Hi,
I have the defined inductive types:
Inductive InL (A:Type) (y:A) : list A -> Prop :=
| InHead : forall xs:list A, InL y (cons y xs)
| InTail : forall (x:A) (xs:list A), InL y xs -> InL y (cons x xs).
Inductive SubSeq (A:Type) : list A -> list A -> Prop :=
| SubNil : forall l:list A, SubSeq nil l
| SubCons1 : forall (x:A) (l1 l2:list A), SubSeq l1 l2 -> SubSeq l1 (x::l2)
| SubCons2 : forall (x:A) (l1 l2:list A), SubSeq l1 l2 -> SubSeq (x::l1) (x::l2).
Now I have to prove a series of properties of that inductive type, but I keep getting stuck.
Lemma proof1: forall (A:Type) (x:A) (l1 l2:list A), SubSeq l1 l2 -> InL x l1 -> InL x l2.
Proof.
intros.
induction l1.
induction l2.
exact H0.
Qed.
Can some one help me advance.