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Example

Take the set List(T) defined inductively as

nil in List(T),

forall e in T, l in List(T): cons(e, l) in List(T).

append: List(T) x List(T) -> List(T)

append(nil, y) := y

append(cons(e, x), y) := cons(e, append(x, y))

forall x in List(T), y in List(T):

length(append(x, y)) = length(x)+length(y).