- new component "s_transition" for the restored fqu and fquq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpx_frees.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_frees.ma
index 6f4aac874a2906db0f775fcb89d24364a0f9811f..fa314630db3645da0e409f57bfebffc7ceaeb8fb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_frees.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_frees.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/multiple/frees_leq.ma".
+include "basic_2/multiple/frees_lreq.ma".
 include "basic_2/multiple/frees_lift.ma".
 include "basic_2/reduction/lpx_drop.ma".
 
@@ -20,13 +20,13 @@ include "basic_2/reduction/lpx_drop.ma".
 
 (* Properties on context-sensitive free variables ***************************)
 
-lemma lpx_cpx_frees_trans: ∀h,g,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2 →
-                           ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+lemma lpx_cpx_frees_trans: ∀h,o,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ➡[h, o] U2 →
+                           ∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 →
                            ∀i. L2 ⊢ i ϵ 𝐅*[0]⦃U2⦄ → L1 ⊢ i ϵ 𝐅*[0]⦃U1⦄.
-#h #g #G #L1 #U1 @(fqup_wf_ind_eq … G L1 U1) -G -L1 -U1
+#h #o #G #L1 #U1 @(fqup_wf_ind_eq … G L1 U1) -G -L1 -U1
 #G0 #L0 #U0 #IH #G #L1 * *
-[ -IH #k #HG #HL #HU #U2 #H1 #L2 #_ #i #H2 elim (cpx_inv_sort1 … H1) -H1
-  [| * #l #_ ] #H destruct elim (frees_inv_sort … H2)
+[ -IH #s #HG #HL #HU #U2 #H1 #L2 #_ #i #H2 elim (cpx_inv_sort1 … H1) -H1
+  [| * #d #_ ] #H destruct elim (frees_inv_sort … H2)
 | #j #HG #HL #HU #U2 #H1 #L2 #HL12 #i #H2 elim (cpx_inv_lref1 … H1) -H1
   [ #H destruct elim (frees_inv_lref … H2) -H2 //
     * #I #K2 #W2 #Hj #Hji #HLK2 #HW2
@@ -36,10 +36,10 @@ lemma lpx_cpx_frees_trans: ∀h,g,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2 
   | * #I #K1 #W1 #W0 #HLK1 #HW10 #HW0U2
     lapply (drop_fwd_drop2 … HLK1) #H0
     elim (lpx_drop_conf … H0 … HL12) -H0 -HL12 #K2 #HK12 #HLK2
-    elim (lt_or_ge i (j+1)) #Hji
-    [ -IH elim (frees_inv_lift_be … H2 … HLK2 … HW0U2) /2 width=1 by monotonic_pred/
-    | lapply (frees_inv_lift_ge … H2 … HLK2 … HW0U2 ?) -L2 -U2 // <minus_plus destruct
-      /4 width=11 by frees_lref_be, fqup_lref/
+    elim (ylt_split i (j+1)) >yplus_SO2 #Hji
+    [ -IH elim (frees_inv_lift_be … H2 … HLK2 … HW0U2) /2 width=1 by ylt_fwd_succ2/
+    | lapply (frees_inv_lift_ge … H2 … HLK2 … HW0U2 ?) -L2 -U2 // destruct
+      /4 width=11 by frees_lref_be, fqup_lref, yle_succ1_inj/
     ]
   ]
 | -IH #p #HG #HL #HU #U2 #H1 >(cpx_inv_gref1 … H1) -H1 destruct
@@ -63,7 +63,7 @@ lemma lpx_cpx_frees_trans: ∀h,g,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2 
     elim (frees_inv_bind … Hi) -Hi #Hi
     [ elim (frees_inv_flat … Hi) -Hi
       /4 width=7 by frees_flat_dx, frees_flat_sn, frees_bind_sn/
-    | lapply (leq_frees_trans … Hi (L2.ⓛV2) ?) /2 width=1 by leq_succ/ -Hi #HU2
+    | lapply (lreq_frees_trans … Hi (L2.ⓛV2) ?) /2 width=1 by lreq_succ/ -Hi #HU2
       lapply (frees_weak … HU2 0 ?) -HU2
       /5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/
     ]
@@ -80,9 +80,9 @@ lemma lpx_cpx_frees_trans: ∀h,g,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2 
 ]
 qed-.
 
-lemma cpx_frees_trans: ∀h,g,G. frees_trans (cpx h g G).
+lemma cpx_frees_trans: ∀h,o,G. frees_trans (cpx h o G).
 /2 width=8 by lpx_cpx_frees_trans/ qed-.
 
-lemma lpx_frees_trans: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+lemma lpx_frees_trans: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 →
                        ∀U,i. L2 ⊢ i ϵ 𝐅*[0]⦃U⦄ → L1 ⊢ i ϵ 𝐅*[0]⦃U⦄.
 /2 width=8 by lpx_cpx_frees_trans/ qed-.