some renaming ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_ldrop.ma
index 57459d1a718a457f52b87b9c0bd814caf1db33e9..705d5695e3b2ff2e441bf37411e6bebaac1da058 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_ldrop.ma
@@ -20,11 +20,59 @@ include "basic_2/reduction/lpx.ma".
 
 (* Properies on local environment slicing ***********************************)
 
-lemma lpx_ldrop_conf: ∀h,g. dropable_sn (lpx h g).
+lemma lpx_ldrop_conf: ∀h,g,G. dropable_sn (lpx h g G).
 /3 width=5 by lpx_sn_deliftable_dropable, cpx_inv_lift1/ qed-.
 
-lemma ldrop_lpx_trans: ∀h,g. dedropable_sn (lpx h g).
+lemma ldrop_lpx_trans: ∀h,g,G. dedropable_sn (lpx h g G).
 /3 width=9 by lpx_sn_liftable_dedropable, cpx_lift/ qed-.
 
-lemma lpx_ldrop_trans_O1: ∀h,g. dropable_dx (lpx h g).
+lemma lpx_ldrop_trans_O1: ∀h,g,G. dropable_dx (lpx h g G).
 /2 width=3 by lpx_sn_dropable/ qed-.
+
+(* Properties on supclosure *************************************************)
+
+lemma fqu_lpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                     ∀K2. ⦃G2, L2⦄ ⊢ ➡[h, g] K2 →
+                     ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h, g] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T & ⦃G1, K1, T⦄ ⊃ ⦃G2, K2, T2⦄.
+#h #g #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_flat_dx, lpx_pair, ex3_2_intro/
+[ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpx_inv_pair1 … H) -H
+  #K2 #W2 #HLK2 #HVW2 #H destruct
+  /3 width=5 by fqu_fquq, cpx_pair_sn, fqu_bind_dx, ex3_2_intro/
+| #G #L1 #K1 #T1 #U1 #e #HLK1 #HTU1 #K2 #HK12
+  elim (ldrop_lpx_trans … HLK1 … HK12) -HK12
+  /3 width=7 by fqu_drop, ex3_2_intro/
+]
+qed-.
+
+lemma fquq_lpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                      ∀K2. ⦃G2, L2⦄ ⊢ ➡[h, g] K2 →
+                      ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h, g] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T & ⦃G1, K1, T⦄ ⊃⸮ ⦃G2, K2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 elim (fquq_inv_gen … H) -H
+[ #HT12 elim (fqu_lpx_trans … HT12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/
+| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
+]
+qed-.
+
+lemma lpx_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                     ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 →
+                     ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[h, g] T & ⦃G1, K1, T⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+/3 width=7 by fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpx_pair, ex3_2_intro/
+[ #I #G1 #L1 #V1 #X #H elim (lpx_inv_pair2 … H) -H
+  #K1 #W1 #HKL1 #HWV1 #H destruct elim (lift_total V1 0 1)
+  /4 width=7 by cpx_delta, fqu_drop, ldrop_ldrop, ex3_2_intro/
+| #G #L1 #K1 #T1 #U1 #e #HLK1 #HTU1 #L0 #HL01
+  elim (lpx_ldrop_trans_O1 … HL01 … HLK1) -L1
+  /3 width=5 by fqu_drop, ex3_2_intro/
+]
+qed-.
+
+lemma lpx_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                      ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 →
+                      ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[h, g] T & ⦃G1, K1, T⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 elim (fquq_inv_gen … H) -H
+[ #HT12 elim (lpx_fqu_trans … HT12 … HKL1) /3 width=5 by fqu_fquq, ex3_2_intro/
+| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
+]
+qed-.