some restyling ...

[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 49ce55082238d18d774b43970648fd2f0c457321..a5237af26b17a96981bda3ef94c805f23a050002 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
@@ -18,7 +18,7 @@ include "ground_2/steps/rtc_isrt.ma".
 
 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〉
    ]
 ].
 
@@ -29,7 +29,7 @@ interpretation "plus (rtc)"
 
 (**) (* 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.
 
@@ -56,38 +56,38 @@ 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⦄.
+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⦄.
+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⦄.
+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⦄.
+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.
+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⦄.
+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.
+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