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From Stdlib Require Import Program Arith.
Program Fixpoint check_n (n : nat) (P : { i | i < n } -> bool) (p : nat)
(H : forall (i : { i | i < n }), i < p -> P i = true)
{measure (n - p)} :
Exc (forall (p : { i | i < n}), P p = true) :=
match le_lt_dec n p with
| left _ => value _
| right cmp =>
if dec (P p) then
check_n n P (S p) _
else
error
end.
From Stdlib Require Import Lia.
Solve Obligations with program_simpl ; auto with *; lia.
Next Obligation.
apply H. simpl. lia.
Defined.
Next Obligation.
case (le_lt_dec p i) ; intros. assert(i = p) by lia. subst.
revert e. clear_subset_proofs. auto.
apply H. simpl. assumption. Defined.
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