update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/tr_pap.ma b/matita/matita/contribs/lambdadelta/ground/relocation/tr_pap.ma
index 7acf280d27780a30b39e24f851a31da035cca2ff..9dfe0c18e4a8c58babe2773923d10b8116a05719 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/tr_pap.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/tr_pap.ma
@@ -12,8 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/notation/functions/apply_2.ma".
-include "ground/relocation/tr_pat.ma".
+include "ground/notation/functions/atsharp_2.ma".
+include "ground/arith/pnat_plus.ma".
+include "ground/relocation/tr_map.ma".
 
 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
 
@@ -28,61 +29,16 @@ defined.
 
 interpretation
   "functional positive application (total relocation maps)"
-  'Apply f i = (tr_pap i f).
+  'AtSharp f i = (tr_pap i f).
 
-(* Constructions with pr_pat ***********************************************)
+(* Basic constructions ******************************************************)
 
-(*** at_total *)
-lemma tr_pat_total: ∀i1,f. @❨i1,𝐭❨f❩❩ ≘ f@❨i1❩.
-#i1 elim i1 -i1
-[ * // | #i #IH * /3 width=1 by pr_pat_succ_sn/ ]
-qed.
-
-(* Inversions with pr_pat ***************************************************)
-
-lemma at_inv_total: ∀f,i1,i2. @❨i1, f❩ ≘ i2 → f@❨i1❩ = i2.
-/2 width=6 by fr2_nat_mono/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma apply_O1: ∀p,f. (p⨮f)@❨𝟏❩ = p.
+(*** apply_O1 *)
+lemma tr_cons_pap_unit (f):
+      ∀p. p = (p⨮f)＠⧣❨𝟏❩.
 // qed.
 
-lemma apply_S1: ∀p,f,i. (p⨮f)@❨↑i❩ = f@❨i❩+p.
+(*** apply_S1 *)
+lemma tr_cons_pap_succ (f):
+      ∀p,i. f＠⧣❨i❩+p = (p⨮f)＠⧣❨↑i❩.
 // qed.
-
-lemma apply_eq_repl (i): gr_eq_repl … (λf1,f2. f1@❨i❩ = f2@❨i❩).
-#i elim i -i [2: #i #IH ] * #p1 #f1 * #p2 #f2 #H
-elim (eq_inv_seq_aux … H) -H #Hp #Hf //
->apply_S1 >apply_S1 /3 width=1 by eq_f2/
-qed.
-
-lemma apply_S2: ∀f,i. (↑f)@❨i❩ = ↑(f@❨i❩).
-* #p #f * //
-qed.
-
-(* Main inversion lemmas ****************************************************)
-
-theorem apply_inj: ∀f,i1,i2,j. f@❨i1❩ = j → f@❨i2❩ = j → i1 = i2.
-/2 width=4 by gr_pat_inj/ qed-.
-
-corec theorem nstream_eq_inv_ext: ∀f1,f2. (∀i. f1@❨i❩ = f2@❨i❩) → f1 ≗ f2.
-* #p1 #f1 * #p2 #f2 #Hf @stream_eq_cons
-[ @(Hf (𝟏))
-| @nstream_eq_inv_ext -nstream_eq_inv_ext #i
-  lapply (Hf (𝟏)) >apply_O1 >apply_O1 #H destruct
-  lapply (Hf (↑i)) >apply_S1 >apply_S1 #H
-  /3 width=2 by eq_inv_pplus_bi_dx, eq_inv_psucc_bi/
-]
-qed-.
-
-(*
-include "ground/relocation/pstream_eq.ma".
-*)
-
-(*
-include "ground/relocation/rtmap_istot.ma".
-
-lemma at_istot: ∀f. 𝐓❨f❩.
-/2 width=2 by ex_intro/ qed.
-*)