(* *)
(**************************************************************************)
-include "basic_2/syntax/theq_simple_vector.ma".
-include "basic_2/relocation/lifts_vector.ma".
+include "static_2/syntax/theq_simple_vector.ma".
+include "static_2/relocation/lifts_vector.ma".
include "basic_2/rt_computation/cpxs_theq.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
(* Vector form of forward lemmas with head equivalence for terms ************)
qed-.
(* Basic_2A1: was: cpxs_fwd_delta_vector *)
-lemma cpxs_fwd_delta_drops_vector: â\88\80h,o,I,G,L,K,V1,i. â¬\87*[i] L â\89¡ K.ⓑ{I}V1 →
- â\88\80V2. â¬\86*[⫯i] V1 â\89¡ V2 →
+lemma cpxs_fwd_delta_drops_vector: â\88\80h,o,I,G,L,K,V1,i. â¬\87*[i] L â\89\98 K.ⓑ{I}V1 →
+ â\88\80V2. â¬\86*[â\86\91i] V1 â\89\98 V2 →
∀Vs,U. ⦃G, L⦄ ⊢ ⒶVs.#i ⬈*[h] U →
ⒶVs.#i ⩳[h, o] U ∨ ⦃G, L⦄ ⊢ ⒶVs.V2 ⬈*[h] U.
#h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs /2 width=5 by cpxs_fwd_delta_drops/
qed-.
(* Basic_1: was just: pr3_iso_appls_abbr *)
-lemma cpxs_fwd_theta_vector: â\88\80h,o,G,L,V1b,V2b. â¬\86*[1] V1b â\89¡ V2b →
+lemma cpxs_fwd_theta_vector: â\88\80h,o,G,L,V1b,V2b. â¬\86*[1] V1b â\89\98 V2b →
∀p,V,T,U. ⦃G, L⦄ ⊢ ⒶV1b.ⓓ{p}V.T ⬈*[h] U →
ⒶV1b.ⓓ{p}V.T ⩳[h, o] U ∨ ⦃G, L⦄ ⊢ ⓓ{p}V.ⒶV2b.T ⬈*[h] U.
#h #o #G #L #V1b #V2b * -V1b -V2b /3 width=1 by or_intror/
@(cpxs_trans … HU) -U
elim (cpxs_inv_abbr1 … HT0) -HT0 *
[ #V1 #T1 #HV1 #HT1 #H destruct
- elim (cpxs_lifts … HV10a (Ⓣ) … (L.ⓓV) … HV12a) -V1a /3 width=1 by drops_refl, drops_drop/ #X #H
- <(lifts_mono … HV0a … H) -V0a -X #HV2a
+ lapply (cpxs_lifts_bi … HV10a (Ⓣ) … (L.ⓓV) … HV12a … HV0a) -V1a -V0a /3 width=1 by drops_refl, drops_drop/ #HV2a
@(cpxs_trans … (ⓓ{p}V.ⓐV2a.T1)) /3 width=1 by cpxs_bind, cpxs_pair_sn, cpxs_flat_dx, cpxs_bind_dx/
| #X #HT1 #H #H0 destruct
elim (lifts_inv_bind1 … H) -H #V1 #T1 #HW01 #HT01 #H destruct
- elim (cpxs_lifts … HV10a (Ⓣ) … (L.ⓓV0) … HV12a) /3 width=1 by drops_refl, drops_drop/ #X #H
- <(lifts_mono … HV0a … H) -V0a -X #HV2a
+ lapply (cpxs_lifts_bi … HV10a (Ⓣ) … (L.ⓓV0) … HV12a … HV0a) -V0a /3 width=1 by drops_refl, drops_drop/ #HV2a
@(cpxs_trans … (+ⓓV.ⓐV2a.ⓓ{q}V1.T1)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T -V2b -V2b
@(cpxs_strap2 … (ⓐV1a.ⓓ{q}V0.T0)) [ /4 width=7 by cpx_zeta, lifts_bind, lifts_flat/ ] -V -V1 -T1
@(cpxs_strap2 … (ⓓ{q}V0.ⓐV2a.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpx_theta/