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include "basic_2/rt_computation/fpbs_cpxs.ma".
-include "basic_2/rt_computation/fpbg_fqup.ma".
-include "basic_2/rt_computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbg_fqus.ma".
(* EXAMPLES *****************************************************************)
(* 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.