renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsuba_lsuba.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_lsuba.ma
index 5d64516a51ebb439409019198a1c6f47ddfac056..28dc2d8ee34eb440fbaec1806207431e08d9872e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_lsuba.ma
@@ -14,22 +14,23 @@
 
 include "basic_2/static/lsuba_aaa.ma".
 
-(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
 
 (* Main properties **********************************************************)
 
-theorem lsuba_trans: ∀L1,L. L1 ⁝⊑ L → ∀L2. L ⁝⊑ L2 → L1 ⁝⊑ L2.
-#L1 #L #H elim H -L1 -L
+theorem lsuba_trans: ∀G. Transitive … (lsuba G).
+#G #L1 #L #H elim H -L1 -L
 [ #X #H >(lsuba_inv_atom1 … H) -H //
-| #I #L1 #L #V #HL1 #IHL1 #X #H
-  elim (lsuba_inv_pair1 … H) -H * #L2
-  [ #HL2 #H destruct /3 width=1/
-  | #V #A #HLV #HL2V #HL2 #H1 #H2 destruct /3 width=3/
+| #I #L1 #L #HL1 #IHL1 #Y #H
+  elim (lsuba_inv_bind1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=1 by lsuba_bind/
+  | #W #V #A #HV #HW #HL2 #H1 #H2 destruct
+    /3 width=3 by lsuba_beta, lsuba_aaa_trans/
   ]
-| #L1 #L #V1 #W #A1 #HV1 #HW #HL1 #IHL1 #X #H
-  elim (lsuba_inv_pair1 … H) -H * #L2
-  [ #HL2 #H destruct /3 width=5/
-  | #V #A2 #_ #_ #_ #_ #H destruct
+| #L1 #L #W #V #A #HV #HW #HL1 #IHL1 #Y #H
+  elim (lsuba_inv_bind1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=5 by lsuba_beta, lsuba_aaa_conf/
+  | #W0 #V0 #A0 #_ #_ #_ #H destruct
   ]
 ]
-qed.
+qed-.