⦄ ⊢ ➡*[g] L2 → R L1 L2.
+                    ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → R L1 L2.
 /3 width=4 by TC_lpx_sn_ind, lpx_cpxs_trans/ qed-.