-(H: (ty3 g c1 t1 t2)).(let TMP_1 \def (\lambda (c: C).(\lambda (t:
-T).(\lambda (t0: T).(\forall (c2: C).((wf3 g c c2) \to (ty3 g c2 t t0))))))
-in (let TMP_9 \def (\lambda (c: C).(\lambda (t3: T).(\lambda (t: T).(\lambda
-(H0: (ty3 g c t3 t)).(\lambda (H1: ((\forall (c2: C).((wf3 g c c2) \to (ty3 g
-c2 t3 t))))).(\lambda (u: T).(\lambda (t4: T).(\lambda (H2: (ty3 g c u
-t4)).(\lambda (H3: ((\forall (c2: C).((wf3 g c c2) \to (ty3 g c2 u
-t4))))).(\lambda (H4: (pc3 c t4 t3)).(\lambda (c2: C).(\lambda (H5: (wf3 g c
-c2)).(let TMP_2 \def (\lambda (t0: T).(ty3 g c t4 t0)) in (let TMP_3 \def
-(ty3 g c2 u t3) in (let TMP_7 \def (\lambda (x: T).(\lambda (H6: (ty3 g c t4
-x)).(let TMP_4 \def (H1 c2 H5) in (let TMP_5 \def (H3 c2 H5) in (let TMP_6
-\def (wf3_pc3_conf g c t4 t3 H4 c2 H5 x H6 t H0) in (ty3_conv g c2 t3 t TMP_4
-u t4 TMP_5 TMP_6)))))) in (let TMP_8 \def (ty3_correct g c u t4 H2) in
-(ex_ind T TMP_2 TMP_3 TMP_7 TMP_8))))))))))))))))) in (let TMP_10 \def
-(\lambda (c: C).(\lambda (m: nat).(\lambda (c2: C).(\lambda (_: (wf3 g c
-c2)).(ty3_sort g c2 m))))) in (let TMP_21 \def (\lambda (n: nat).(\lambda (c:
-C).(\lambda (d: C).(\lambda (u: T).(\lambda (H0: (getl n c (CHead d (Bind
-Abbr) u))).(\lambda (t: T).(\lambda (H1: (ty3 g d u t)).(\lambda (H2:
-((\forall (c2: C).((wf3 g d c2) \to (ty3 g c2 u t))))).(\lambda (c2:
-C).(\lambda (H3: (wf3 g c c2)).(let H_x \def (wf3_getl_conf Abbr n c d u H0 g
-c2 H3 t H1) in (let H4 \def H_x in (let TMP_13 \def (\lambda (d2: C).(let
-TMP_11 \def (Bind Abbr) in (let TMP_12 \def (CHead d2 TMP_11 u) in (getl n c2
-TMP_12)))) in (let TMP_14 \def (\lambda (d2: C).(wf3 g d d2)) in (let TMP_15
-\def (TLRef n) in (let TMP_16 \def (S n) in (let TMP_17 \def (lift TMP_16 O
-t) in (let TMP_18 \def (ty3 g c2 TMP_15 TMP_17) in (let TMP_20 \def (\lambda
-(x: C).(\lambda (H5: (getl n c2 (CHead x (Bind Abbr) u))).(\lambda (H6: (wf3
-g d x)).(let TMP_19 \def (H2 x H6) in (ty3_abbr g n c2 x u H5 t TMP_19)))))
-in (ex2_ind C TMP_13 TMP_14 TMP_18 TMP_20 H4)))))))))))))))))))) in (let
-TMP_32 \def (\lambda (n: nat).(\lambda (c: C).(\lambda (d: C).(\lambda (u:
-T).(\lambda (H0: (getl n c (CHead d (Bind Abst) u))).(\lambda (t: T).(\lambda
+(H: (ty3 g c1 t1 t2)).(ty3_ind g (\lambda (c: C).(\lambda (t: T).(\lambda
+(t0: T).(\forall (c2: C).((wf3 g c c2) \to (ty3 g c2 t t0)))))) (\lambda (c:
+C).(\lambda (t3: T).(\lambda (t: T).(\lambda (H0: (ty3 g c t3 t)).(\lambda
+(H1: ((\forall (c2: C).((wf3 g c c2) \to (ty3 g c2 t3 t))))).(\lambda (u:
+T).(\lambda (t4: T).(\lambda (H2: (ty3 g c u t4)).(\lambda (H3: ((\forall
+(c2: C).((wf3 g c c2) \to (ty3 g c2 u t4))))).(\lambda (H4: (pc3 c t4
+t3)).(\lambda (c2: C).(\lambda (H5: (wf3 g c c2)).(ex_ind T (\lambda (t0:
+T).(ty3 g c t4 t0)) (ty3 g c2 u t3) (\lambda (x: T).(\lambda (H6: (ty3 g c t4
+x)).(ty3_conv g c2 t3 t (H1 c2 H5) u t4 (H3 c2 H5) (wf3_pc3_conf g c t4 t3 H4
+c2 H5 x H6 t H0)))) (ty3_correct g c u t4 H2)))))))))))))) (\lambda (c:
+C).(\lambda (m: nat).(\lambda (c2: C).(\lambda (_: (wf3 g c c2)).(ty3_sort g
+c2 m))))) (\lambda (n: nat).(\lambda (c: C).(\lambda (d: C).(\lambda (u:
+T).(\lambda (H0: (getl n c (CHead d (Bind Abbr) u))).(\lambda (t: T).(\lambda