using System;

​

public static partial class ExtensionMethods {

  public static bool Equals<TSrc, TBase>(this TSrc inst, object obj, Func<TSrc, bool> f) where TSrc : IEquatable<TSrc>, TBase where TBase : class {

    if (object.ReferenceEquals(inst, obj)) return true; // same reference ->  equal

    if (obj is null) return false; // this is not null but obj is -> not equal

    if (!(obj is TSrc o)) return false; // obj cannot be cast to this type -> not equal

    if (obj.GetType() != inst.GetType()) return false; // obj is more derived than this -> not equal

    if (inst.GetHashCode() != o.GetHashCode()) return false; // optimization, hash codes are different -> not equal

    if (typeof(TBase) != typeof(Object) && !((inst as TBase).Equals(obj))) return false; // has a base but base.Equal is false -> not equal

​

    return f(o);

  }

}

class Base: IEquatable<Base> {

  public readonly int X;

  readonly int Y;

​

  public Base(int X, int Y) { 

    this.X = X; 

    this.Y = Y; 

  }

​

  public override bool Equals(object obj) {

    return this.Equals<Base, Object>(obj, o => 

      X.Equals(o.X) && Y.Equals(o.Y));

  }

​

  public bool Equals(Base o) => object.Equals(this, o);

  public static bool operator ==(Base o1, Base o2) => object.Equals(o1, o2);

  public static bool operator !=(Base o1, Base o2) => !object.Equals(o1, o2);

​

  public override int GetHashCode() => X ^ Y;

}

​

class Derived : Base, IEquatable<Derived> {

  public readonly int Z;

  readonly int K;

​

  public Derived(int X, int Y, int Z, int K) : base(X, Y) {

    this.Z = Z; 

    this.K = K; 

  }

​

  public override bool Equals(object obj) {

    return this.Equals<Derived, Base>(obj, o => 

      Z.Equals(o.Z) && K.Equals(o.K));

  }

​

  public bool Equals(Derived o) => object.Equals(this, o);

  public static bool operator ==(Derived o1, Derived o2) => object.Equals(o1, o2);

  public static bool operator !=(Derived o1, Derived o2) => !object.Equals(o1, o2);

​

  public override int GetHashCode() => base.GetHashCode() ^ Z ^ K;

}

​

public class Program

{

    public static void Main()

    {

        Derived d1 = new Derived(0, 1, 2, 3), d2 = new Derived(0, 1, 4, 5), d3 = new Derived(0, 1, 2, 3), d4 = null;

        Base b1 = d1, b2 = d2, b3 = d3, b4 = d4;

        Console.WriteLine("  d1==d2 => "+ (d1==d2));

        Console.WriteLine("  d1.Equals(d2) => " + (d1.Equals(d2)));

        Console.WriteLine("  d1==d3 => " + (d1==d3));

        Console.WriteLine("  d1.Equals(d3) => " + (d1.Equals(d3)));

        Console.WriteLine("  d1==d4 => " + (d1 == d4));

        Console.WriteLine("  d1.Equals(d4) => " + (d1.Equals(d4)));

        Console.WriteLine("  b1==b2 => "+ (b1==b2));

        Console.WriteLine("  b1.Equals(b2) => " + (b1.Equals(b2)));

        Console.WriteLine("  b1==b3 => " + (b1==b3));

        Console.WriteLine("  b1.Equals(b3) => " + (b1.Equals(b3)));

        Console.WriteLine("  b1==b4 => " + (b1 == b4));

        Console.WriteLine("  b1.Equals(b4) => " + (b1.Equals(b4)));

​

        Base b = new Base(0, 1);

        Console.WriteLine("  b==d1 => " + (b == d1));

        Console.WriteLine("  b.Equals(d1) => " + (b.Equals(d1)));

    }

}