- commit of the "s_computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
index 494eee301d0e4750c8f12a8e6cfc005834709782..1d5a3e778afeedb73f2b54c4ec2823e518c5c5c1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -20,19 +20,19 @@ include "basic_2/computation/cpxs.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpxs_delta: ∀h,g,I,G,L,K,V,V2,i.
-                  ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, g] V2 →
-                  ∀W2. ⬆[0, i+1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2.
-#h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2
+lemma cpxs_delta: ∀h,o,I,G,L,K,V,V2,i.
+                  ⬇[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, o] V2 →
+                  ∀W2. ⬆[0, i+1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, o] W2.
+#h #o #I #G #L #K #V #V2 #i #HLK #H elim H -V2
 [ /3 width=9 by cpx_cpxs, cpx_delta/
 | #V1 lapply (drop_fwd_drop2 … HLK) -HLK
   elim (lift_total V1 0 (i+1)) /4 width=12 by cpx_lift, cpxs_strap1/
 ]
 qed.
 
-lemma lstas_cpxs: ∀h,g,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
-                  ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, g] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
-#h #g #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
+lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
+                  ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2.
+#h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
 [ /3 width=3 by cpxs_sort, da_inv_sort/
 | #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
   elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
@@ -50,11 +50,11 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_lref1: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, g] T2 →
+lemma cpxs_inv_lref1: ∀h,o,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, o] T2 →
                       T2 = #i ∨
-                      ∃∃I,K,V1,T1. ⬇[i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 &
+                      ∃∃I,K,V1,T1. ⬇[i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, o] T1 &
                                    ⬆[0, i+1] T1 ≡ T2.
-#h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
+#h #o #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
 [ #H destruct
   elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
@@ -68,57 +68,57 @@ qed-.
 
 (* Relocation properties ****************************************************)
 
-lemma cpxs_lift: ∀h,g,G. d_liftable (cpxs h g G).
+lemma cpxs_lift: ∀h,o,G. d_liftable (cpxs h o G).
 /3 width=10 by cpx_lift, cpxs_strap1, d_liftable_LTC/ qed.
 
-lemma cpxs_inv_lift1: ∀h,g,G. d_deliftable_sn (cpxs h g G).
+lemma cpxs_inv_lift1: ∀h,o,G. d_deliftable_sn (cpxs h o G).
 /3 width=6 by d_deliftable_sn_LTC, cpx_inv_lift1/
 qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+lemma fqu_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, o] U2 →
                       ∀T1. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
+#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fquq_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+lemma fquq_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H
 [ #HT12 elim (fqu_cpxs_trans … HTU2 … HT12) /3 width=3 by fqu_fquq, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fquq_lstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
                         ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
-                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] d2 → d1 ≤ d2 →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
+                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
 /3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-.
 
-lemma fqup_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+lemma fqup_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
+#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqus_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+lemma fqus_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H
 [ #HT12 elim (fqup_cpxs_trans … HTU2 … HT12) /3 width=3 by fqup_fqus, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fqus_lstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
                         ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
-                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, g] d2 → d1 ≤ d2 →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+                        ∀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-.