include "basic_1/wcpr0/defs.ma".
-implied let rec wcpr0_ind (P: (C \to (C \to Prop))) (f: (\forall (c: C).(P c
-c))) (f0: (\forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to ((P c1 c2) \to
-(\forall (u1: T).(\forall (u2: T).((pr0 u1 u2) \to (\forall (k: K).(P (CHead
-c1 k u1) (CHead c2 k u2))))))))))) (c: C) (c0: C) (w: wcpr0 c c0) on w: P c
-c0 \def match w with [(wcpr0_refl c1) \Rightarrow (f c1) | (wcpr0_comp c1 c2
-w0 u1 u2 p k) \Rightarrow (f0 c1 c2 w0 ((wcpr0_ind P f f0) c1 c2 w0) u1 u2 p
-k)].
+implied rec lemma wcpr0_ind (P: (C \to (C \to Prop))) (f: (\forall (c: C).(P
+c c))) (f0: (\forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to ((P c1 c2)
+\to (\forall (u1: T).(\forall (u2: T).((pr0 u1 u2) \to (\forall (k: K).(P
+(CHead c1 k u1) (CHead c2 k u2))))))))))) (c: C) (c0: C) (w: wcpr0 c c0) on
+w: P c c0 \def match w with [(wcpr0_refl c1) \Rightarrow (f c1) | (wcpr0_comp
+c1 c2 w0 u1 u2 p k) \Rightarrow (f0 c1 c2 w0 ((wcpr0_ind P f f0) c1 c2 w0) u1
+u2 p k)].
lemma wcpr0_gen_sort:
\forall (x: C).(\forall (n: nat).((wcpr0 (CSort n) x) \to (eq C x (CSort