Fixpoint fcat' (s1 : fmap) (s2 : seq (K * V)) {struct s2} : fmap :=
if s2 is (k, v)::t then fcat' (ins k v s1) t else s1.
Definition fcat s1 s2 := fcat' s1 (seq_of s2).

Lemma fcat0s s : fcat nil s = s. Proof. by apply: fcat_nil'. Qed.