Section list_embeding.
Variable A : Set.
Variable leA : A -> A -> Prop.
Hypothesis eqA_dec : forall a a' : A, {a = a'} + {a <> a'}.
Hypothesis leA_dec : forall a a', {leA a a'} + {~ leA a a'}.
Hypothesis leA_trans : forall a a' a'', leA a a' -> leA a' a'' -> leA a a''.
Definition embeds : list A -> list A -> Prop := Embeds leA.
Definition sublist : list (list A) -> list (list A) -> Prop := Embeds (eq (A:= list A)).
Fact nil_embeds : forall w, embeds nil w.

Lemma bad_remove_letter : forall a w ws,
bad embeds ((a::w)::ws) -> bad embeds (w::ws).