(* *)
(**************************************************************************)
-include "basic_2/syntax/theq_tdeq.ma".
+include "static_2/syntax/theq_tdeq.ma".
include "basic_2/rt_computation/cpxs_lsubr.ma".
include "basic_2/rt_computation/cpxs_cnx.ma".
-include "basic_2/rt_computation/lfpxs_cpxs.ma".
+include "basic_2/rt_computation/lpxs_cpxs.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
(* Forward lemmas with head equivalence for terms ***************************)
(* Note: probably this is an inversion lemma *)
(* Basic_2A1: was: cpxs_fwd_delta *)
-lemma cpxs_fwd_delta_drops: 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: 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 →
∀U. ⦃G, L⦄ ⊢ #i ⬈*[h] U →
#i ⩳[h, o] U ∨ ⦃G, L⦄ ⊢ V2 ⬈*[h] U.
#h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
elim (cpxs_inv_lref1_drops … H) -H /2 width=1 by or_introl/
* #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
lapply (drops_mono … HLK0 … HLK) -HLK0 #H destruct
-elim (cpxs_lifts … HVU0 (Ⓣ) … L … HV12) -HVU0 -HV12 /2 width=3 by drops_isuni_fwd_drop2/ #X #H
-<(lifts_mono … HU0 … H) -U0 -X /2 width=1 by or_intror/
+/4 width=9 by cpxs_lifts_bi, drops_isuni_fwd_drop2, or_intror/
qed-.
(* Basic_1: was just: pr3_iso_beta *)
qed-.
lemma cpxs_fwd_theta: ∀h,o,p,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] U →
- â\88\80V2. â¬\86*[1] V1 â\89¡ V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
+ â\88\80V2. â¬\86*[1] V1 â\89\98 V2 → ⓐV1.ⓓ{p}V.T ⩳[h, o] U ∨
⦃G, L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] U.
#h #o #p #G #L #V1 #V #T #U #H #V2 #HV12
elim (cpxs_inv_appl1 … H) -H *
[ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1 by theq_pair, or_introl/
| #q #W #T0 #HT0 #HU
- elim (cpxs_inv_abbr1 … HT0) -HT0 *
+ elim (cpxs_inv_abbr1_dx … HT0) -HT0 *
[ #V3 #T3 #_ #_ #H destruct
| #X #HT2 #H #H0 destruct
elim (lifts_inv_bind1 … H) -H #W2 #T2 #HW2 #HT02 #H destruct
]
| #q #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
@or_intror @(cpxs_trans … HU) -U (**) (* explicit constructor *)
- elim (cpxs_inv_abbr1 … HT0) -HT0 *
+ elim (cpxs_inv_abbr1_dx … HT0) -HT0 *
[ #V5 #T5 #HV5 #HT5 #H destruct
- elim (cpxs_lifts … HV13 (Ⓣ) … (L.ⓓV) … HV12) -V1 /3 width=1 by drops_refl, drops_drop/ #X #H
- <(lifts_mono … HV34 … H) -V3 -X /3 width=1 by cpxs_flat, cpxs_bind/
+ /6 width=9 by cpxs_lifts_bi, drops_refl, drops_drop, cpxs_flat, cpxs_bind/
| #X #HT1 #H #H0 destruct
elim (lifts_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
- elim (cpxs_lifts … HV13 (Ⓣ) … (L.ⓓV0) … HV12) -HV13 /3 width=1 by drops_refl, drops_drop/ #X #H
- <(lifts_mono … HV34 … H) -V3 -X #HV24
+ lapply (cpxs_lifts_bi … HV13 (Ⓣ) … (L.ⓓV0) … HV12 … HV34) -V3 /3 width=1 by drops_refl, drops_drop/ #HV24
@(cpxs_trans … (+ⓓV.ⓐV2.ⓓ{q}V5.T5)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T
@(cpxs_strap2 … (ⓐV1.ⓓ{q}V0.T0)) [ /4 width=7 by cpx_zeta, lifts_bind, lifts_flat/ ] -V -V5 -T5
@(cpxs_strap2 … (ⓓ{q}V0.ⓐV2.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpx_theta/