From 057ac901b257ea183aa3bac3f7b358a5543f8815 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sat, 5 Jul 2014 10:46:41 +0000
Subject: [PATCH] improved example: Delta must be a family of terms

---
 .../basic_2/examples/ex_cpr_omega.ma          | 20 ++++++++++---------
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  2 +-
 2 files changed, 12 insertions(+), 10 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/examples/ex_cpr_omega.ma b/matita/matita/contribs/lambdadelta/basic_2/examples/ex_cpr_omega.ma
index 84713bce6..6a2586ff1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/examples/ex_cpr_omega.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/examples/ex_cpr_omega.ma
@@ -18,24 +18,26 @@ include "basic_2/reduction/cpr.ma".
 
 (* A reduction cycle in two steps: the term Omega ***************************)
 
-definition Delta: term ≝ +ⓛ⋆0.ⓐ#0.#0.
+definition Delta: term → term ≝ λW. +ⓛW.ⓐ#0.#0.
 
-definition Omega1: term ≝ ⓐDelta.Delta.
+definition Omega1: term → term ≝ λW. ⓐ(Delta W).(Delta W).
 
-definition Omega2: term ≝ +ⓓⓝ⋆0.Delta.ⓐ#0.#0.
+definition Omega2: term → term ≝ λW. +ⓓⓝW.(Delta W).ⓐ#0.#0.
 
 (* Basic properties *********************************************************)
 
-lemma Delta_lift: ∀d,e. ⇧[d, e] Delta ≡ Delta.
+lemma Delta_lift: ∀W1,W2,d,e. ⇧[d, e] W1 ≡ W2 →
+                  ⇧[d, e] (Delta W1) ≡ (Delta W2).
 /4 width=1 by lift_flat, lift_bind, lift_lref_lt/ qed.
 
 (* Main properties **********************************************************)
 
-theorem cpr_Omega_12: ⦃⋆, ⋆⦄ ⊢ Omega1 ➡ Omega2.
+theorem cpr_Omega_12: ∀W. ⦃⋆, ⋆⦄ ⊢ Omega1 W ➡ Omega2 W.
 /2 width=1 by cpr_beta/ qed.
 
-theorem cpr_Omega_21: ⦃⋆, ⋆⦄ ⊢ Omega2 ➡ Omega1.
-@(cpr_zeta … Omega1) /2 width=1 by lift_flat/
-@cpr_flat @(cpr_delta … Delta ? 0)
-[3,5,8,10: // |4,9: /2 width=1 by cpr_eps/ |*: skip ]
+theorem cpr_Omega_21: ∀W. ⦃⋆, ⋆⦄ ⊢ Omega2 W ➡ Omega1 W.
+#W1 elim (lift_total W1 0 1) #W2 #HW12
+@(cpr_zeta … (Omega1 W2)) /3 width=1 by Delta_lift, lift_flat/
+@cpr_flat @(cpr_delta … (Delta W1) ? 0)
+[3,5,8,10: /2 width=2 by Delta_lift/ |4,9: /2 width=1 by cpr_eps/ |*: skip ]
 qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 456a2b0e3..7ff91fa2d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -11,7 +11,7 @@ table {
    ]
    class "wine"
    [ { "examples" * } {
-        [ { "" * } {
+        [ { "terms with special features" * } {
              [ "ex_cpr_omega" * ]
           }
         ]
-- 
2.39.2