\lambda (A: Type[0]).(\lambda (x: A).(\lambda (P: ((A \to Prop))).(eq_rect A
x P))).
-implied let rec le_ind (n: nat) (P: (nat \to Prop)) (f: P n) (f0: (\forall
+implied rec lemma le_ind (n: nat) (P: (nat \to Prop)) (f: P n) (f0: (\forall
(m: nat).((le n m) \to ((P m) \to (P (S m)))))) (n0: nat) (l: le n n0) on l:
P n0 \def match l with [le_n \Rightarrow f | (le_S m l0) \Rightarrow (f0 m l0
((le_ind n P f f0) m l0))].
-implied let rec Acc_ind (A: Type[0]) (R: (A \to (A \to Prop))) (P: (A \to
+implied rec lemma Acc_ind (A: Type[0]) (R: (A \to (A \to Prop))) (P: (A \to
Prop)) (f: (\forall (x: A).(((\forall (y: A).((R y x) \to (Acc A R y)))) \to
(((\forall (y: A).((R y x) \to (P y)))) \to (P x))))) (a: A) (a0: Acc A R a)
on a0: P a \def match a0 with [(Acc_intro x a1) \Rightarrow (f x a1 (\lambda