update in ground_2, static_2, basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / steps / rtc_plus.ma

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 a5237af26b17a96981bda3ef94c805f23a050002..24b261949a4065a2d114d8c2442cd8d75525b99e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/steps/rtc_isrt.ma".
+include "ground_2/xoa/ex_6_8.ma".
+include "ground_2/steps/rtc.ma".
 
 (* RT-TRANSITION COUNTER ****************************************************)
 
@@ -27,7 +28,7 @@ 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,rs1,ti1,ts1〉) + (〈ri2,rs2,ti2,ts2〉).
@@ -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-.