lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
index 3ebe6e4853b82c10dbdcbaf969410138c783029d..32807a499edd037e3693da43bcc3613a4c08a115 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -13,23 +13,22 @@
 (**************************************************************************)
 
 include "basic_2/computation/csn_aaa.ma".
-include "basic_2/computation/dxprs_lift.ma".
-include "basic_2/computation/dxprs_aaa.ma".
+include "basic_2/computation/cpds_aaa.ma".
 include "basic_2/equivalence/cpcs_aaa.ma".
 include "basic_2/dynamic/snv.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
 
-(* Properties on atomic arity assignment for terms **************************)
+(* Forward lemmas on atomic arity assignment for terms **********************)
 
-lemma snv_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃A. L ⊢ T ⁝ A.
+lemma snv_fwd_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ¡[g] → ∃A. L ⊢ T ⁝ A.
 #h #g #L #T #H elim H -L -T
 [ /2 width=2/
 | #I #L #K #V #i #HLK #_ * /3 width=6/
 | #a * #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
 | #a #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
-  lapply (dxprs_aaa h g … HV W0 ?) [ -HTU /2 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
-  lapply (dxprs_aaa … HT … HTU) -HTU #H
+  lapply (cpds_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
+  lapply (cpds_aaa … HT … HTU) -HTU #H
   elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
   lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
 | #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
@@ -37,6 +36,6 @@ lemma snv_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃A. L ⊢ T ⁝ A.
 ]
 qed-.
 
-lemma snv_csn: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → L ⊢ ⬊* T.
-#h #g #L #T #H elim (snv_aaa … H) -H /2 width=2/
+lemma snv_fwd_csn: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ¡[g] → ⦃h, L⦄ ⊢ ⬊*[g] T.
+#h #g #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
 qed-.