X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fsteps%2Frtc_plus.ma;h=24b261949a4065a2d114d8c2442cd8d75525b99e;hb=1fd63df4c77f5c24024769432ea8492748b4ac79;hp=49ce55082238d18d774b43970648fd2f0c457321;hpb=397413c4196f84c81d61ba7dd79b54ab1c428ebb;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
index 49ce55082..24b261949 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
@@ -12,13 +12,14 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/steps/rtc_isrt.ma".
+include "ground_2/xoa/ex_6_8.ma".
+include "ground_2/steps/rtc.ma".
 
 (* RT-TRANSITION COUNTER ****************************************************)
 
 definition plus (c1:rtc) (c2:rtc): rtc ≝ match c1 with [
    mk_rtc ri1 rs1 ti1 ts1 ⇒ match c2 with [
-      mk_rtc ri2 rs2 ti2 ts2 ⇒ 〈ri1+ri2, rs1+rs2, ti1+ti2, ts1+ts2〉
+      mk_rtc ri2 rs2 ti2 ts2 ⇒ 〈ri1+ri2,rs1+rs2,ti1+ti2,ts1+ts2〉
    ]
 ].
 
@@ -27,9 +28,9 @@ interpretation "plus (rtc)"
 
 (* Basic properties *********************************************************)
 
-(**) (* plus is not disambiguated parentheses *) 
+(**) (* plus is not disambiguated parentheses *)
 lemma plus_rew: ∀ri1,ri2,rs1,rs2,ti1,ti2,ts1,ts2.
-                 〈ri1+ri2, rs1+rs2, ti1+ti2, ts1+ts2〉 =
+                 〈ri1+ri2,rs1+rs2,ti1+ti2,ts1+ts2〉 =
                  (〈ri1,rs1,ti1,ts1〉) + (〈ri2,rs2,ti2,ts2〉).
 // qed.
 
@@ -53,43 +54,3 @@ theorem plus_assoc: associative … plus.
 * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2 * #ri3 #rs3 #ti3 #ts3
 <plus_rew //
 qed.
-
-(* Properties with test for constrained rt-transition counter ***************)
-
-lemma isrt_plus: ∀n1,n2,c1,c2. 𝐑𝐓⦃n1, c1⦄ → 𝐑𝐓⦃n2, c2⦄ → 𝐑𝐓⦃n1+n2, c1+c2⦄.
-#n1 #n2 #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct
-/2 width=3 by ex1_2_intro/
-qed.
-
-lemma isrt_plus_O1: ∀n,c1,c2. 𝐑𝐓⦃0, c1⦄ → 𝐑𝐓⦃n, c2⦄ → 𝐑𝐓⦃n, c1+c2⦄.
-/2 width=1 by isrt_plus/ qed.
-
-lemma isrt_plus_O2: ∀n,c1,c2. 𝐑𝐓⦃n, c1⦄ → 𝐑𝐓⦃0, c2⦄ → 𝐑𝐓⦃n, c1+c2⦄.
-#n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by isrt_plus/
-qed.
-
-lemma isrt_succ: ∀n,c. 𝐑𝐓⦃n, c⦄ → 𝐑𝐓⦃↑n, c+𝟘𝟙⦄.
-/2 width=1 by isrt_plus/ qed.
-
-(* Inversion properties with test for constrained rt-transition counter *****)
-
-lemma isrt_inv_plus: ∀n,c1,c2. 𝐑𝐓⦃n, c1 + c2⦄ →
-                     ∃∃n1,n2. 𝐑𝐓⦃n1, c1⦄ & 𝐑𝐓⦃n2, c2⦄ & n1 + n2 = n.
-#n #c1 #c2 * #ri #rs #H
-elim (plus_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2 #H3 #H4
-elim (plus_inv_O3 … H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/
-qed-.
-
-lemma isrt_inv_plus_O_dx: ∀n,c1,c2. 𝐑𝐓⦃n, c1 + c2⦄ → 𝐑𝐓⦃0, c2⦄ → 𝐑𝐓⦃n, c1⦄.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj … Hn2 H2) -c2 #H destruct //
-qed-.
-
-lemma isrt_inv_plus_SO_dx: ∀n,c1,c2. 𝐑𝐓⦃n, c1 + c2⦄ → 𝐑𝐓⦃1, c2⦄ →
-                           ∃∃m. 𝐑𝐓⦃m, c1⦄ & n = ↑m.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj … Hn2 H2) -c2 #H destruct
-/2 width=3 by ex2_intro/
-qed-.