- strongly normalizing terms form a candidate of reducibility

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
index 4bacb47f6d7457db6462dc2a3ffcaf5e39bd11f5..82e21018e18e735dfd149b3a2bc3ec9443ee9a0f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
@@ -68,3 +68,66 @@ lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L
                         ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
 /3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-.
+
+(* Properties on supclosure *************************************************)
+
+lemma fqu_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
+                          ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[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)
+  [1,3: /3 width=7 by fqu_drop, cpxs_delta, drop_pair, drop_drop/
+  | #H destruct 
+    lapply (lift_inv_lref2_be … HVU2 ? ?) -HVU2 //
+  ]
+| #I #G #L #V1 #T #V2 #HV12 #H @(ex3_intro … (②{I}V2.T))
+  [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/
+  | #H0 destruct /2 width=1 by/
+  ]
+| #a #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓑ{a,I}V.T2))
+  [1,3: /2 width=4 by fqu_bind_dx, cpxs_bind/
+  | #H0 destruct /2 width=1 by/
+  ]
+| #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓕ{I}V.T2))
+  [1,3: /2 width=4 by fqu_flat_dx, cpxs_flat/
+  | #H0 destruct /2 width=1 by/
+  ]
+| #G #L #K #T1 #U1 #k #HLK #HTU1 #T2 #HT12 #H elim (lift_total T2 0 (k+1))
+  #U2 #HTU2 @(ex3_intro … U2)
+  [1,3: /2 width=10 by cpxs_lift, fqu_drop/
+  | #H0 destruct /3 width=5 by lift_inj/
+]
+qed-.
+
+lemma fquq_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
+                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[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_cpxs_trans_neq … 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_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
+                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[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_cpxs_trans_neq … 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
+  #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_neq … H1 … HTU1 H) -T1
+  /3 width=8 by fqup_strap2, ex3_intro/
+]
+qed-.
+
+lemma fqus_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
+                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[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_cpxs_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-.