(* Main properties with atomic arity assignment for terms *******************)
-theorem aaa_fsb: â\88\80h,G,L,T,A. â¦\83G,Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â\89¥[h] ð\9d\90\92â¦\83G,L,Tâ¦\84.
+theorem aaa_fsb: â\88\80h,G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\89¥[h] ð\9d\90\92â\9dªG,L,Tâ\9d«.
/3 width=2 by aaa_csx, csx_fsb/ qed.
(* Advanced eliminators with atomic arity assignment for terms **************)
fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1,L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89»[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+ (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\88\80A. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\88\80A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
#h #R #IH #G #L #T #H @(csx_ind_fpb … 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
qed-.
lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1,L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89»[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+ (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T,A. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T,A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
/4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1,L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+ (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\88\80A. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\88\80A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
#h #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
qed-.
lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1,L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 >[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2) →
+ (â\88\80G1,L1,T1,A. â\9dªG1,L1â\9d« ⊢ T1 ⁝ A →
+ (â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2) →
Q G1 L1 T1
) →
- â\88\80G,L,T,A. â¦\83G,Lâ¦\84 ⊢ T ⁝ A → Q G L T.
+ â\88\80G,L,T,A. â\9dªG,Lâ\9d« ⊢ T ⁝ A → Q G L T.
/4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.