update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / ibfr_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma
index 2a98609ad69ee662ded9f6c78296e4a88e6adc83..112a98c3918eae4fd3d86fc64505d06cd575d790 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma
@@ -68,8 +68,11 @@ lemma ibfr_beta_0 (v) (t) (q) (n):
       q ϵ 𝐂❨Ⓕ,n❩ → q◖𝗱↑n ϵ t →
       ＠v.𝛌.t ➡𝐢𝐛𝐟[𝗔◗𝗟◗q] ＠v.𝛌.(t[⋔q←🠡[𝐮❨↑n❩]v]).
 #v #t #q #n #Hn #Ht
-@(ex6_5_intro … (𝐞) (𝐞) q (𝟎) … Hn) -Hn //
-[ /3 width=1 by in_comp_appl_hd, in_comp_abst_hd/
+@(ex6_5_intro … (𝐞) (𝐞) q (𝟎) … Hn) -Hn
+[ //
+| //
+| //
+| /3 width=1 by in_comp_appl_hd, in_comp_abst_hd/
 | @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
   @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
   @fsubst_eq_repl // <nplus_zero_sn @lift_term_eq_repl_dx
@@ -77,3 +80,22 @@ lemma ibfr_beta_0 (v) (t) (q) (n):
   @(subset_eq_canc_sn … (grafted_empty_dx … )) //
 ]
 qed.
+
+lemma ibfr_beta_1 (v) (v1) (t) (q) (n):
+      q ϵ 𝐂❨Ⓕ,n❩ → q◖𝗱↑n ϵ t →
+      ＠v.＠v1.𝛌.𝛌.t ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝗟◗q] ＠v.＠v1.𝛌.𝛌.(t[⋔q←🠡[𝐮❨↑↑n❩]v]).
+#v #v1 #t #q #n #Hn #Ht
+@(ex6_5_intro … (𝐞) (𝗔◗𝗟◗𝐞) q (𝟏) … Hn) -Hn
+[ //
+| /2 width=1 by pbc_empty, pbc_redex/
+| /3 width=1 by pcc_A_sn, pcc_L_sn, pcc_empty/
+| /5 width=1 by in_comp_appl_hd, in_comp_abst_hd/
+| @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @fsubst_eq_repl // <nplus_unit_sn @lift_term_eq_repl_dx
+  >list_cons_comm @(subset_eq_canc_sn … (grafted_appl_sd … ))
+  @(subset_eq_canc_sn … (grafted_empty_dx … )) //
+]
+qed.