(* Properties with proper parallel rst-reduction on closures ****************)
lemma fpbc_fpbs:
- â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« →
- â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â\89» â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
/3 width=1 by fpb_fpbs, fpbc_fwd_fpb/ qed.
(* Inversion lemmas with proper parallel rst-reduction on closures **********)
lemma fpbs_inv_fpbc_sn:
- â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d« →
- â\88¨â\88¨ â\9dªG1,L1,T1â\9d« â\89\85 â\9dªG2,L2,T2â\9d«
- | â\88\83â\88\83G,L,T. â\9dªG1,L1,T1â\9d« â\89» â\9dªG,L,Tâ\9d« & â\9dªG,L,Tâ\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d© →
+ â\88¨â\88¨ â\9d¨G1,L1,T1â\9d© â\89\85 â\9d¨G2,L2,T2â\9d©
+ | â\88\83â\88\83G,L,T. â\9d¨G1,L1,T1â\9d© â\89» â\9d¨G,L,Tâ\9d© & â\9d¨G,L,Tâ\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
#G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
[ /3 width=1 by feqg_refl, or_introl/
| #G #G2 #L #L2 #T #T2 #_ #H2 * [ #H1 | * #G0 #L0 #T0 #H10 #H0 ]