-let rec pr3_ind (c: C) (P: (T \to (T \to Prop))) (f: (\forall (t: T).(P t
-t))) (f0: (\forall (t2: T).(\forall (t1: T).((pr2 c t1 t2) \to (\forall (t3:
-T).((pr3 c t2 t3) \to ((P t2 t3) \to (P t1 t3)))))))) (t: T) (t0: T) (p: pr3
-c t t0) on p: P t t0 \def match p with [(pr3_refl t1) \Rightarrow (f t1) |
-(pr3_sing t2 t1 p0 t3 p1) \Rightarrow (f0 t2 t1 p0 t3 p1 ((pr3_ind c P f f0)
-t2 t3 p1))].
+implied let rec pr3_ind (c: C) (P: (T \to (T \to Prop))) (f: (\forall (t:
+T).(P t t))) (f0: (\forall (t2: T).(\forall (t1: T).((pr2 c t1 t2) \to
+(\forall (t3: T).((pr3 c t2 t3) \to ((P t2 t3) \to (P t1 t3)))))))) (t: T)
+(t0: T) (p: pr3 c t t0) on p: P t t0 \def match p with [(pr3_refl t1)
+\Rightarrow (f t1) | (pr3_sing t2 t1 p0 t3 p1) \Rightarrow (f0 t2 t1 p0 t3 p1
+((pr3_ind c P f f0) t2 t3 p1))].