- we polarized binders to control zeta reduction

[helm.git] / matita / matita / contribs / lambda_delta / apps_2 / functional / subst.ma

diff --git a/matita/matita/contribs/lambda_delta/apps_2/functional/subst.ma b/matita/matita/contribs/lambda_delta/apps_2/functional/subst.ma
index 6aa75625d26e063e5d27fd4a2971639a685f464e..e19af61080a832de416cea39ba09caa844cded00 100644 (file)
--- a/matita/matita/contribs/lambda_delta/apps_2/functional/subst.ma
+++ b/matita/matita/contribs/lambda_delta/apps_2/functional/subst.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/unfold/delift_lift.ma".
-include "Apps_2/functional/lift.ma".
+include "basic_2/unfold/delift_lift.ma".
+include "apps_2/functional/lift.ma".
 
 (* CORE SUBSTITUTION ********************************************************)
 
@@ -24,8 +24,8 @@ let rec fsubst W d U on U ≝ match U with
   | GRef _ ⇒ U
   ]
 | TPair I V T ⇒ match I with
-  [ Bind2 I ⇒ ⓑ{I} (fsubst W d V). (fsubst W (d+1) T)
-  | Flat2 I ⇒ ⓕ{I} (fsubst W d V). (fsubst W d T)
+  [ Bind2 a I ⇒ ⓑ{a,I} (fsubst W d V). (fsubst W (d+1) T)
+  | Flat2 I   ⇒ ⓕ{I} (fsubst W d V). (fsubst W d T)
   ]
 ].
 
@@ -34,12 +34,12 @@ interpretation "functional core substitution" 'Subst V d T = (fsubst V d T).
 (* Main properties **********************************************************)
 
 theorem fsubst_delift: ∀K,V,T,L,d.
-                       ⇩[0, d] L ≡ K. ⓓV → L ⊢ T [d, 1] ≡ [d ← V] T.
+                       ⇩[0, d] L ≡ K. ⓓV → L ⊢ ▼*[d, 1] T ≡ [d ← V] T.
 #K #V #T elim T -T
 [ * #i #L #d #HLK normalize in ⊢ (? ? ? ? ? %); /2 width=3/
   elim (lt_or_eq_or_gt i d) #Hid
   [ -HLK >(tri_lt ?????? Hid) /3 width=3/
-  | destruct >tri_eq /4 width=4 by tpss_strap, tps_subst, le_n, ex2_1_intro/ (**) (* too slow without trace *)   
+  | destruct >tri_eq /4 width=4 by tpss_strap2, tps_subst, le_n, ex2_1_intro/ (**) (* too slow without trace *)   
   | -HLK >(tri_gt ?????? Hid) /3 width=3/
   ]
 | * /3 width=1/ /4 width=1/
@@ -49,24 +49,24 @@ qed.
 (* Main inversion properties ************************************************)
 
 theorem fsubst_inv_delift: ∀K,V,T1,L,T2,d. ⇩[0, d] L ≡ K. ⓓV →
-                           L ⊢ T1 [d, 1] ≡ T2 → [d ← V] T1 = T2.
+                           L ⊢ ▼*[d, 1] T1 ≡ T2 → [d ← V] T1 = T2.
 #K #V #T1 elim T1 -T1
 [ * #i #L #T2 #d #HLK #H
-  [ -HLK >(delift_fwd_sort1 … H) -H //
+  [ -HLK >(delift_inv_sort1 … H) -H //
   | elim (lt_or_eq_or_gt i d) #Hid normalize
-    [ -HLK >(delift_fwd_lref1_lt … H) -H // /2 width=1/
+    [ -HLK >(delift_inv_lref1_lt … H) -H // /2 width=1/
     | destruct
-      elim (delift_fwd_lref1_be … H ? ?) -H // #K0 #V0 #V2 #HLK0
+      elim (delift_inv_lref1_be … H ? ?) -H // #K0 #V0 #V2 #HLK0
       lapply (ldrop_mono … HLK0 … HLK) -HLK0 -HLK #H >minus_plus <minus_n_n #HV2 #HVT2 destruct
       >(delift_inv_refl_O2 … HV2) -V >(flift_inv_lift … HVT2) -V2 //
-    | -HLK >(delift_fwd_lref1_ge … H) -H // /2 width=1/
+    | -HLK >(delift_inv_lref1_ge … H) -H // /2 width=1/
     ]
-  | -HLK >(delift_fwd_gref1 … H) -H //
+  | -HLK >(delift_inv_gref1 … H) -H //
   ]
-| * #I #V1 #T1 #IHV1 #IHT1 #L #X #d #HLK #H
-  [ elim (delift_fwd_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
+| * [ #a ] #I #V1 #T1 #IHV1 #IHT1 #L #X #d #HLK #H
+  [ elim (delift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
     <(IHV1 … HV12) -IHV1 -HV12 // <(IHT1 … HT12) -IHT1 -HT12 // /2 width=1/
-  | elim (delift_fwd_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
+  | elim (delift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
     <(IHV1 … HV12) -IHV1 -HV12 // <(IHT1 … HT12) -IHT1 -HT12 //
   ]
 ]