X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fsteps%2Frtc.ma;h=1e08d2474be31943ed50dcfd6fd1e55c50051768;hp=75960e4cbde202255edf4aee43b63bb6eec66a54;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hpb=e31ce850917b3e95f5158a687626c679e551fd25

diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc.ma
index 75960e4cb..1e08d2474 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc.ma
@@ -12,38 +12,55 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/constructors/tuple_4.ma".
-include "ground_2/notation/constructors/zerozero_0.ma".
-include "ground_2/notation/constructors/zeroone_0.ma".
-include "ground_2/notation/constructors/onezero_0.ma".
+include "ground_2/notation/functions/tuple_4.ma".
+include "ground_2/notation/functions/zerozero_0.ma".
+include "ground_2/notation/functions/zeroone_0.ma".
+include "ground_2/notation/functions/onezero_0.ma".
 include "ground_2/lib/arith.ma".
 
 (* RT-TRANSITION COUNTER ****************************************************)
 
 record rtc: Type[0] ≝ {
    ri: nat; (* Note: inner r-steps *)
-   rh: nat; (* Note: head  r-steps *)
+   rs: nat; (* Note: spine r-steps *)
    ti: nat; (* Note: inner t-steps *)
-   th: nat  (* Note: head  t-steps *)
+   ts: nat  (* Note: spine t-steps *)
 }.
 
 interpretation "constructor (rtc)"
-   'Tuple ri rh ti th = (mk_rtc ri rh ti th).
-
-(* Note: for one structural step *)
-definition OO: rtc ≝ 〈0, 0, 0, 0〉.
+   'Tuple ri rs ti ts = (mk_rtc ri rs ti ts).
 
 interpretation "one structural step (rtc)"
-   'ZeroZero = (OO).
-
-(* Note: for one r-step *)
-definition UO: rtc ≝ 〈0, 1, 0, 0〉.
+   'ZeroZero = (mk_rtc O O O O).
 
 interpretation "one r-step (rtc)"
-   'OneZero = (UO).
-
-(* Note: for one t-step *)
-definition OU: rtc ≝ 〈0, 0, 0, 1〉.
+   'OneZero = (mk_rtc O (S O) O O).
 
 interpretation "one t-step (rtc)"
-   'ZeroOne = (OU).
+   '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-.