renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubf_frees.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.ma
index 47fc2f75ec691cd66c02678c213a57ce4adc5b4b..390e6f13a368c47fb2b4b42f80506dba3f179ece 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.ma
@@ -18,34 +18,34 @@ include "basic_2/static/lsubf.ma".
 
 (* Properties with context-sensitive free variables *************************)
 
-axiom lsubf_frees_trans: ∀f2,L2,T. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 → ∀f,L1. ⦃L1, f⦄ ⫃𝐅* ⦃L2, f2⦄ →
-                         ∃∃f1. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 & f1 ⊆ f.
-(*
+lemma lsubf_frees_trans: ∀f2,L2,T. L2 ⊢ 𝐅*⦃T⦄ ≘ f2 →
+                         ∀f1,L1. ⦃L1, f1⦄ ⫃𝐅* ⦃L2, f2⦄ → L1 ⊢ 𝐅*⦃T⦄ ≘ f1.
 #f2 #L2 #T #H elim H -f2 -L2 -T
-[ #f2 #I #Hf2 #f #L1 #H elim (lsubf_inv_atom2 … H) -H
-  #H #_ destruct /3 width=3 by frees_atom, sle_isid_sn, ex2_intro/
-| #f2 #I #K2 #W #s #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
-  [ #K1 #_ #H12 #H | #g #K1 #V #Hg #Hf #_ #H12 #H1 #H2 ]
-  destruct elim (IH … H12) -K2
-  /3 width=3 by frees_sort, sle_inv_tl_dx, ex2_intro/
-| #f2 #I #K2 #W #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
-  [ #K1 #H elim (sle_inv_nx … H ??) -H [ <tl_next_rew |*: // ]
-    #g2 #_ #H1 #H12 #H2 destruct elim (IH … H12) -K2
-    /3 width=7 by frees_zero, sle_next, ex2_intro/
-  | #g #K1 #V #Hg <tl_next_rew #Hf lapply (sor_sym … Hf) -Hf
-    #Hf #H elim (sle_inv_nx … H ??) -H [|*: // ]
-    #g2 #_ #H1 #H12 #H2 #H3 destruct elim (IH … H12) -K2
-    #f1 #Hf1 elim (sor_isfin_ex … f1 g ??)
-    /5 width=10 by frees_fwd_isfin, frees_flat, frees_zero, monotonic_sle_sor, sor_inv_sle_dx, sor_sym, sor_sle_sn, sle_next, ex2_intro/
+[ /3 width=5 by lsubf_fwd_isid_dx, frees_sort/
+| #f2 #i #Hf2 #g1 #Y1 #H
+  elim (lsubf_inv_atom2 … H) -H #Hg1 #H destruct
+  elim (eq_inv_pushs_dx … Hg1) -Hg1 #g #Hg #H destruct
+  elim (eq_inv_xn … Hg) -Hg
+  /3 width=3 by frees_atom, isid_eq_repl_fwd/
+| #f2 #I #K2 #W #_ #IH #g1 #Y1 #H elim (lsubf_inv_pair2 … H) -H *
+  [ #f1 #K1 #H12 #H1 #H2 destruct /3 width=1 by frees_pair/
+  | #f #f0 #f1 #K1 #V #H12 #Hf #Hf1 #H1 #H2 #H3 destruct
+    /4 width=5 by frees_pair, frees_flat/
   ]
-| #f2 #I #K2 #W #i #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
-  [ #K1 #_ #H12 #H | #g #K1 #V #Hg #Hf #_ #H12 #H1 #H2 ]
-  destruct elim (IH … H12) -K2
-  /3 width=3 by frees_lref, sle_inv_tl_dx, ex2_intro/
-| #f2 #I #K2 #W #l #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
-  [ #K1 #_ #H12 #H | #g #K1 #V #Hg #Hf #_ #H12 #H1 #H2 ]
-  destruct elim (IH … H12) -K2
-  /3 width=3 by frees_gref, sle_inv_tl_dx, ex2_intro/
-| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
-| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
-*)
+| #f2 #I #L2 #Hf2 #g1 #Y1 #H elim (lsubf_inv_unit2 … H) -H *
+  [ #f1 #L1 #H12 #H1 #H2 destruct
+    /3 width=5 by lsubf_fwd_isid_dx, frees_unit/
+  | #f #f0 #f1 #J #L1 #V #H12 #Hf #Hf1 #H1 #H2 destruct
+    /5 width=9 by lsubf_fwd_isid_dx, frees_eq_repl_back, frees_pair, sor_isid_inv_sn/
+  ]
+| #f2 #I #L2 #i #_ #IH #g1 #L1 #H elim (lsubf_inv_push2 … H) -H
+  /3 width=1 by frees_lref/
+| /3 width=5 by lsubf_fwd_isid_dx, frees_gref/
+| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+  elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 #f1V #g1T #HV #HT #Hf1
+  elim (lsubf_bind_tl_dx … (BPair I V) … HT) -HT #f1T #HT #H destruct
+  /3 width=5 by frees_bind/
+| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+  elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 /3 width=5 by frees_flat/
+]
+qed-.