commit in ground_2, static_2, basic_2, apps_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / examples / ex_fpbg_refl.ma

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 e37f8831f0689d63dfb49c72c875ad3da8ab7fd0..f15bbd19c1bde336d8f8b33c8a60e2d1352ba4ed 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
@@ -12,11 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbs_cpxs.ma".
+include "basic_2/rt_computation/fpbg_fqup.ma".
+include "basic_2/rt_computation/fpbg_fpbs.ma".
 
 (* EXAMPLES *****************************************************************)
 
-(* Reflexivity of proper qrst-computation: the term ApplOmega ***************)
+(* Reflexivity of proper rst-computation: the term ApplOmega ****************)
 
 definition ApplDelta: term → nat → term ≝ λW,s. +ⓛW.ⓐ⋆s.ⓐ#0.#0.
 
@@ -28,27 +30,28 @@ definition ApplOmega3: term → nat → term ≝ λW,s. ⓐ⋆s.(ApplOmega1 W s)
 
 (* Basic properties *********************************************************)
 
-lemma ApplDelta_lift: ∀W1,W2,s,l,k. ⬆[l, k] W1 ≡ W2 →
-                      ⬆[l, k] (ApplDelta W1 s) ≡ (ApplDelta W2 s).
-/5 width=1 by lift_flat, lift_bind, lift_lref_lt/ qed.
+lemma ApplDelta_lifts (f:rtmap):
+                      ∀W1,W2,s. ⬆*[f] W1 ≘ W2 →
+                      ⬆*[f] (ApplDelta W1 s) ≘ (ApplDelta W2 s).
+/5 width=1 by lifts_sort, lifts_lref, lifts_bind, lifts_flat/ qed.
 
-lemma cpr_ApplOmega_12: ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡ ApplOmega2 W s.
-/2 width=1 by cpr_beta/ qed.
+lemma cpr_ApplOmega_12 (h): ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡[h] ApplOmega2 W s.
+/2 width=1 by cpm_beta/ qed.
 
-lemma cpr_ApplOmega_23: ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega2 W s ➡ ApplOmega3 W s.
-#G #L #W1 #s elim (lift_total W1 0 1) #W2 #HW12
-@(cpr_zeta … (ApplOmega3 W2 s)) /4 width=1 by ApplDelta_lift, lift_flat/
-@cpr_flat // @cpr_flat @(cpr_delta … (ApplDelta W1 s) ? 0)
-[3,5,8,10: /2 width=2 by ApplDelta_lift/ |4,9: /2 width=1 by cpr_eps/ |*: skip ]
+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 cpxs_ApplOmega_13: ∀h,o,G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡*[h,o] ApplOmega3 W s.
-/4 width=3 by cpxs_strap1, cpr_cpx/ 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 fqup_ApplOmega_13: ∀G,L,W,s. ⦃G, L, ApplOmega3 W s⦄ ⊐+ ⦃G, L, ApplOmega1 W 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) (o): ∀G,L,W,s. ⦃G, L, ApplOmega1 W s⦄ >[h,o] ⦃G, L, ApplOmega1 W s⦄.
 /3 width=5 by fpbs_fpbg_trans, fqup_fpbg, cpxs_fpbs/ qed.