partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / head / lift_rmap_head.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_rmap_head.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_rmap_head.etc
new file mode 100644 (file)
index 0000000..033a2c1
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_rmap_head.etc
@@ -0,0 +1,57 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/substitution/lift_rmap_eq.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* LIFT MAP FOR PATH ********************************************************)
+
+(* Constructions with path_head *********************************************)
+
+lemma tls_plus_lift_rmap_closed (f) (q) (n) (m):
+      q = ↳[n]q →
+      ⇂*[m]f ≗ ⇂*[n+m]↑[q]f.
+#f #q elim q -q
+[ #n #m #Hq
+  <(eq_inv_path_empty_head … Hq) -n //
+| #l #q #IH #n @(nat_ind_succ … n) -n //
+  #n #_ #m cases l [ #k ]
+  [ <path_head_d_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq <nrplus_inj_sn
+    @(stream_eq_trans … (tls_lift_rmap_d_dx …))
+    >nrplus_inj_dx >nrplus_inj_sn >nrplus_inj_sn <nplus_plus_comm_23
+    >nsucc_unfold /2 width=1 by/
+  | <path_head_m_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_m_dx /2 width=1 by/
+  | <path_head_L_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_L_dx <nplus_succ_sn /2 width=1 by/
+  | <path_head_A_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_A_dx /2 width=2 by/
+  | <path_head_S_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_S_dx /2 width=2 by/
+  ]
+]
+qed-.
+
+lemma tls_lift_rmap_closed (f) (q) (n):
+      q = ↳[n]q →
+      f ≗ ⇂*[n]↑[q]f.
+#f #q #n #H0
+/2 width=1 by tls_plus_lift_rmap_closed/
+qed.