X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpx_fqus.ma;h=147114a113181412e76e273831d305c951c0373f;hb=21827c7db90ddb4fd30adec6becd94e201898f9c;hp=453d2b5e1749b26ac653a1c50b13a5fa5fd19939;hpb=86d7622f88247d83b2c366a722d2994a4af91929;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
index 453d2b5e1..147114a11 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
@@ -17,36 +17,38 @@
 include "basic_2/relocation/lifts_tdeq.ma".
 include "basic_2/s_computation/fqus_fqup.ma".
 include "basic_2/rt_transition/cpx_drops.ma".
+include "basic_2/rt_transition/cpx_lsubr.ma".
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+lemma fqu_cpx_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                      ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 →
-                     ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=3 by fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, cpx_pair_sn, cpx_bind, cpx_flat, ex2_intro/
+                     ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+/3 width=3 by cpx_pair_sn, cpx_bind, cpx_flat, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ex2_intro/
 [ #I #G #L2 #V2 #X2 #HVX2
   elim (lifts_total X2 (𝐔❴1❵))
   /3 width=3 by fqu_drop, cpx_delta, ex2_intro/
-| #I #G #L2 #V #T2 #X2 #HTX2 #U2 #HTU2
-  elim (cpx_lifts_sn … HTU2 (Ⓣ) … (L2.ⓑ{I}V) … HTX2)
+| /5 width=4 by lsubr_cpx_trans, cpx_bind, lsubr_unit, fqu_clear, ex2_intro/
+| #I #G #L2 #T2 #X2 #HTX2 #U2 #HTU2
+  elim (cpx_lifts_sn … HTU2 (Ⓣ) … (L2.ⓘ{I}) … HTX2)
   /3 width=3 by fqu_drop, drops_refl, drops_drop, ex2_intro/
 ]
 qed-.
 
-lemma fquq_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpx_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H
 [ #HT12 #U2 #HTU2 elim (fqu_cpx_trans … HT12 … HTU2) /3 width=3 by fqu_fquq, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fqup_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+lemma fqup_cpx_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 [ #G2 #L2 #T2 #H12 #U2 #HTU2 elim (fqu_cpx_trans … H12 … HTU2) -T2
   /3 width=3 by fqu_fqup, ex2_intro/
 | #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
@@ -55,19 +57,19 @@ lemma fqup_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T
 ]
 qed-.
 
-lemma fqus_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+lemma fqus_cpx_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_fqup … H) -H
 [ #HT12 #U2 #HTU2 elim (fqup_cpx_trans … HT12 … HTU2) /3 width=3 by fqup_fqus, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fqu_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+lemma fqu_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 𝐔❴1❵)
   #U2 #HVU2 @(ex3_intro … U2)
   [1,3: /3 width=7 by cpx_delta, fqu_drop/
@@ -82,30 +84,34 @@ lemma fqu_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2,
   [1,3: /2 width=4 by fqu_bind_dx, cpx_bind/
   | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
+| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
+  [1,3: /4 width=4 by lsubr_cpx_trans, cpx_bind, lsubr_unit, fqu_clear/
+  | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
+  ]
 | #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓕ{I}V.T2))
   [1,3: /2 width=4 by fqu_flat_dx, cpx_flat/
   | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
-| #I #G #L #V #T1 #U1 #HTU1 #T2 #HT12 #H0
-  elim (cpx_lifts_sn … HT12 (Ⓣ) … (L.ⓑ{I}V) … HTU1) -HT12
+| #I #G #L #T1 #U1 #HTU1 #T2 #HT12 #H0
+  elim (cpx_lifts_sn … HT12 (Ⓣ) … (L.ⓘ{I}) … HTU1) -HT12
   /4 width=6 by fqu_drop, drops_refl, drops_drop, tdeq_inv_lifts_bi, ex3_intro/
 ]
 qed-.
 
-lemma fquq_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12 
+                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12 
 [ #H12 #U2 #HTU2 #H elim (fqu_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]
 qed-.
 
-lemma fqup_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+lemma fqup_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
+                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
 | #G #G1 #L #L1 #T #T1 #H1 #_ #IH12 #U2 #HTU2 #H elim (IH12 … HTU2 H) -T2
@@ -114,10 +120,10 @@ lemma fqup_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G
 ]
 qed-.
 
-lemma fqus_cpx_trans_ntdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+lemma fqus_cpx_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
-                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
+                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
 [ #H12 elim (fqup_cpx_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/