- exclusion binder in local environments

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lfpr_fquq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fquq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fquq.ma
index 72c313796c5f9e544c1dbe9fd89754cd05f6e0ae..79208e25ff69039fc3c728d19a876ae7e90b6539 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fquq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fquq.ma
@@ -14,6 +14,7 @@
 
 include "basic_2/s_transition/fquq.ma".
 include "basic_2/rt_transition/cpm_drops.ma".
+include "basic_2/rt_transition/cpm_lsubr.ma".
 include "basic_2/rt_transition/cpr.ma".
 include "basic_2/rt_transition/lfpr_fqup.ma".
 
@@ -21,41 +22,45 @@ include "basic_2/rt_transition/lfpr_fqup.ma".
 
 (* Properties with supclosure ***********************************************)
 
-lemma fqu_cpr_trans_dx: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+lemma fqu_cpr_trans_dx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
-                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 /3 width=5 by lfpr_pair, cpr_pair_sn, cpr_flat, cpm_bind, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ex3_2_intro/
-#I #G #L #V #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
-/3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
+[ /5 width=5 by lsubr_cpm_trans, cpm_bind, lsubr_unit, fqu_clear, ex3_2_intro/
+| #I #G #L #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
+  /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
+]
 qed-.
 
 (* Basic_2A1: uses: fqu_lpr_trans *)
-lemma fqu_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+lemma fqu_cpr_trans_sn: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
-                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 /3 width=5 by lfpr_pair, cpr_pair_sn, cpr_flat, cpm_bind, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ex3_2_intro/
-#I #G #L #V #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
-/3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
+[ /5 width=5 by lsubr_cpm_trans, cpm_bind, lsubr_unit, fqu_clear, ex3_2_intro/
+| #I #G #L #U #T #HUT #U2 #HU2 elim (cpm_lifts_sn … HU2 (Ⓣ) … HUT) -U
+  /3 width=9 by fqu_drop, drops_refl, drops_drop, ex3_2_intro/
+]
 qed-.
 
 (* Properties with optional supclosure **************************************)
 
-lemma fquq_cpr_trans_dx: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpr_trans_dx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
-                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
+                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
 ]
 qed-.
 
 (* Basic_2A1: uses: fquq_lpr_trans *)
-lemma fquq_cpr_trans_sn: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpr_trans_sn: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h] U2 →
-                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
+                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[h, T1] L & ⦃G1, L1⦄ ⊢ T1 ➡[h] U1 & ⦃G1, L, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
 [ #HT12 #U2 #HTU2 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
 ]