update in ground and delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / nap.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/nap.ma b/matita/matita/contribs/lambdadelta/ground/relocation/nap.ma
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+++ b/matita/matita/contribs/lambdadelta/ground/relocation/nap.ma
@@ -0,0 +1,51 @@
+include "ground/relocation/tr_uni_pap.ma".
+include "ground/relocation/tr_compose_pap.ma".
+include "ground/notation/functions/applysucc_2.ma".
+include "ground/arith/nat_lt.ma".
+include "ground/arith/nat_plus_rplus.ma".
+include "ground/arith/nat_pred_succ.ma".
+
+lemma nlt_npsucc_bi (n1) (n2):
+      n1 < n2 → npsucc n1 < npsucc n2.
+#n1 #n2 #Hn elim Hn -n2 //
+#n2 #_ #IH /2 width=1 by plt_succ_dx_trans/
+qed.
+
+definition tr_nap (f) (l:nat): nat ≝
+           ↓(f＠⧣❨↑l❩).
+
+interpretation
+  "functional non-negative application (total relocation maps)"
+  'ApplySucc f l = (tr_nap f l).
+
+lemma tr_nap_unfold (f) (l):
+      ↓(f＠⧣❨↑l❩) = f@↑❨l❩.
+// qed.
+
+lemma tr_compose_nap (f2) (f1) (l):
+      f2@↑❨f1@↑❨l❩❩ = (f2∘f1)@↑❨l❩.
+#f2 #f1 #l
+<tr_nap_unfold <tr_nap_unfold <tr_nap_unfold
+<tr_compose_pap <npsucc_pred //
+qed.
+
+lemma tr_uni_nap (n) (m):
+      m + n = 𝐮❨n❩@↑❨m❩.
+#n #m
+<tr_nap_unfold
+<tr_uni_pap <nrplus_npsucc_sn //
+qed.
+
+lemma tr_nap_push (f):
+      ∀l. ↑(f@↑❨l❩) = (⫯f)@↑❨↑l❩.
+#f #l
+<tr_nap_unfold <tr_nap_unfold
+<tr_pap_push <pnpred_psucc //
+qed.
+
+lemma tr_nap_pushs_lt (f) (n) (m):
+      m < n → m = (⫯*[n]f)@↑❨m❩.
+#f #n #m #Hmn
+<tr_nap_unfold <tr_pap_pushs_le
+/2 width=1 by nlt_npsucc_bi/
+qed-.