Nat Emulation in C#

Nat.cs

using System;

namespace NatEmulation
{
    public abstract record Nat()
    {
        public static Nat operator +(Nat left, Nat right) =>
            left switch
            {
                Zero => right,
                Succ(Nat x) => new Succ(x + right),
                _ => throw new InvalidOperationException()
            };

        public static Nat operator -(Nat left, Nat right) =>
            (left, right) switch
            {
                (Zero, _) or (_, Zero) => left,
                (Succ(Nat x), Succ(Nat y)) => x - y,
                _ => throw new InvalidOperationException()
            };


        public static Nat operator *(Nat left, Nat right) =>
            (left, right) switch
            {
                (Zero, _) => left,
                (Succ(Nat x), _) => right + x * right,
                _ => throw new InvalidOperationException()
            };

        public static Nat operator /(Nat left, Nat right) =>
            (left, right) switch
            {
                (Zero, _) => left,
                _ => new Succ((left - right) / right)
            };

        public static implicit operator Nat(int i) => i switch
        {
            0 => new Zero(),
            > 0 => new Succ(i - 1),
            _ => throw new InvalidOperationException()
        };

        public static explicit operator int(Nat i) => i switch
        {
            Zero => 0,
            Succ(Nat x) => 1 + (int)x,
            _ => throw new InvalidOperationException()
        };
    }
    public record Zero() : Nat;
    public record Succ(Nat Value) : Nat;

    public class Program
    {
        public static void Print(Nat value, string expr)
        {
            Console.WriteLine($"{expr} = {(int)value}, express: {value}");
        }

        public static void Main()
        {
            Nat n1 = 2;
            Nat n2 = 6;
            Print(n1 + n2, "n1 + n2");
            Print(n2 - n1, "n2 - n1");
            Print(n1 * n2, "n1 * n2");
            Print(n2 / n1, "n2 / n1");
            Console.WriteLine(n1 == n2 / 3);
        }
    }
}