new definition of lleq allows to complete the proof of lemma 1000

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
index 412d422078cb9a08074e3ba50698526c5243629b..29bc6a97562d8b6c6ea408c360f9357a8a74cfd1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_ldrop.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/fsup.ma".
+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".
@@ -22,24 +22,33 @@ 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 fsup_cpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ➡ U2 →
-                      ∃∃L,U1. L1 ⊢ ➡ L & L ⊢ T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
-#L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
-#L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
-elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HT2
-elim (lift_total T d e) #U #HTU
-elim (ldrop_lpr_trans … HLK1 … HK1) -HLK1 -HK1 #L2 #HL12 #HL2K
-lapply (cpr_lift … HT1 … HL2K … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
+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-.