update in groud_2 and models

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

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 1c8861fa89c239582dd8074ff06a363af8b4fa56..058b1a3c0163f0660ce5b3af805225558f6257c6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
@@ -36,6 +36,10 @@ lemma max_O_dx: ∀c. c = (c ∨ 𝟘𝟘).
 * #ri #rs #ti #ts <max_rew //
 qed.
 
+lemma max_idem: ∀c. c = (c ∨ c).
+* #ri #rs #ti #ts <max_rew //
+qed.
+
 (* Basic inversion properties ***********************************************)
 
 lemma max_inv_dx: ∀ri,rs,ti,ts,c1,c2. 〈ri,rs,ti,ts〉 = (c1 ∨ c2) →
@@ -46,6 +50,13 @@ lemma max_inv_dx: ∀ri,rs,ti,ts,c1,c2. 〈ri,rs,ti,ts〉 = (c1 ∨ c2) →
 <max_rew #H destruct /2 width=14 by ex6_8_intro/
 qed-.
 
+(* Main Properties **********************************************************)
+
+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⦄.
@@ -60,6 +71,10 @@ lemma isrt_max_O2: ∀n,c1,c2. 𝐑𝐓⦃n, c1⦄ → 𝐑𝐓⦃0, 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⦄ →
@@ -69,16 +84,22 @@ elim (max_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2
 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_mono … Hn2 H2) -c2 #H destruct //
+lapply (isrt_inj … Hn2 H2) -c2 #H destruct //
 qed-.
 
 (* Properties with shift ****************************************************)
-(*
-lemma max_shift: ∀c1,c2. (↓c1) ∨ (↓c2) = ↓(c1∨c2).
+
+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.
-*)