(* Main properties with atomic arity assignment for terms *******************)
theorem aaa_fsb (G) (L) (T) (A):
- â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\89¥ð\9d\90\92 â\9dªG,L,Tâ\9d«.
+ â\9d¨G,Lâ\9d© â\8a¢ T â\81\9d A â\86\92 â\89¥ð\9d\90\92 â\9d¨G,L,Tâ\9d©.
/3 width=2 by aaa_csx, csx_fsb/ qed.
(* Advanced eliminators with atomic arity assignment for terms **************)
fact aaa_ind_fpbc_aux (Q:relation3 …):
(∀G1,L1,T1,A.
- â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+ â\9d¨G1,L1â\9d© ⊢ T1 ⁝ A →
+ (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\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\88\80A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\88\80A. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q G L T.
#R #IH #G #L #T #H @(csx_ind_fpbc … H) -G -L -T
#G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
lemma aaa_ind_fpbc (Q:relation3 …):
(∀G1,L1,T1,A.
- â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+ â\9d¨G1,L1â\9d© ⊢ T1 ⁝ A →
+ (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,A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T,A. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q G L T.
/4 width=4 by aaa_ind_fpbc_aux, aaa_csx/ qed-.
fact aaa_ind_fpbg_aux (Q:relation3 …):
(∀G1,L1,T1,A.
- â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+ â\9d¨G1,L1â\9d© ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\88\80A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T. â\9d¨G,Lâ\9d© â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\88\80A. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q G L T.
#Q #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
#G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
lemma aaa_ind_fpbg (Q:relation3 …):
(∀G1,L1,T1,A.
- â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
+ â\9d¨G1,L1â\9d© ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T,A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T,A. â\9d¨G,Lâ\9d© ⊢ T ⁝ A → Q G L T.
/4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.