- ldrop is now drop as in basic_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / crr_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/crr_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/crr_lift.ma
index 731d00bb2088d161701f5086d6ea699e723184e0..27a6951bdf9874413559c6e877e2211c870ccbd0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/crr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/crr_lift.ma
@@ -12,63 +12,63 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/ldrop_ldrop.ma".
+include "basic_2/substitution/drop_drop.ma".
 include "basic_2/reduction/crr.ma".
 
-(* CONTEXT-SENSITIVE REDUCIBLE TERMS ****************************************)
+(* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE REDUCTION **************************)
 
 (* Properties on relocation *************************************************)
 
-lemma crr_lift: ∀K,T. K ⊢ 𝐑⦃T⦄ → ∀L,d,e. ⇩[d, e] L ≡ K →
-                ∀U. ⇧[d, e] T ≡ U → L ⊢ 𝐑⦃U⦄.
-#K #T #H elim H -K -T
-[ #K #K0 #V #i #HK0 #L #d #e #HLK #X #H
+lemma crr_lift: ∀G,K,T. ⦃G, K⦄ ⊢ ➡ 𝐑⦃T⦄ → ∀L,s,d,e. ⇩[s, d, e] L ≡ K →
+                ∀U. ⇧[d, e] T ≡ U → ⦃G, L⦄ ⊢ ➡ 𝐑⦃U⦄.
+#G #K #T #H elim H -K -T
+[ #K #K0 #V #i #HK0 #L #s #d #e #HLK #X #H
   elim (lift_inv_lref1 … H) -H * #Hid #H destruct
-  [ elim (ldrop_trans_lt … HLK … HK0) -K // /2 width=4/
-  | lapply (ldrop_trans_ge … HLK … HK0 ?) -K // /2 width=4/
+  [ elim (drop_trans_lt … HLK … HK0) -K /2 width=4 by crr_delta/
+  | lapply (drop_trans_ge … HLK … HK0 ?) -K /3 width=4 by crr_delta, drop_inv_gen/
   ]
-| #K #V #T #_ #IHV #L #d #e #HLK #X #H
-  elim (lift_inv_flat1 … H) -H #W #U #HVW #_ #H destruct /3 width=4/
-| #K #V #T #_ #IHT #L #d #e #HLK #X #H
-  elim (lift_inv_flat1 … H) -H #W #U #_ #HTU #H destruct /3 width=4/
-| #I #K #V #T #HI #L #d #e #_ #X #H
-  elim (lift_fwd_pair1 … H) -H #W #U #_ #H destruct /2 width=1/
-| #a #I #K #V #T #HI #_ #IHV #L #d #e #HLK #X #H
-  elim (lift_inv_bind1 … H) -H #W #U #HVW #_ #H destruct /3 width=4/
-| #a #I #K #V #T #HI #_ #IHT #L #d #e #HLK #X #H
-  elim (lift_inv_bind1 … H) -H #W #U #HVW #HTU #H destruct /4 width=4/
-| #a #K #V #V0 #T #L #d #e #_ #X #H
+| #K #V #T #_ #IHV #L #s #d #e #HLK #X #H
+  elim (lift_inv_flat1 … H) -H #W #U #HVW #_ #H destruct /3 width=5 by crr_appl_sn/
+| #K #V #T #_ #IHT #L #s #d #e #HLK #X #H
+  elim (lift_inv_flat1 … H) -H #W #U #_ #HTU #H destruct /3 width=5 by crr_appl_dx/
+| #I #K #V #T #HI #L #s #d #e #_ #X #H
+  elim (lift_fwd_pair1 … H) -H #W #U #_ #H destruct /2 width=1 by crr_ri2/
+| #a #I #K #V #T #HI #_ #IHV #L #s #d #e #HLK #X #H
+  elim (lift_inv_bind1 … H) -H #W #U #HVW #_ #H destruct /3 width=5 by crr_ib2_sn/
+| #a #I #K #V #T #HI #_ #IHT #L #s #d #e #HLK #X #H
+  elim (lift_inv_bind1 … H) -H #W #U #HVW #HTU #H destruct /4 width=5 by crr_ib2_dx, drop_skip/
+| #a #K #V #V0 #T #L #s #d #e #_ #X #H
   elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
-  elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1/
-| #a #K #V #V0 #T #L #d #e #_ #X #H
+  elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1 by crr_beta/
+| #a #K #V #V0 #T #L #s #d #e #_ #X #H
   elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
-  elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1/
+  elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1 by crr_theta/
 ]
 qed.
 
