Ltac elim_if :=  match goal with
| |- context [if ?c then ?c1 else ?c2]  => case_eq c
end.

Lemma div'_correct v1 v2 v3 :
unary v1 = true -> unary v2 = true -> unary v3 = true ->
length (sem div'_e [v1;v2] [v3]) =
div' (length v1) (length v2) (length v3).