include "basic_1/pr1/defs.ma".
-implied let rec pr1_ind (P: (T \to (T \to Prop))) (f: (\forall (t: T).(P t
+implied rec lemma pr1_ind (P: (T \to (T \to Prop))) (f: (\forall (t: T).(P t
t))) (f0: (\forall (t2: T).(\forall (t1: T).((pr0 t1 t2) \to (\forall (t3:
T).((pr1 t2 t3) \to ((P t2 t3) \to (P t1 t3)))))))) (t: T) (t0: T) (p: pr1 t
t0) on p: P t t0 \def match p with [(pr1_refl t1) \Rightarrow (f t1) |