(* Main properties with atomic arity assignment for terms *******************)
-(* Note: this is the "big tree" theorem *)
-theorem aaa_fsb: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ≥[h, o] 𝐒⦃G, L, T⦄.
+theorem aaa_fsb: ∀h,G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ≥[h] 𝐒❪G,L,T❫.
/3 width=2 by aaa_csx, csx_fsb/ qed.
(* Advanced eliminators with atomic arity assignment for terms **************)
-fact aaa_ind_fpb_aux: ∀h,o. ∀R: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, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
- R G1 L1 T1
+fact aaa_ind_fpb_aux: ∀h. ∀Q:relation3 ….
+ (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« â\86\92 Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\88\80A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpb … H) -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« â\8a¢ T â\81\9d A â\86\92 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 h o … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
/2 width=2 by fpb_fpbs/
qed-.
-lemma aaa_ind_fpb: ∀h,o. ∀R: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, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
- R G1 L1 T1
+lemma aaa_ind_fpb: ∀h. ∀Q:relation3 ….
+ (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« â\86\92 Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- â\88\80G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
+ â\88\80G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 Q G L T.
/4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
-fact aaa_ind_fpbg_aux: ∀h,o. ∀R:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1, L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
- R G1 L1 T1
+fact aaa_ind_fpbg_aux: ∀h. ∀Q:relation3 ….
+ (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« â\86\92 Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\88\80A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
-#h #o #R #IH #G #L #T #H @(csx_ind_fpbg … H) -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« â\8a¢ T â\81\9d A â\86\92 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 h o … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf … G2 … L2 … T2 … HTA1) -A1
/2 width=2 by fpbg_fwd_fpbs/
qed-.
-lemma aaa_ind_fpbg: ∀h,o. ∀R:relation3 ….
- (â\88\80G1,L1,T1,A. â¦\83G1, L1â¦\84 ⊢ T1 ⁝ A →
- (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 R G2 L2 T2) →
- R G1 L1 T1
+lemma aaa_ind_fpbg: ∀h. ∀Q:relation3 ….
+ (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« â\86\92 Q G2 L2 T2) →
+ Q G1 L1 T1
) →
- â\88\80G,L,T,A. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R G L T.
+ â\88\80G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 Q G L T.
/4 width=4 by aaa_ind_fpbg_aux, aaa_csx/ qed-.