some restyling ...

[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 bfa170972e886103eac16ea7eceac7984358da86..bf31a291fec87b2d9d48ab1008e1245e4d3f2173 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_max.ma
@@ -18,7 +18,7 @@ include "ground_2/steps/rtc_shift.ma".
 
 definition max (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〉
    ]
 ].
 
@@ -28,7 +28,7 @@ interpretation "maximum (rtc)"
 (* Basic properties *********************************************************)
 
 lemma max_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.
 
@@ -59,46 +59,46 @@ 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⦄.
+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⦄.
+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⦄.
+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⦄.
+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.
+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⦄.
+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⦄.
+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⦄.
+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
@@ -115,8 +115,8 @@ qed.
 
 (* Inversion lemmaswith shift ***********************************************)
 
-lemma isrt_inv_max_shift_sn: ∀n,c1,c2. 𝐑𝐓⦃n, ↕*c1 ∨ c2⦄ →
-                             ∧∧ 𝐑𝐓⦃0, c1⦄ & 𝐑𝐓⦃n, c2⦄.
+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