-lemma crr_inv_lift: ∀L,U. L ⊢ 𝐑⦃U⦄ → ∀K,d,e. ⇩[d, e] L ≡ K →
-                    ∀T. ⇧[d, e] T ≡ U → K ⊢ 𝐑⦃T⦄.
-#L #U #H elim H -L -U
-[ #L #L0 #W #i #HK0 #K #d #e #HLK #X #H
+lemma crr_inv_lift: ∀G,L,U. ⦃G, L⦄ ⊢ ➡ 𝐑⦃U⦄ → ∀K,s,d,e. ⇩[s, d, e] L ≡ K →
+                    ∀T. ⇧[d, e] T ≡ U → ⦃G, K⦄ ⊢ ➡ 𝐑⦃T⦄.
+#G #L #U #H elim H -L -U
+[ #L #L0 #W #i #HK0 #K #s #d #e #HLK #X #H
   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
-  [ elim (ldrop_conf_lt … HLK … HK0) -L // /2 width=4/
-  | lapply (ldrop_conf_ge … HLK … HK0 ?) -L // /2 width=4/
+  [ elim (drop_conf_lt … HLK … HK0) -L /2 width=4 by crr_delta/
+  | lapply (drop_conf_ge … HLK … HK0 ?) -L /2 width=4 by crr_delta/
   ]
-| #L #W #U #_ #IHW #K #d #e #HLK #X #H
-  elim (lift_inv_flat2 … H) -H #V #T #HVW #_ #H destruct /3 width=4/
-| #L #W #U #_ #IHU #K #d #e #HLK #X #H
-  elim (lift_inv_flat2 … H) -H #V #T #_ #HTU #H destruct /3 width=4/
-| #I #L #W #U #HI #K #d #e #_ #X #H
-  elim (lift_fwd_pair2 … H) -H #V #T #_ #H destruct /2 width=1/
-| #a #I #L #W #U #HI #_ #IHW #K #d #e #HLK #X #H
-  elim (lift_inv_bind2 … H) -H #V #T #HVW #_ #H destruct /3 width=4/
-| #a #I #L #W #U #HI #_ #IHU #K #d #e #HLK #X #H
-  elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct /4 width=4/
-| #a #L #W #W0 #U #K #d #e #_ #X #H
+| #L #W #U #_ #IHW #K #s #d #e #HLK #X #H
+  elim (lift_inv_flat2 … H) -H #V #T #HVW #_ #H destruct /3 width=5 by crr_appl_sn/
+| #L #W #U #_ #IHU #K #s #d #e #HLK #X #H
+  elim (lift_inv_flat2 … H) -H #V #T #_ #HTU #H destruct /3 width=5 by crr_appl_dx/
+| #I #L #W #U #HI #K #s #d #e #_ #X #H
+  elim (lift_fwd_pair2 … H) -H #V #T #_ #H destruct /2 width=1 by crr_ri2/
+| #a #I #L #W #U #HI #_ #IHW #K #s #d #e #HLK #X #H
+  elim (lift_inv_bind2 … H) -H #V #T #HVW #_ #H destruct /3 width=5 by crr_ib2_sn/
+| #a #I #L #W #U #HI #_ #IHU #K #s #d #e #HLK #X #H
+  elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct /4 width=5 by crr_ib2_dx, drop_skip/
+| #a #L #W #W0 #U #K #s #d #e #_ #X #H
   elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
-  elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1/
-| #a #L #W #W0 #U #K #d #e #_ #X #H
+  elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1 by crr_beta/
+| #a #L #W #W0 #U #K #s #d #e #_ #X #H
   elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
-  elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1/
+  elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1 by crr_theta/
 ]
-qed.
+qed-.