(* 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): â¦\83G,Lâ¦\84 â\8a¢ ApplOmega1 s0 s â\9e¡[h] ApplOmega2 s0 s.
+lemma cpr_ApplOmega_12 (h) (G) (L) (s0) (s): â\9dªG,Lâ\9d« â\8a¢ ApplOmega1 s0 s â\9e¡[h,0] ApplOmega2 s0 s.
/2 width=1 by cpm_beta/ qed.
-lemma cpr_ApplOmega_23 (h) (G) (L) (s0) (s): â¦\83G,Lâ¦\84 â\8a¢ ApplOmega2 s0 s â\9e¡[h] ApplOmega3 s0 s.
+lemma cpr_ApplOmega_23 (h) (G) (L) (s0) (s): â\9dªG,Lâ\9d« â\8a¢ ApplOmega2 s0 s â\9e¡[h,0] 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): â¦\83G,Lâ¦\84 â\8a¢ ApplOmega3 s0 s â\9e¡[h] ApplOmega4 s0 s.
+lemma cpr_ApplOmega_34 (h) (G) (L) (s0) (s): â\9dªG,Lâ\9d« â\8a¢ ApplOmega3 s0 s â\9e¡[h,0] ApplOmega4 s0 s.
/4 width=3 by cpm_zeta, ApplDelta_lifts, lifts_sort, lifts_flat/ qed.
-lemma cpxs_ApplOmega_14 (h) (G) (L) (s0) (s): â¦\83G,Lâ¦\84 ⊢ ApplOmega1 s0 s ⬈*[h] ApplOmega4 s0 s.
+lemma cpxs_ApplOmega_14 (h) (G) (L) (s0) (s): â\9dªG,Lâ\9d« ⊢ ApplOmega1 s0 s ⬈*[h] ApplOmega4 s0 s.
/5 width=4 by cpxs_strap1, cpm_fwd_cpx/ qed.
-lemma fqup_ApplOmega_41 (G) (L) (s0) (s): â¦\83G,L,ApplOmega4 s0 sâ¦\84 â\8a\90+ â¦\83G,L,ApplOmega1 s0 sâ¦\84.
+lemma fqup_ApplOmega_41 (G) (L) (s0) (s): â\9dªG,L,ApplOmega4 s0 sâ\9d« â¬\82+ â\9dªG,L,ApplOmega1 s0 sâ\9d«.
/2 width=1 by/ qed.
(* Main properties **********************************************************)
-theorem fpbg_refl (h) (G) (L) (s0) (s): â¦\83G,L,ApplOmega1 s0 sâ¦\84 >[h] â¦\83G,L,ApplOmega1 s0 sâ¦\84.
+theorem fpbg_refl (h) (G) (L) (s0) (s): â\9dªG,L,ApplOmega1 s0 sâ\9d« >[h] â\9dªG,L,ApplOmega1 s0 sâ\9d«.
/3 width=5 by fpbs_fpbg_trans, fqup_fpbg, cpxs_fpbs/ qed.