-(let TMP_1 \def (\lambda (t: T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t:
-T).(pr3 c t2 t)) in (let TMP_3 \def (eq T t1 t2) in (let TMP_9 \def (\lambda
-(x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2 x)).(let H_y \def
-(nf2_pr3_unfold c t1 x H3 H0) in (let TMP_4 \def (\lambda (t: T).(pr3 c t2
-t)) in (let H5 \def (eq_ind_r T x TMP_4 H4 t1 H_y) in (let TMP_5 \def
-(\lambda (t: T).(pr3 c t1 t)) in (let H6 \def (eq_ind_r T x TMP_5 H3 t1 H_y)
-in (let H_y0 \def (nf2_pr3_unfold c t2 t1 H5 H1) in (let TMP_6 \def (\lambda
-(t: T).(pr3 c t t1)) in (let H7 \def (eq_ind T t2 TMP_6 H5 t1 H_y0) in (let
-TMP_7 \def (\lambda (t: T).(eq T t1 t)) in (let TMP_8 \def (refl_equal T t1)
-in (eq_ind_r T t1 TMP_7 TMP_8 t2 H_y0)))))))))))))) in (ex2_ind T TMP_1 TMP_2
-TMP_3 TMP_9 H2))))))))))).
+(ex2_ind T (\lambda (t: T).(pr3 c t1 t)) (\lambda (t: T).(pr3 c t2 t)) (eq T
+t1 t2) (\lambda (x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2
+x)).(let H_y \def (nf2_pr3_unfold c t1 x H3 H0) in (let H5 \def (eq_ind_r T x
+(\lambda (t: T).(pr3 c t2 t)) H4 t1 H_y) in (let H6 \def (eq_ind_r T x
+(\lambda (t: T).(pr3 c t1 t)) H3 t1 H_y) in (let H_y0 \def (nf2_pr3_unfold c
+t2 t1 H5 H1) in (let H7 \def (eq_ind T t2 (\lambda (t: T).(pr3 c t t1)) H5 t1
+H_y0) in (eq_ind_r T t1 (\lambda (t: T).(eq T t1 t)) (refl_equal T t1) t2
+H_y0))))))))) H2))))))).