- \lambda (b: B).(\lambda (hds: PList).(let TMP_9 \def (\lambda (p:
-PList).(\forall (u: T).(\forall (t: T).(let TMP_1 \def (Bind b) in (let TMP_2
-\def (THead TMP_1 u t) in (let TMP_3 \def (lift1 p TMP_2) in (let TMP_4 \def
-(Bind b) in (let TMP_5 \def (lift1 p u) in (let TMP_6 \def (Ss p) in (let
-TMP_7 \def (lift1 TMP_6 t) in (let TMP_8 \def (THead TMP_4 TMP_5 TMP_7) in
-(eq T TMP_3 TMP_8)))))))))))) in (let TMP_12 \def (\lambda (u: T).(\lambda
-(t: T).(let TMP_10 \def (Bind b) in (let TMP_11 \def (THead TMP_10 u t) in
-(refl_equal T TMP_11))))) in (let TMP_69 \def (\lambda (n: nat).(\lambda (n0:
-nat).(\lambda (p: PList).(\lambda (H: ((\forall (u: T).(\forall (t: T).(eq T
-(lift1 p (THead (Bind b) u t)) (THead (Bind b) (lift1 p u) (lift1 (Ss p)
-t))))))).(\lambda (u: T).(\lambda (t: T).(let TMP_13 \def (Bind b) in (let
-TMP_14 \def (lift1 p u) in (let TMP_15 \def (Ss p) in (let TMP_16 \def (lift1
-TMP_15 t) in (let TMP_17 \def (THead TMP_13 TMP_14 TMP_16) in (let TMP_27
-\def (\lambda (t0: T).(let TMP_18 \def (lift n n0 t0) in (let TMP_19 \def
-(Bind b) in (let TMP_20 \def (lift1 p u) in (let TMP_21 \def (lift n n0
-TMP_20) in (let TMP_22 \def (S n0) in (let TMP_23 \def (Ss p) in (let TMP_24
-\def (lift1 TMP_23 t) in (let TMP_25 \def (lift n TMP_22 TMP_24) in (let
-TMP_26 \def (THead TMP_19 TMP_21 TMP_25) in (eq T TMP_18 TMP_26))))))))))) in
-(let TMP_28 \def (Bind b) in (let TMP_29 \def (lift1 p u) in (let TMP_30 \def
-(lift n n0 TMP_29) in (let TMP_31 \def (S n0) in (let TMP_32 \def (Ss p) in
-(let TMP_33 \def (lift1 TMP_32 t) in (let TMP_34 \def (lift n TMP_31 TMP_33)
-in (let TMP_35 \def (THead TMP_28 TMP_30 TMP_34) in (let TMP_44 \def (\lambda
-(t0: T).(let TMP_36 \def (Bind b) in (let TMP_37 \def (lift1 p u) in (let
-TMP_38 \def (lift n n0 TMP_37) in (let TMP_39 \def (S n0) in (let TMP_40 \def
-(Ss p) in (let TMP_41 \def (lift1 TMP_40 t) in (let TMP_42 \def (lift n
-TMP_39 TMP_41) in (let TMP_43 \def (THead TMP_36 TMP_38 TMP_42) in (eq T t0
-TMP_43)))))))))) in (let TMP_45 \def (Bind b) in (let TMP_46 \def (lift1 p u)
-in (let TMP_47 \def (lift n n0 TMP_46) in (let TMP_48 \def (S n0) in (let
-TMP_49 \def (Ss p) in (let TMP_50 \def (lift1 TMP_49 t) in (let TMP_51 \def
-(lift n TMP_48 TMP_50) in (let TMP_52 \def (THead TMP_45 TMP_47 TMP_51) in
-(let TMP_53 \def (refl_equal T TMP_52) in (let TMP_54 \def (Bind b) in (let
-TMP_55 \def (lift1 p u) in (let TMP_56 \def (Ss p) in (let TMP_57 \def (lift1
-TMP_56 t) in (let TMP_58 \def (THead TMP_54 TMP_55 TMP_57) in (let TMP_59
-\def (lift n n0 TMP_58) in (let TMP_60 \def (lift1 p u) in (let TMP_61 \def
-(Ss p) in (let TMP_62 \def (lift1 TMP_61 t) in (let TMP_63 \def (lift_bind b
-TMP_60 TMP_62 n n0) in (let TMP_64 \def (eq_ind_r T TMP_35 TMP_44 TMP_53
-TMP_59 TMP_63) in (let TMP_65 \def (Bind b) in (let TMP_66 \def (THead TMP_65
-u t) in (let TMP_67 \def (lift1 p TMP_66) in (let TMP_68 \def (H u t) in
-(eq_ind_r T TMP_17 TMP_27 TMP_64 TMP_67
-TMP_68)))))))))))))))))))))))))))))))))))))))))))))) in (PList_ind TMP_9
-TMP_12 TMP_69 hds))))).
+ \lambda (b: B).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
+(u: T).(\forall (t: T).(eq T (lift1 p (THead (Bind b) u t)) (THead (Bind b)
+(lift1 p u) (lift1 (Ss p) t)))))) (\lambda (u: T).(\lambda (t: T).(refl_equal
+T (THead (Bind b) u t)))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p:
+PList).(\lambda (H: ((\forall (u: T).(\forall (t: T).(eq T (lift1 p (THead
+(Bind b) u t)) (THead (Bind b) (lift1 p u) (lift1 (Ss p) t))))))).(\lambda
+(u: T).(\lambda (t: T).(eq_ind_r T (THead (Bind b) (lift1 p u) (lift1 (Ss p)
+t)) (\lambda (t0: T).(eq T (lift n n0 t0) (THead (Bind b) (lift n n0 (lift1 p
+u)) (lift n (S n0) (lift1 (Ss p) t))))) (eq_ind_r T (THead (Bind b) (lift n
+n0 (lift1 p u)) (lift n (S n0) (lift1 (Ss p) t))) (\lambda (t0: T).(eq T t0
+(THead (Bind b) (lift n n0 (lift1 p u)) (lift n (S n0) (lift1 (Ss p) t)))))
+(refl_equal T (THead (Bind b) (lift n n0 (lift1 p u)) (lift n (S n0) (lift1
+(Ss p) t)))) (lift n n0 (THead (Bind b) (lift1 p u) (lift1 (Ss p) t)))
+(lift_bind b (lift1 p u) (lift1 (Ss p) t) n n0)) (lift1 p (THead (Bind b) u
+t)) (H u t)))))))) hds)).