update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / fsubst_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
index c9d6560286a32f854e2577852c8a4b6e261e9811..bf5c9b6f660346131dd52ad058b14545fc059bcd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -13,35 +13,38 @@
 (**************************************************************************)
 
 include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
 include "delayed_updating/substitution/lift_structure.ma".
 include "delayed_updating/syntax/preterm.ma".
 include "delayed_updating/syntax/prototerm_proper.ma".
 
 (* FOCALIZED SUBSTITUTION ***************************************************)
 
-lemma lift_fsubst_sn (f) (t) (u) (p): Ꝕu → p ⧸ϵ t →
+lemma lift_fsubst_sn (f) (t) (u) (p): u ϵ 𝐏 →
       (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u] ⊆ ↑[f](t[⋔p←u]).
-#f #t #u #p #Hu #Hp #ql * *
+#f #t #u #p #Hu #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
   >lift_append_proper_dx
-  /4 width=1 by subset_in_ext_f1_dx, or_introl/
+  /4 width=5 by in_comp_lift_bi, in_ppc_comp_trans, or_introl, ex2_intro/
 | * #q #Hq #H1 #H0
-  @(ex2_intro … H1) @or_intror @conj //
-  #r #H2 destruct
-  @H0 -H0 [| <lift_append_proper_dx /2 width=1 by/ ]
+  @(ex2_intro … H1) @or_intror @conj // *
+  [ <list_append_empty_dx #H2 destruct
+    elim (lift_path_root f q) #r #_ #Hr /2 width=2 by/
+  | #l #r #H2 destruct
+    @H0 -H0 [| <lift_append_proper_dx /2 width=3 by ppc_lcons/ ]
+  ]
 ]
 qed-.
 
-lemma lift_fsubst_dx (f) (t) (u) (p): Ꝕu → p ϵ ▵t → structure_injective t →
+lemma lift_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       ↑[f](t[⋔p←u]) ⊆ (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u].
 #f #t #u #p #Hu #H1p #H2p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
-  [|| <lift_append_proper_dx /2 width=1 by/ ]
+  [|| <lift_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
   /2 width=3 by ex2_intro/
 | #Hq #H0 #H1 destruct
-  @or_intror @conj [ /2 width=1 by subset_in_ext_f1_dx/ ] *
+  @or_intror @conj [ /2 width=1 by in_comp_lift_bi/ ] *
   [ <list_append_empty_dx #Hr @(H0 … (𝐞)) -H0
     <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
   | #l #r #Hr
@@ -51,6 +54,6 @@ lemma lift_fsubst_dx (f) (t) (u) (p): Ꝕu → p ϵ ▵t → structure_injective
 ]
 qed-.
 
-lemma lift_fsubst (f) (t) (u) (p): Ꝕu → p ⧸ϵ t → p ϵ ▵t → structure_injective t →
+lemma lift_fsubst (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       (↑[f]t)[⋔(⊗p)←↑[↑[p]f]u] ⇔ ↑[f](t[⋔p←u]).
 /4 width=3 by lift_fsubst_sn, conj, lift_fsubst_dx/ qed.