X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fapps_2%2Fexamples%2Fex_fpbg_refl.ma;h=232f9e8a7385abd28434cf61c94786d707d9cd7d;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=f15bbd19c1bde336d8f8b33c8a60e2d1352ba4ed;hpb=d71e53021b0c17e1a00c2d623e7139c6d18069d5;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
index f15bbd19c..232f9e8a7 100644
--- a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
@@ -20,38 +20,38 @@ include "basic_2/rt_computation/fpbg_fpbs.ma".
 
 (* Reflexivity of proper rst-computation: the term ApplOmega ****************)
 
-definition ApplDelta: term → nat → term ≝ λW,s. +ⓛW.ⓐ⋆s.ⓐ#0.#0.
+definition ApplDelta (s0) (s): term ≝ +ⓛ⋆s0.ⓐ⋆s.ⓐ#0.#0.
 
-definition ApplOmega1: term → nat → term ≝ λW,s. ⓐ(ApplDelta W s).(ApplDelta W s).
+definition ApplOmega1 (s0) (s): term ≝ ⓐ(ApplDelta s0 s).(ApplDelta s0 s).
 
-definition ApplOmega2: term → nat → term ≝ λW,s. +ⓓⓝW.(ApplDelta W s).ⓐ⋆s.ⓐ#0.#0.
+definition ApplOmega2 (s0) (s): term ≝ +ⓓⓝ⋆s0.(ApplDelta s0 s).ⓐ⋆s.ⓐ#0.#0.
 
-definition ApplOmega3: term → nat → term ≝ λW,s. ⓐ⋆s.(ApplOmega1 W s).
+definition ApplOmega3 (s0) (s): term ≝ +ⓓⓝ⋆s0.(ApplDelta s0 s).ⓐ⋆s.(ApplOmega1 s0 s).
+
+definition ApplOmega4 (s0) (s): term ≝ ⓐ⋆s.(ApplOmega1 s0 s).
 
 (* Basic properties *********************************************************)
 
-lemma ApplDelta_lifts (f:rtmap):
-                      ∀W1,W2,s. ⬆*[f] W1 ≘ W2 →
-                      ⬆*[f] (ApplDelta W1 s) ≘ (ApplDelta W2 s).
+lemma ApplDelta_lifts (f:rtmap) (s0) (s):
+                      ⇧*[f] (ApplDelta s0 s) ≘ (ApplDelta s0 s).
 /5 width=1 by lifts_sort, lifts_lref, lifts_bind, lifts_flat/ qed.
 
-lemma cpr_ApplOmega_12 (h): ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡[h] ApplOmega2 W s.
+lemma cpr_ApplOmega_12 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega1 s0 s ➡[h] ApplOmega2 s0 s.
 /2 width=1 by cpm_beta/ qed.
 
-lemma cpr_ApplOmega_23 (h): ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega2 W s ➡[h] ApplOmega3 W s.
-#h #G #L #W1 #s elim (lifts_total W1 (𝐔❴1❵)) #W2 #HW12
-@(cpm_zeta … (ApplOmega3 W2 s)) /4 width=1 by ApplDelta_lifts, lifts_flat/
-@cpm_appl // @cpm_appl @(cpm_delta … (ApplDelta W1 s))
-/2 width=1 by ApplDelta_lifts, cpm_eps/
-qed.
+lemma cpr_ApplOmega_23 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega2 s0 s ➡[h] ApplOmega3 s0 s.
+/6 width=3 by cpm_eps, cpm_appl, cpm_bind, cpm_delta, ApplDelta_lifts/ qed.
+
+lemma cpr_ApplOmega_34 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega3 s0 s ➡[h] ApplOmega4 s0 s.
+/4 width=3 by cpm_zeta, ApplDelta_lifts, lifts_sort, lifts_flat/ qed.
 
-lemma cpxs_ApplOmega_13 (h): ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ⬈*[h] ApplOmega3 W s.
-/4 width=4 by cpxs_strap1, cpm_fwd_cpx/ qed.
+lemma cpxs_ApplOmega_14 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega1 s0 s ⬈*[h] ApplOmega4 s0 s.
+/5 width=4 by cpxs_strap1, cpm_fwd_cpx/ qed.
 
-lemma fqup_ApplOmega_13: ∀G,L,W,s. ⦃G, L, ApplOmega3 W s⦄ ⊐+ ⦃G, L, ApplOmega1 W s⦄.
+lemma fqup_ApplOmega_41 (G) (L) (s0) (s): ❪G,L,ApplOmega4 s0 s❫ ⬂+ ❪G,L,ApplOmega1 s0 s❫.
 /2 width=1 by/ qed.
 
 (* Main properties **********************************************************)
 
-theorem fpbg_refl (h) (o): ∀G,L,W,s. ⦃G, L, ApplOmega1 W s⦄ >[h,o] ⦃G, L, ApplOmega1 W s⦄.
+theorem fpbg_refl (h) (G) (L) (s0) (s): ❪G,L,ApplOmega1 s0 s❫ >[h] ❪G,L,ApplOmega1 s0 s❫.
 /3 width=5 by fpbs_fpbg_trans, fqup_fpbg, cpxs_fpbs/ qed.