-implied let rec csubv_ind (P: (C \to (C \to Prop))) (f: (\forall (n: nat).(P
-(CSort n) (CSort n)))) (f0: (\forall (c1: C).(\forall (c2: C).((csubv c1 c2)
-\to ((P c1 c2) \to (\forall (v1: T).(\forall (v2: T).(P (CHead c1 (Bind Void)
-v1) (CHead c2 (Bind Void) v2))))))))) (f1: (\forall (c1: C).(\forall (c2:
-C).((csubv c1 c2) \to ((P c1 c2) \to (\forall (b1: B).((not (eq B b1 Void))
-\to (\forall (b2: B).(\forall (v1: T).(\forall (v2: T).(P (CHead c1 (Bind b1)
-v1) (CHead c2 (Bind b2) v2)))))))))))) (f2: (\forall (c1: C).(\forall (c2:
-C).((csubv c1 c2) \to ((P c1 c2) \to (\forall (f2: F).(\forall (f3:
-F).(\forall (v1: T).(\forall (v2: T).(P (CHead c1 (Flat f2) v1) (CHead c2
-(Flat f3) v2))))))))))) (c: C) (c0: C) (c1: csubv c c0) on c1: P c c0 \def
-match c1 with [(csubv_sort n) \Rightarrow (f n) | (csubv_void c2 c3 c4 v1 v2)
-\Rightarrow (f0 c2 c3 c4 ((csubv_ind P f f0 f1 f2) c2 c3 c4) v1 v2) |
-(csubv_bind c2 c3 c4 b1 n b2 v1 v2) \Rightarrow (f1 c2 c3 c4 ((csubv_ind P f
-f0 f1 f2) c2 c3 c4) b1 n b2 v1 v2) | (csubv_flat c2 c3 c4 f3 f4 v1 v2)
-\Rightarrow (f2 c2 c3 c4 ((csubv_ind P f f0 f1 f2) c2 c3 c4) f3 f4 v1 v2)].
+implied rec lemma csubv_ind (P: (C \to (C \to Prop))) (f: (\forall (n:
+nat).(P (CSort n) (CSort n)))) (f0: (\forall (c1: C).(\forall (c2: C).((csubv
+c1 c2) \to ((P c1 c2) \to (\forall (v1: T).(\forall (v2: T).(P (CHead c1
+(Bind Void) v1) (CHead c2 (Bind Void) v2))))))))) (f1: (\forall (c1:
+C).(\forall (c2: C).((csubv c1 c2) \to ((P c1 c2) \to (\forall (b1: B).((not
+(eq B b1 Void)) \to (\forall (b2: B).(\forall (v1: T).(\forall (v2: T).(P
+(CHead c1 (Bind b1) v1) (CHead c2 (Bind b2) v2)))))))))))) (f2: (\forall (c1:
+C).(\forall (c2: C).((csubv c1 c2) \to ((P c1 c2) \to (\forall (f2:
+F).(\forall (f3: F).(\forall (v1: T).(\forall (v2: T).(P (CHead c1 (Flat f2)
+v1) (CHead c2 (Flat f3) v2))))))))))) (c: C) (c0: C) (c1: csubv c c0) on c1:
+P c c0 \def match c1 with [(csubv_sort n) \Rightarrow (f n) | (csubv_void c2
+c3 c4 v1 v2) \Rightarrow (f0 c2 c3 c4 ((csubv_ind P f f0 f1 f2) c2 c3 c4) v1
+v2) | (csubv_bind c2 c3 c4 b1 n b2 v1 v2) \Rightarrow (f1 c2 c3 c4
+((csubv_ind P f f0 f1 f2) c2 c3 c4) b1 n b2 v1 v2) | (csubv_flat c2 c3 c4 f3
+f4 v1 v2) \Rightarrow (f2 c2 c3 c4 ((csubv_ind P f f0 f1 f2) c2 c3 c4) f3 f4
+v1 v2)].