-t))))))).(\lambda (ts: TList).(let TMP_1 \def (\lambda (t: TList).(P t)) in
-(let TMP_28 \def (\lambda (ts2: TList).(let TMP_2 \def (\lambda (t:
-TList).(((\forall (ts1: TList).((tslt ts1 t) \to (P ts1)))) \to (P t))) in
-(let TMP_3 \def (\lambda (_: ((\forall (ts1: TList).((tslt ts1 TNil) \to (P
-ts1))))).H) in (let TMP_27 \def (\lambda (t: T).(\lambda (t0: TList).(\lambda
-(_: ((((\forall (ts1: TList).((tslt ts1 t0) \to (P ts1)))) \to (P
-t0)))).(\lambda (H2: ((\forall (ts1: TList).((tslt ts1 (TCons t t0)) \to (P
-ts1))))).(let H_x \def (tcons_tapp_ex t0 t) in (let H3 \def H_x in (let TMP_6
-\def (\lambda (ts3: TList).(\lambda (t2: T).(let TMP_4 \def (TCons t t0) in
-(let TMP_5 \def (TApp ts3 t2) in (eq TList TMP_4 TMP_5))))) in (let TMP_9
-\def (\lambda (ts3: TList).(\lambda (_: T).(let TMP_7 \def (tslen t0) in (let
-TMP_8 \def (tslen ts3) in (eq nat TMP_7 TMP_8))))) in (let TMP_10 \def (TCons
-t t0) in (let TMP_11 \def (P TMP_10) in (let TMP_26 \def (\lambda (x0:
-TList).(\lambda (x1: T).(\lambda (H4: (eq TList (TCons t t0) (TApp x0
-x1))).(\lambda (H5: (eq nat (tslen t0) (tslen x0))).(let TMP_12 \def (TApp x0
-x1) in (let TMP_13 \def (\lambda (t1: TList).(P t1)) in (let TMP_14 \def
-(tslen t0) in (let TMP_17 \def (\lambda (n: nat).(let TMP_15 \def (TCons t
-t0) in (let TMP_16 \def (tslen TMP_15) in (lt n TMP_16)))) in (let TMP_18
-\def (TCons t t0) in (let TMP_19 \def (tslen TMP_18) in (let TMP_20 \def
-(le_n TMP_19) in (let TMP_21 \def (tslen x0) in (let TMP_22 \def (eq_ind nat
-TMP_14 TMP_17 TMP_20 TMP_21 H5) in (let TMP_23 \def (H2 x0 TMP_22) in (let
-TMP_24 \def (H0 x0 x1 TMP_23) in (let TMP_25 \def (TCons t t0) in (eq_ind_r
-TList TMP_12 TMP_13 TMP_24 TMP_25 H4))))))))))))))))) in (ex2_2_ind TList T
-TMP_6 TMP_9 TMP_11 TMP_26 H3)))))))))))) in (TList_ind TMP_2 TMP_3 TMP_27
-ts2))))) in (tslt_wf_ind TMP_1 TMP_28 ts)))))).
+t))))))).(\lambda (ts: TList).(tslt_wf_ind (\lambda (t: TList).(P t))
+(\lambda (ts2: TList).(TList_ind (\lambda (t: TList).(((\forall (ts1:
+TList).((tslt ts1 t) \to (P ts1)))) \to (P t))) (\lambda (_: ((\forall (ts1:
+TList).((tslt ts1 TNil) \to (P ts1))))).H) (\lambda (t: T).(\lambda (t0:
+TList).(\lambda (_: ((((\forall (ts1: TList).((tslt ts1 t0) \to (P ts1))))
+\to (P t0)))).(\lambda (H2: ((\forall (ts1: TList).((tslt ts1 (TCons t t0))
+\to (P ts1))))).(let H_x \def (tcons_tapp_ex t0 t) in (let H3 \def H_x in
+(ex2_2_ind TList T (\lambda (ts3: TList).(\lambda (t2: T).(eq TList (TCons t
+t0) (TApp ts3 t2)))) (\lambda (ts3: TList).(\lambda (_: T).(eq nat (tslen t0)
+(tslen ts3)))) (P (TCons t t0)) (\lambda (x0: TList).(\lambda (x1:
+T).(\lambda (H4: (eq TList (TCons t t0) (TApp x0 x1))).(\lambda (H5: (eq nat
+(tslen t0) (tslen x0))).(eq_ind_r TList (TApp x0 x1) (\lambda (t1: TList).(P
+t1)) (H0 x0 x1 (H2 x0 (eq_ind nat (tslen t0) (\lambda (n: nat).(lt n (tslen
+(TCons t t0)))) (le_n (tslen (TCons t t0))) (tslen x0) H5))) (TCons t t0)
+H4))))) H3))))))) ts2)) ts)))).