update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
index 8143f860051118b38bbde6d5aa2e27ce6c7adb9c..d2bbd15be5b82421eba69572bf683b7fe41dd1aa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
@@ -55,31 +55,27 @@ lemma lift_grafted (f) (t) (p): p ϵ 𝐈 → p ϵ ▵t → t ϵ 𝐓 →
       ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(⊗p).
 /3 width=1 by lift_grafted_sn, conj, lift_grafted_dx/ qed.
 
-(*
 
--lemma lift_grafted_S_dx (f) (t) (p): p ϵ ▵t → t ϵ ������ →
--      (↑[f]t)⋔((⊗p)◖������) ⊆ ↑[↑[p]f](t⋔(p◖������)).
--#f #t #p #Hp #Ht #q * #r #Hr
--<list_append_rcons_sn #H0
--elim (lift_inv_append_proper_dx … (sym_eq … H0)) -H0 //
-+lemma lift_grafted_dx (f) (t) (p): p ϵ ������ → p ϵ ▵t → t ϵ ������ →
-+      (↑[f]t)⋔(⊗p) ⊆ ↑[↑[p]f](t⋔p).
-+#f #t #p #H1p #H2p #Ht #q * #r #Hr #H0
-+elim (lift_inv_append_inner_sn … (sym_eq … H0)) -H0 //
- #p0 #q0 #Hp0 #Hq0 #H0 destruct
- <(Ht … Hp0) [|*: /2 width=2 by ex_intro/ ] -p
--elim (lift_path_inv_S_sn … (sym_eq … Hq0)) -Hq0
--#r1 #r2 #Hr1 #Hr2 #H0 destruct
--lapply (preterm_in_root_append_inv_structure_empty_dx … p0 … Ht Hr1)
--[ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
- /2 width=1 by in_comp_lift_bi/
- qed-.
- 
--lemma lift_grafted_S (f) (t) (p): p ϵ ▵t → t ϵ ������ →
--      ↑[↑[p]f](t⋔(p◖������)) ⇔ (↑[f]t)⋔((⊗p)◖������).
--/3 width=1 by lift_grafted_S_sn, conj, lift_grafted_S_dx/ qed.
-+lemma lift_grafted (f) (t) (p): p ϵ ������ → p ϵ ▵t → t ϵ ������ →
-+      ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(⊗p).
-+/3 width=1 by lift_grafted_sn, conj, lift_grafted_dx/ qed.
+lemma lift_grafted_S_dx (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
+      (↑[f]t)⋔((⊗p)◖𝗦) ⊆ ↑[↑[p]f](t⋔(p◖𝗦)).
+#f #t #p #Hp #Ht #q * #r #Hr
+<list_append_rcons_sn #H0
+elim (lift_inv_append_proper_dx … (sym_eq … H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht … Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+elim (lift_path_inv_S_sn … (sym_eq … Hq0)) -Hq0
+#r1 #r2 #Hr1 #Hr2 #H0 destruct
+lapply (preterm_in_root_append_inv_structure_empty_dx … p0 … Ht Hr1)
+[ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
+/2 width=1 by in_comp_lift_bi/
+qed-.
 
-*)
+lemma lift_grafted_S (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
+      ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((⊗p)◖𝗦).
+#f #t #p #Hp #Ht
+@conj
+[ >lift_rmap_S_dx >structure_S_dx
+  @lift_grafted_sn //
+| /2 width=1 by lift_grafted_S_dx/
+]
+qed.