-T).(\lambda (w1: T).(\lambda (i: nat).(\lambda (H0: (subst1 i v1 t1 w1)).(let
-TMP_3 \def (\lambda (t: T).(\forall (v2: T).((pr0 v1 v2) \to (let TMP_1 \def
-(\lambda (w2: T).(pr0 t w2)) in (let TMP_2 \def (\lambda (w2: T).(subst1 i v2
-t2 w2)) in (ex2 T TMP_1 TMP_2)))))) in (let TMP_7 \def (\lambda (v2:
-T).(\lambda (_: (pr0 v1 v2)).(let TMP_4 \def (\lambda (w2: T).(pr0 t1 w2)) in
-(let TMP_5 \def (\lambda (w2: T).(subst1 i v2 t2 w2)) in (let TMP_6 \def
-(subst1_refl i v2 t2) in (ex_intro2 T TMP_4 TMP_5 t2 H TMP_6)))))) in (let
-TMP_30 \def (\lambda (t0: T).(\lambda (H1: (subst0 i v1 t1 t0)).(\lambda (v2:
-T).(\lambda (H2: (pr0 v1 v2)).(let TMP_8 \def (pr0 t0 t2) in (let TMP_9 \def
-(\lambda (w2: T).(pr0 t0 w2)) in (let TMP_10 \def (\lambda (w2: T).(subst0 i
-v2 t2 w2)) in (let TMP_11 \def (ex2 T TMP_9 TMP_10) in (let TMP_12 \def
-(\lambda (w2: T).(pr0 t0 w2)) in (let TMP_13 \def (\lambda (w2: T).(subst1 i
-v2 t2 w2)) in (let TMP_14 \def (ex2 T TMP_12 TMP_13) in (let TMP_18 \def
-(\lambda (H3: (pr0 t0 t2)).(let TMP_15 \def (\lambda (w2: T).(pr0 t0 w2)) in
-(let TMP_16 \def (\lambda (w2: T).(subst1 i v2 t2 w2)) in (let TMP_17 \def
-(subst1_refl i v2 t2) in (ex_intro2 T TMP_15 TMP_16 t2 H3 TMP_17))))) in (let
-TMP_28 \def (\lambda (H3: (ex2 T (\lambda (w2: T).(pr0 t0 w2)) (\lambda (w2:
-T).(subst0 i v2 t2 w2)))).(let TMP_19 \def (\lambda (w2: T).(pr0 t0 w2)) in
-(let TMP_20 \def (\lambda (w2: T).(subst0 i v2 t2 w2)) in (let TMP_21 \def
-(\lambda (w2: T).(pr0 t0 w2)) in (let TMP_22 \def (\lambda (w2: T).(subst1 i
-v2 t2 w2)) in (let TMP_23 \def (ex2 T TMP_21 TMP_22) in (let TMP_27 \def
-(\lambda (x: T).(\lambda (H4: (pr0 t0 x)).(\lambda (H5: (subst0 i v2 t2
-x)).(let TMP_24 \def (\lambda (w2: T).(pr0 t0 w2)) in (let TMP_25 \def
-(\lambda (w2: T).(subst1 i v2 t2 w2)) in (let TMP_26 \def (subst1_single i v2
-t2 x H5) in (ex_intro2 T TMP_24 TMP_25 x H4 TMP_26))))))) in (ex2_ind T
-TMP_19 TMP_20 TMP_23 TMP_27 H3)))))))) in (let TMP_29 \def (pr0_subst0 t1 t2
-H v1 t0 i H1 v2 H2) in (or_ind TMP_8 TMP_11 TMP_14 TMP_18 TMP_28
-TMP_29))))))))))))))) in (subst1_ind i v1 t1 TMP_3 TMP_7 TMP_30 w1
-H0)))))))))).
+T).(\lambda (w1: T).(\lambda (i: nat).(\lambda (H0: (subst1 i v1 t1
+w1)).(subst1_ind i v1 t1 (\lambda (t: T).(\forall (v2: T).((pr0 v1 v2) \to
+(ex2 T (\lambda (w2: T).(pr0 t w2)) (\lambda (w2: T).(subst1 i v2 t2 w2))))))
+(\lambda (v2: T).(\lambda (_: (pr0 v1 v2)).(ex_intro2 T (\lambda (w2: T).(pr0
+t1 w2)) (\lambda (w2: T).(subst1 i v2 t2 w2)) t2 H (subst1_refl i v2 t2))))
+(\lambda (t0: T).(\lambda (H1: (subst0 i v1 t1 t0)).(\lambda (v2: T).(\lambda
+(H2: (pr0 v1 v2)).(or_ind (pr0 t0 t2) (ex2 T (\lambda (w2: T).(pr0 t0 w2))
+(\lambda (w2: T).(subst0 i v2 t2 w2))) (ex2 T (\lambda (w2: T).(pr0 t0 w2))
+(\lambda (w2: T).(subst1 i v2 t2 w2))) (\lambda (H3: (pr0 t0 t2)).(ex_intro2
+T (\lambda (w2: T).(pr0 t0 w2)) (\lambda (w2: T).(subst1 i v2 t2 w2)) t2 H3
+(subst1_refl i v2 t2))) (\lambda (H3: (ex2 T (\lambda (w2: T).(pr0 t0 w2))
+(\lambda (w2: T).(subst0 i v2 t2 w2)))).(ex2_ind T (\lambda (w2: T).(pr0 t0
+w2)) (\lambda (w2: T).(subst0 i v2 t2 w2)) (ex2 T (\lambda (w2: T).(pr0 t0
+w2)) (\lambda (w2: T).(subst1 i v2 t2 w2))) (\lambda (x: T).(\lambda (H4:
+(pr0 t0 x)).(\lambda (H5: (subst0 i v2 t2 x)).(ex_intro2 T (\lambda (w2:
+T).(pr0 t0 w2)) (\lambda (w2: T).(subst1 i v2 t2 w2)) x H4 (subst1_single i
+v2 t2 x H5))))) H3)) (pr0_subst0 t1 t2 H v1 t0 i H1 v2 H2)))))) w1 H0))))))).