- improved fqu allows to prove fqu_cpx_trans and its derivatives

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

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 645f59987be2fcf8278cc3c2d04d94985ea3f38d..c8aaacf06c83e47e5fd77219d175b55d36acb3bb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
@@ -12,35 +12,40 @@
 (*                                                                        *)
 (**************************************************************************)
 
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
+
+include "basic_2/s_computation/fqus_fqup.ma".
+include "basic_2/rt_transition/cpx_drops.ma".
+
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                     â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 →
-                     â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[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 
+lemma fqu_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                     â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h] U2 →
+                     â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[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/
-[ #I #G #L #V2 #U2 #HVU2
-  elim (lift_total U2 0 1)
-  /4 width=7 by fqu_drop, cpx_delta, drop_pair, drop_drop, ex2_intro/
-| #G #L #K #T1 #U1 #k #HLK1 #HTU1 #T2 #HTU2
-  elim (lift_total T2 0 (k+1))
-  /3 width=11 by cpx_lift, fqu_drop, 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 … HTU2 (Ⓣ) … (L2.ⓑ{I}V) … HTX2)
+  /3 width=3 by fqu_drop, drops_refl, drops_drop, ex2_intro/
 ]
 qed-.
 
-lemma fquq_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
-[ #HT12 elim (fqu_cpx_trans … HT12 … HTU2) /3 width=3 by fqu_fquq, ex2_intro/
+lemma fquq_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h] U2 →
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+#h #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,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+lemma fqup_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h] U2 →
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
+#h #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
@@ -49,18 +54,18 @@ lemma fqup_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2,
 ]
 qed-.
 
-lemma fqus_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fqus_inv_gen … H) -H
-[ #HT12 elim (fqup_cpx_trans … HT12 … HTU2) /3 width=3 by fqup_fqus, ex2_intro/
+lemma fqus_cpx_trans: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+                      â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h] U2 →
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+#h #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_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                         â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 → (T2 = U2 → ⊥) →
-                         â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
+                         â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h, o] U2 → (T2 = U2 → ⊥) →
+                         â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1)
   #U2 #HVU2 @(ex3_intro … U2)
@@ -88,8 +93,8 @@ lemma fqu_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L
 qed-.
 
 lemma fquq_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h, o] U2 → (T2 = U2 → ⊥) →
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fquq_inv_gen … H12) -H12
 [ #H12 elim (fqu_cpx_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -98,8 +103,8 @@ lemma fquq_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G
 qed-.
 
 lemma fqup_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
+                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h, o] U2 → (T2 = U2 → ⊥) →
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
 #h #o #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_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -110,11 +115,12 @@ lemma fqup_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2,
 qed-.
 
 lemma fqus_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡[h, o] U2 → (T2 = U2 → ⊥) →
-                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+                          â\88\80U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88[h, o] U2 → (T2 = U2 → ⊥) →
+                          â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_gen … H12) -H12
 [ #H12 elim (fqup_cpx_trans_neq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]
 qed-.
+*)
\ No newline at end of file