Hi! I have wrote this Inductive predicate and part of the proof for its specification:

```
Inductive SumPairs : (nat*nat) -> list (nat*nat) -> Prop :=
| sp_base : SumPairs (0,0) nil
| sp_step : forall (l0:list (nat*nat)) (n0 n1: nat) (y:(nat*nat)), SumPairs (n0,n1) l0 -> SumPairs ((n0+(fst y)),(n1+(snd y))) (cons y l0).
Theorem sumPairs_correct : forall (l:list (nat*nat)), { n: nat | SumPairs (n,n) l }.
Proof.
...
```

The thing is I can’t complete it because I think I need a step like `exists ((x+(fst a))`

for the first part of the pair and `exists ((x+(snd a))`

for the second part but I don’t know how to express that in Coq. Is there a way to do that or am I thinking wrong?

Thank you!