intros.
unfold iffH, fol.iffH in |- *.
rewrite subFormulaAnd.
repeat rewrite subFormulaImp.
reflexivity.
Qed.

(* Specifications: *)
Lemma subFormulaIfThenElse :
forall (f1 f2 f3 : fol.Formula L) (v : nat) (s : fol.Term L),
substituteFormula (ifThenElseH f1 f2 f3) v s =
ifThenElseH (substituteFormula f1 v s) (substituteFormula f2 v s)
(substituteFormula f3 v s).