(* *)
(**************************************************************************)
+include "basic_2/relocation/fquq_alt.ma".
include "basic_2/relocation/ldrop_lpx_sn.ma".
include "basic_2/reduction/cpr_lift.ma".
include "basic_2/reduction/lpr.ma".
(* Properies on local environment slicing ***********************************)
(* Basic_1: includes: wcpr0_drop *)
-lemma lpr_ldrop_conf: dropable_sn lpr.
+lemma lpr_ldrop_conf: ∀G. dropable_sn (lpr G).
/3 width=5 by lpx_sn_deliftable_dropable, cpr_inv_lift1/ qed-.
(* Basic_1: includes: wcpr0_drop_back *)
-lemma ldrop_lpr_trans: dedropable_sn lpr.
+lemma ldrop_lpr_trans: ∀G. dedropable_sn (lpr G).
/3 width=9 by lpx_sn_liftable_dedropable, cpr_lift/ qed-.
-lemma lpr_ldrop_trans_O1: dropable_dx lpr.
+lemma lpr_ldrop_trans_O1: ∀G. dropable_dx (lpr G).
/2 width=3 by lpx_sn_dropable/ qed-.
+
+(* Properties on context-sensitive parallel reduction for terms *************)
+
+lemma fqu_cpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+ ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
+ ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃ ⦃G2, L2, U2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/
+#G #L #K #U #T #e #HLK #HUT #U2 #HU2
+elim (lift_total U2 0 (e+1)) #T2 #HUT2
+lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
+qed-.
+
+lemma fquq_cpr_trans: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+ ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
+ ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
+[ #HT12 elim (fqu_cpr_trans … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
+| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
+]
+qed-.