propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / counters / rtc.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/counters/rtc.ma b/matita/matita/contribs/lambdadelta/ground/counters/rtc.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/xoa/ex_1_2.ma".
+include "ground/notation/functions/tuple_4.ma".
+include "ground/notation/functions/zerozero_0.ma".
+include "ground/notation/functions/zeroone_0.ma".
+include "ground/notation/functions/onezero_0.ma".
+include "ground/insert_eq/insert_eq_1.ma".
+include "ground/arith/nat.ma".
+
+(* RT-TRANSITION COUNTERS ***************************************************)
+
+record rtc: Type[0] ≝ {
+(* Note: inner r-steps *)
+   ri: nat;
+(* Note: spine r-steps *)
+   rs: nat;
+(* Note: inner t-steps *)
+   ti: nat;
+(* Note: spine t-steps *)
+   ts: nat
+}.
+
+interpretation
+  "constructor (rtc)"
+  'Tuple ri rs ti ts = (mk_rtc ri rs ti ts).
+
+interpretation
+  "one structural step (rtc)"
+  'ZeroZero = (mk_rtc nzero nzero nzero nzero).
+
+interpretation
+  "one r-step (rtc)"
+  'OneZero = (mk_rtc nzero (ninj punit) nzero nzero).
+
+interpretation
+  "one t-step (rtc)"
+  'ZeroOne = (mk_rtc nzero nzero nzero (ninj punit)).
+
+definition rtc_eq_f: relation rtc ≝ λc1,c2. ⊤.
+
+inductive rtc_eq_t: relation rtc ≝
+| eq_t_intro: ∀ri1,ri2,rs1,rs2,ti,ts.
+              rtc_eq_t (〈ri1,rs1,ti,ts〉) (〈ri2,rs2,ti,ts〉)
+.
+
+(* Basic constructions ******************************************************)
+
+lemma rtc_eq_t_refl: reflexive …  rtc_eq_t.
+* // qed.
+
+(* Basic inversions *********************************************************)
+
+lemma rtc_eq_t_inv_dx:
+      ∀ri1,rs1,ti,ts,y. rtc_eq_t (〈ri1,rs1,ti,ts〉) y →
+      ∃∃ri2,rs2. y = 〈ri2,rs2,ti,ts〉.
+#ri0 #rs0 #ti0 #ts0 #y @(insert_eq_1 … (〈ri0,rs0,ti0,ts0〉))
+#x * -x -y
+#ri1 #ri2 #rs1 #rs2 #ti1 #ts1 #H destruct -ri1 -rs1
+/2 width=3 by ex1_2_intro/
+qed-.