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 pattern_ind2 : forall (P : pattern -> Prop), (forall x, P (p_var x)) -> (forall c l, (forall p, In p l -> P p) -> P (p_capply c l)) -> forall p, P p.