Inductive value : Type :=
| c_capply : constructor -> list value -> value.Inductive value : Type :=
| c_capply : constructor -> list value -> value.Inductive term : Type :=
| var : variable -> term
| capply : constructor -> list term -> term
| fapply : function -> list term -> term.Inductive term : Type :=
| var : variable -> term
| capply : constructor -> list term -> term
| fapply : function -> list term -> term.Inductive term : Type :=
| var : variable -> term
| capply : constructor -> list term -> term
| fapply : function -> list term -> term.Inductive term : Type :=
| var : variable -> term
| capply : constructor -> list term -> term
| fapply : function -> list term -> term.Inductive pattern : Type :=
| p_var : variable -> pattern
| p_capply : constructor -> list pattern -> pattern.Inductive pattern : Type :=
| p_var : variable -> pattern
| p_capply : constructor -> list pattern -> pattern.Inductive pattern : Type :=
| p_var : variable -> pattern
| p_capply : constructor -> list pattern -> pattern.Inductive rule : Type :=
| rule_intro : function -> list pattern -> term -> rule.Inductive rule : Type :=
| rule_intro : function -> list pattern -> term -> rule.

Lemma term_ind2 : forall (P : term -> Prop), (forall x, P (var x)) -> (forall c l, (forall t, In t l -> P t) -> P (capply c l)) -> (forall f l, (forall t, In t l -> P t) -> P (fapply f l)) -> forall t, P t.