X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fsteps%2Frtc_max.ma;h=a6e0efa87c5cb4ec93ceaaff7820e23c2b2ab82f;hb=25c634037771dff0138e5e8e3d4378183ff49b86;hp=bf31a291fec87b2d9d48ab1008e1245e4d3f2173;hpb=5b5dca0c118dfbe3ba8f0514ef07549544eb7810;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
index bf31a291f..a6e0efa87 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/steps/rtc_shift.ma".
+include "ground_2/xoa/ex_6_8.ma".
+include "ground_2/steps/rtc.ma".
 
 (* RT-TRANSITION COUNTER ****************************************************)
 
@@ -56,69 +57,3 @@ theorem max_assoc: associative … max.
 * #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2 * #ri3 #rs3 #ti3 #ts3
 <max_rew <max_rew //
 qed.
-
-(* Properties with test for constrained rt-transition counter ***************)
-
-lemma isrt_max: ∀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_max_O1: ∀n,c1,c2. 𝐑𝐓⦃0,c1⦄ → 𝐑𝐓⦃n,c2⦄ → 𝐑𝐓⦃n,c1∨c2⦄.
-/2 width=1 by isrt_max/ qed.
-
-lemma isrt_max_O2: ∀n,c1,c2. 𝐑𝐓⦃n,c1⦄ → 𝐑𝐓⦃0,c2⦄ → 𝐑𝐓⦃n,c1∨c2⦄.
-#n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by isrt_max/
-qed.
-
-lemma isrt_max_idem1: ∀n,c1,c2. 𝐑𝐓⦃n,c1⦄ → 𝐑𝐓⦃n,c2⦄ → 𝐑𝐓⦃n,c1∨c2⦄.
-#n #c1 #c2 #H1 #H2 >(idempotent_max n) /2 width=1 by isrt_max/
-qed.
-
-(* Inversion properties with test for constrained rt-transition counter *****)
-
-lemma isrt_inv_max: ∀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 (max_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2 #H3 #H4
-elim (max_inv_O3 … H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/
-qed-.
-
-lemma isrt_O_inv_max: ∀c1,c2. 𝐑𝐓⦃0,c1 ∨ c2⦄ → ∧∧ 𝐑𝐓⦃0,c1⦄ & 𝐑𝐓⦃0,c2⦄.
-#c1 #c2 #H
-elim (isrt_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H
-elim (max_inv_O3 … H) -H #H1 #H2 destruct
-/2 width=1 by conj/
-qed-.
-
-lemma isrt_inv_max_O_dx: ∀n,c1,c2. 𝐑𝐓⦃n,c1 ∨ c2⦄ → 𝐑𝐓⦃0,c2⦄ → 𝐑𝐓⦃n,c1⦄.
-#n #c1 #c2 #H #H2
-elim (isrt_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct
-lapply (isrt_inj … Hn2 H2) -c2 #H destruct //
-qed-.
-
-lemma isrt_inv_max_eq_t: ∀n,c1,c2. 𝐑𝐓⦃n,c1 ∨ c2⦄ → eq_t c1 c2 →
-                         ∧∧ 𝐑𝐓⦃n,c1⦄ & 𝐑𝐓⦃n,c2⦄.
-#n #c1 #c2 #H #Hc12
-elim (isrt_inv_max … H) -H #n1 #n2 #Hc1 #Hc2 #H destruct
-lapply (isrt_eq_t_trans … Hc1 … Hc12) -Hc12 #H
-<(isrt_inj … H … Hc2) -Hc2
-<idempotent_max /2 width=1 by conj/
-qed-.
-
-(* Properties with shift ****************************************************)
-
-lemma max_shift: ∀c1,c2. ((↕*c1) ∨ (↕*c2)) = ↕*(c1∨c2).
-* #ri1 #rs1 #ti1 #ts1 * #ri2 #rs2 #ti2 #ts2
-<shift_rew <shift_rew <shift_rew <max_rew //
-qed.
-
-(* Inversion lemmaswith shift ***********************************************)
-
-lemma isrt_inv_max_shift_sn: ∀n,c1,c2. 𝐑𝐓⦃n,↕*c1 ∨ c2⦄ →
-                             ∧∧ 𝐑𝐓⦃0,c1⦄ & 𝐑𝐓⦃n,c2⦄.
-#n #c1 #c2 #H
-elim (isrt_inv_max … H) -H #n1 #n2 #Hc1 #Hc2 #H destruct
-elim (isrt_inv_shift … Hc1) -Hc1 #Hc1 * -n1
-/2 width=1 by conj/
-qed-.