intros.
unfold ifThenElseH, fol.ifThenElseH in |- *.
rewrite subFormulaAnd.
repeat rewrite subFormulaImp.
rewrite subFormulaNot.
reflexivity.
Qed.
End Extensions.

Lemma subFormulaDepth :
forall (f : fol.Formula L) (v : nat) (s : fol.Term L),
depth L (substituteFormula f v s) = depth L f.