include "basic_2/rt_computation/cpxs_lfpx.ma".
include "basic_2/rt_computation/lfpxs_fqup.ma".
-(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
+(* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
-(* Properties with uncounted context-sensitive rt-computation for terms *****)
+(* Properties with unbound context-sensitive rt-computation for terms *******)
(* Basic_2A1: uses: lpxs_pair lpxs_pair_refl *)
lemma lfpxs_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
/2 width=1 by tc_lfxs_pair_refl/ qed.
lemma lfpxs_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (lfpxs h G).
-#h #G @s_r_trans_LTC2 @lfpx_cpxs_trans (**) (* auto fails *)
+#h #G @s_r_trans_CTC2 @lfpx_cpxs_trans (**) (* auto fails *)
qed-.
-(* Note: lfpxs_cpx_conf does not hold, thus we cannot invoke s_r_trans_LTC1 *)
+(* Note: lfpxs_cpx_conf does not hold, thus we cannot invoke s_r_trans_CTC1 *)
lemma lfpxs_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (lfpxs h G).
-#h #G @s_r_to_s_rs_trans @s_r_trans_LTC2
+#h #G @s_r_to_s_rs_trans @s_r_trans_CTC2
@s_rs_trans_TC1 /2 width=3 by lfpx_cpxs_trans/ (**) (* full auto too slow *)
qed-.
-(* Advanced properties on uncounted rt-computation for terms ****************)
+(* Advanced properties on unbound rt-computation for terms ******************)
lemma cpxs_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
/4 width=3 by lfpxs_cpxs_trans, lfpxs_pair_refl, cpxs_bind/ qed.
-(* Advanced inversion lemmas on uncounted rt-computation for terms **********)
+(* Advanced inversion lemmas on unbound rt-computation for terms ************)
lemma cpxs_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2 →
∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈*[h] T2 &
∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 &
U2 = ⓓ{p}V2.T2
) ∨
- â\88\83â\88\83T2. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â¬\88*[h] T2 & â¬\86*[1] U2 â\89¡ T2 & p = true.
+ â\88\83â\88\83T2. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â¬\88*[h] T2 & â¬\86*[1] U2 â\89\98 T2 & p = true.
#h #p #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
#U0 #U2 #_ #HU02 * *
[ #V0 #T0 #HV10 #HT10 #H destruct