update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
index 44ec5a36610d38f35e0893af7ec9c4d69311aeb8..70d41140bd2d28c7c71b5cd993b5a8c4ea2e42b0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
@@ -12,8 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
+(**) (* reverse include *)
 include "ground/lib/subset_ext_equivalence.ma".
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_path_eq.ma".
 include "delayed_updating/substitution/lift_prototerm.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
@@ -21,20 +22,34 @@ include "delayed_updating/substitution/lift_prototerm.ma".
 (* Constructions with subset_equivalence ************************************)
 
 lemma lift_term_eq_repl_sn (f1) (f2) (t):
-      f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
+      f1 ≗ f2 → 🠡[f1]t ⇔ 🠡[f2]t.
 /3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
 qed.
 
 lemma lift_term_eq_repl_dx (f) (t1) (t2):
-      t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
+      t1 ⇔ t2 → 🠡[f]t1 ⇔ 🠡[f]t2.
 /2 width=1 by subset_equivalence_ext_f1_bi/
 qed.
 
-lemma lift_term_after (f1) (f2) (t):
-      ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
-#f1 #f2 #t @subset_eq_trans
-[
-| @subset_inclusion_ext_f1_compose
-| @subset_equivalence_ext_f1_exteq /2 width=5/
-]
-qed. 
+lemma lift_term_grafted_sn (f) (t) (p):
+      🠡[🠢[f]p](t⋔p) ⊆ (🠡[f]t)⋔(🠡[f]p).
+#f #t #p #q * #r #Hr #H0 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lift_term_grafted_dx (f) (t) (p):
+      (🠡[f]t)⋔(🠡[f]p) ⊆ 🠡[🠢[f]p](t⋔p).
+#f #t #p #q * #r #Hr #H0
+elim (lift_path_inv_append_sn … (sym_eq … H0)) -H0
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+lapply (lift_path_inj … Hp0) -Hp0 #Hp0 destruct
+/2 width=1 by in_comp_lift_path_term/
+qed-.
+
+lemma lift_term_grafted (f) (t) (p):
+      🠡[🠢[f]p](t⋔p) ⇔ (🠡[f]t)⋔(🠡[f]p).
+/3 width=1 by lift_term_grafted_sn, lift_term_grafted_dx, conj/ qed.
+
+lemma lift_term_grafted_S (f) (t) (p):
+      🠡[🠢[f]p](t⋔(p◖𝗦)) ⇔ (🠡[f]t)⋔((🠡[f]p)◖𝗦).
+// qed.