(* Basic properties *********************************************************)
lemma fsb_intro (G1) (L1) (T1):
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92 â\9dªG2,L2,T2â\9d«) â\86\92 â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d«.
+ (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© â\89» â\9d¨G2,L2,T2â\9d© â\86\92 â\89¥ð\9d\90\92 â\9d¨G2,L2,T2â\9d©) â\86\92 â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d©.
/5 width=1 by fpbc_intro, SN3_intro/ qed.
(* Basic eliminators ********************************************************)
(* Note: eliminator with shorter ground hypothesis *)
lemma fsb_ind (Q:relation3 …):
- (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+ (â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+ (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© â\89» â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T. â\89¥ð\9d\90\92 â\9dªG,L,Tâ\9d« → Q G L T.
+ â\88\80G,L,T. â\89¥ð\9d\90\92 â\9d¨G,L,Tâ\9d© → Q G L T.
#Q #IH #G #L #T #H elim H -G -L -T
#G1 #L1 #T1 #H1 #IH1
@IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H