public class Imp1 implements Inter1 {
    private int num;

    @Override
    public void apply() {
        num++;
    }

    public void doubler() {
        num = num * 2;
    }

    public boolean equals(Imp1 o) {
        if (!(o instanceof Imp1))
            return false;
        return o.num == num;
    }

    public int getNum() {
        return num;
    }

    public static void main(String[] args) {
        final Inter1 a = new Imp1();
        final Imp1 b = new Imp1();
        a.apply();
        b.apply();
        System.out.println("a equals b " + a.equals(b));
        System.out.println("b equals a " + b.equals(a));
    }

}

System.out.println("a equals b " + ((Imp1)a).equals(b));

public class Imp1 implements Inter1 {
private int num;

@Override
public void apply() {
    num++;
}

public void doubler() {
    num = num * 2;
}

@Override//<-----need to override the equals of the superClass Object!!!
public boolean equals(Object o) {//<---must be Object!!!
    if (!(o instanceof Imp1))
        return false;
    return ((Imp1)o).num == num;
}

public int getNum() {
    return num;
}

public static void main(String[] args) {
    final Inter1 a = new Imp1();
    final Imp1 b = new Imp1();
    a.apply();
    b.apply();
    System.out.println("a equals b " + a.equals(b));
    System.out.println("b equals a " + b.equals(a));
}

}

public class Imp1 implements Inter1 {
    private int num;

    @Override
    public void apply() {
        num++;
    }

    public void doubler() {
        num = num * 2;
    }

    @Override  //<---------------need to be implemented from the interface!
    public boolean equals(Inter1 o) {//<----the class must to be from the specific interface!!!
        if (!(o instanceof Imp1))
            return false;
        return ((Imp1)o).num == num;//<-----must to cast the object to the specific object in the "if"
    }

    public int getNum() {
        return num;
    }

    public static void main(String[] args) {
        final Inter1 a = new Imp1();
        final Imp1 b = new Imp1();
        a.apply();
        b.apply();
        System.out.println("a equals b " + a.equals(b));
        System.out.println("b equals a " + b.equals(a));
    }

}