ground_2 released and permanently renamed as ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/steps/rtc.ma b/matita/matita/contribs/lambdadelta/ground/steps/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/lib/arith.ma".
+
+(* RT-TRANSITION COUNTER ****************************************************)
+
+record rtc: Type[0] ≝ {
+   ri: nat; (* Note: inner r-steps *)
+   rs: nat; (* Note: spine r-steps *)
+   ti: nat; (* Note: inner t-steps *)
+   ts: nat  (* Note: spine t-steps *)
+}.
+
+interpretation "constructor (rtc)"
+   'Tuple ri rs ti ts = (mk_rtc ri rs ti ts).
+
+interpretation "one structural step (rtc)"
+   'ZeroZero = (mk_rtc O O O O).
+
+interpretation "one r-step (rtc)"
+   'OneZero = (mk_rtc O (S O) O O).
+
+interpretation "one t-step (rtc)"
+   'ZeroOne = (mk_rtc O O O (S O)).
+
+definition eq_f: relation rtc ≝ λc1,c2. ⊤.
+
+inductive eq_t: relation rtc ≝
+| eq_t_intro: ∀ri1,ri2,rs1,rs2,ti,ts.
+              eq_t (〈ri1,rs1,ti,ts〉) (〈ri2,rs2,ti,ts〉)
+.
+
+(* Basic properties *********************************************************)
+
+lemma eq_t_refl: reflexive …  eq_t.
+* // qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+fact eq_t_inv_dx_aux: ∀x,y. eq_t x y →
+                      ∀ri1,rs1,ti,ts. x = 〈ri1,rs1,ti,ts〉 →
+                      ∃∃ri2,rs2. y = 〈ri2,rs2,ti,ts〉.
+#x #y * -x -y
+#ri1 #ri #rs1 #rs #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H destruct -ri2 -rs2
+/2 width=3 by ex1_2_intro/
+qed-.
+
+lemma eq_t_inv_dx: ∀ri1,rs1,ti,ts,y. eq_t (〈ri1,rs1,ti,ts〉) y →
+                   ∃∃ri2,rs2. y = 〈ri2,rs2,ti,ts〉.
+/2 width=5 by eq_t_inv_dx_aux/ qed-.