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=fea399443dafe8d3a00ced2888886b478a4a9a47;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=6ee55d8d0634d8c347c9f3b55e42a88a09fa5c34;hpb=4173283e148199871d787c53c0301891deb90713;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 6ee55d8d0..fea399443 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
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/fpbs_cpxs.ma".
 include "basic_2/rt_computation/fpbg_fqup.ma".
+include "basic_2/rt_computation/fpbs_cpxs.ma".
 include "basic_2/rt_computation/fpbg_fpbs.ma".
 
 (* EXAMPLES *****************************************************************)
@@ -32,26 +32,32 @@ definition ApplOmega4 (s0) (s): term ≝ ⓐ⋆s.(ApplOmega1 s0 s).
 
 (* Basic properties *********************************************************)
 
-lemma ApplDelta_lifts (f:rtmap) (s0) (s):
-                      ⬆*[f] (ApplDelta s0 s) ≘ (ApplDelta s0 s).
+lemma ApplDelta_lifts (f) (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) (s0) (s): ⦃G, L⦄ ⊢ ApplOmega1 s0 s ➡[h] ApplOmega2 s0 s.
-/2 width=1 by cpm_beta/ qed.
+lemma cpr_ApplOmega_12 (G) (L) (s0) (s):
+      ❪G,L❫ ⊢ ApplOmega1 s0 s ⬈ ApplOmega2 s0 s.
+/2 width=1 by cpx_beta/ 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_23 (G) (L) (s0) (s):
+      ❪G,L❫ ⊢ ApplOmega2 s0 s ⬈ ApplOmega3 s0 s.
+/6 width=3 by cpx_eps, cpx_flat, cpx_bind, cpx_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 cpr_ApplOmega_34 (G) (L) (s0) (s):
+      ❪G,L❫ ⊢ ApplOmega3 s0 s ⬈ ApplOmega4 s0 s.
+/4 width=3 by cpx_zeta, ApplDelta_lifts, lifts_sort, lifts_flat/ 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 cpxs_ApplOmega_14 (G) (L) (s0) (s):
+      ❪G,L❫ ⊢ ApplOmega1 s0 s ⬈* ApplOmega4 s0 s.
+/5 width=5 by cpxs_strap1, cpx_cpxs/ qed.
 
-lemma fqup_ApplOmega_41 (G) (L) (s0) (s): ⦃G,L,ApplOmega4 s0 s⦄ ⊐+ ⦃G,L,ApplOmega1 s0 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) (G) (L) (s0) (s): ⦃G,L,ApplOmega1 s0 s⦄ >[h] ⦃G,L,ApplOmega1 s0 s⦄.
+theorem fpbg_refl (G) (L) (s0) (s):
+        ❪G,L,ApplOmega1 s0 s❫ > ❪G,L,ApplOmega1 s0 s❫.
 /3 width=5 by fpbs_fpbg_trans, fqup_fpbg, cpxs_fpbs/ qed.