Section funTable.
Variable X : finType.
Variable Y : Type.
Variable f : X -> Y.
Definition funTable :=
map (fun x => (x,f x)) (elem X).
Variable (eqbX : X -> X -> bool).
Context `{eqbClass X eqbX}.
End funTable.

Lemma lookup_complete (A: Type) (B: Type) eqbA `{eqbClass (X:=A) eqbA} (L : list (prod A B)) a def :
{(a,lookup a L def) el L } + {~(exists b, (a,b) el L) /\ lookup a L def  = def}.