include "basic_1/sty1/defs.ma".
-implied let rec sty1_ind (g: G) (c: C) (t1: T) (P: (T \to Prop)) (f: (\forall
-(t2: T).((sty0 g c t1 t2) \to (P t2)))) (f0: (\forall (t: T).((sty1 g c t1 t)
-\to ((P t) \to (\forall (t2: T).((sty0 g c t t2) \to (P t2))))))) (t: T) (s0:
-sty1 g c t1 t) on s0: P t \def match s0 with [(sty1_sty0 t2 s1) \Rightarrow
-(f t2 s1) | (sty1_sing t0 s1 t2 s2) \Rightarrow (f0 t0 s1 ((sty1_ind g c t1 P
-f f0) t0 s1) t2 s2)].
+implied rec lemma sty1_ind (g: G) (c: C) (t1: T) (P: (T \to Prop)) (f:
+(\forall (t2: T).((sty0 g c t1 t2) \to (P t2)))) (f0: (\forall (t: T).((sty1
+g c t1 t) \to ((P t) \to (\forall (t2: T).((sty0 g c t t2) \to (P t2)))))))
+(t: T) (s0: sty1 g c t1 t) on s0: P t \def match s0 with [(sty1_sty0 t2 s1)
+\Rightarrow (f t2 s1) | (sty1_sing t0 s1 t2 s2) \Rightarrow (f0 t0 s1
+((sty1_ind g c t1 P f f0) t0 s1) t2 s2)].