update in delayed_updating

+ new operator on update functions

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.ma
new file mode 100644 (file)
index 0000000..4232017
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ground/arith/pnat_minus.ma".
+include "ground/arith/nat_minus.ma".
+include "ground/relocation/tr_map.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+corec definition tr_minus: nat → tr_map → tr_map.
+* [ #f @f ] #q * #p #f
+@((p-q)⨮(tr_minus (ninj (↑q)-ninj p) f))
+defined.
+
+interpretation
+  "right minus (total relocation maps)"
+  'minus f n = (tr_minus n f).
+
+(* Basic constructions ******************************************************)
+
+lemma tr_minus_zero_dx (f):
+      f = f - 𝟎 .
+* #f #p <(stream_unfold … ((f⨮p)-𝟎)) //
+qed.
+
+lemma tr_minus_cons_inj (f) (p) (q):
+      (p-q)⨮(f-(ninj (↑q)-ninj p)) = (p⨮f)-(ninj q).
+#f #p #q <(stream_unfold … ((p⨮f)-(ninj q))) //
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma
new file mode 100644 (file)
index 0000000..46a7696
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_eq.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/tr_minus.ma".
+include "ground/lib/stream_eq.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+(* Constructions with tr_eq *************************************************)
+
+corec lemma tr_minus_eq_repl (n):
+            stream_eq_repl … (λf1,f2. f1-n ≗ f2-n).
+cases n -n
+[ #f1 #f2 #Hf -tr_minus_eq_repl //
+| #q * #p1 #f1 * #p2 #f2 #Hf
+  cases (stream_eq_inv_cons_bi … Hf) -Hf  [|*: // ] * #Hf -p2
+  cases tr_minus_cons_inj cases tr_minus_cons_inj
+  @stream_eq_cons //
+  @tr_minus_eq_repl //
+]
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pap.ma
new file mode 100644 (file)
index 0000000..f27e43c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pap.ma
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/tr_minus_pn.ma".
+include "ground/relocation/tr_pap_pn.ma".
+include "ground/relocation/tr_pap_lt.ma".
+include "ground/arith/nat_rplus_succ.ma".
+include "ground/arith/pnat_le.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+(* Constructions with tr_pap ************************************************)
+
+lemma tr_pap_minus_le (n) (p) (f):
+      f＠⧣❨p❩ ≤ p + n →
+      p = (f-n)＠⧣❨p❩.
+#n @(nat_ind_succ … n) -n [| #n #IHn ]
+[ #p #f #H1f
+  lapply (tr_pap_increasing f p) #H2f
+  >(ple_antisym … H2f H1f) in ⊢ (??%?); -H1f -H2f //
+| #p elim p -p [| #p #IHp ]
+  #f elim (tr_map_split f) * #g #H0 destruct
+  [ //
+  |2,4:
+    <tr_pap_next <nrplus_succ_dx #Hf
+    lapply (ple_inv_succ_bi … Hf) -Hf #Hf
+    <tr_minus_next_succ /2 width=1 by/
+  | <tr_minus_push_succ <tr_pap_push <tr_pap_push <nrplus_succ_sn #Hf
+    lapply (ple_inv_succ_bi … Hf) -Hf #Hf
+    <IHp -IHp //
+  ]
+]
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma
new file mode 100644 (file)
index 0000000..0bff109
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus_pn.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/tr_minus.ma".
+include "ground/relocation/tr_pn.ma".
+include "ground/arith/nat_succ.ma".
+
+(* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
+
+(* Constructions with tr_push ***********************************************)
+
+lemma tr_minus_push_succ (f) (n):
+      (⫯(f-↑n)) = (⫯f)-↑n.
+#f #n <tr_minus_cons_inj //
+qed.
+
+(* Constructions with tr_next ***********************************************)
+
+lemma tr_minus_next_succ (n) (f:tr_map):
+      f-n = (↑f)-↑n.
+* [| #n ] * #p #f
+<tr_minus_cons_inj //
+<tr_minus_cons_inj //
+qed.