class Program
    {
        interface IBase
        {
            void f();
        }

        interface IDerived : IBase
        {
            new void f();
            void g();
        }

        class C : /*IBase,*/ IDerived
        {
            public void f() { }
            public void g() { }
        }

        static void Main(string[] args) {
            C c = new C();
            c.f();
            c.g();

            IBase b = c;
            b.f();

            IDerived d = c;
            d.f();
            d.g();
        }
    }

Interfaces shall declare that they require the implementation of zero or more other interfaces. If one interface, A, declares that it requires the implementation of another interface, B, then A implicitly declares that it requires the implementation of all interfaces required by B. If a class or value type declares that it implements A, then all concrete instances shall provide implementations of the virtual methods declared in A and all of the interfaces A requires. [Note: The class need not explicitly declare that it implements the interfaces required by A. end note]

TK>Interfaces shall declare that they require the implementation of zero or more other interfaces. If one interface, A, declares that it requires the implementation of another interface, B, then A implicitly declares that it requires the implementation of all interfaces required by B. If a class or value type declares that it implements A, then all concrete instances shall provide implementations of the virtual methods declared in A and all of the interfaces A requires. [Note: The class need not explicitly declare that it implements the interfaces required by A. end note]

13.1.4 Implicit reference conversions
The implicit reference conversions are:
...
— From any class-type S to any interface-type T, provided S implements T.

13.1.4 Implicit reference conversions
The implicit reference conversions are:
...
— From any class-type S to any interface-type T, provided S (explicit) inherits from T.

public abstract class Array : ICloneable, IList, ICollection, IEnumerable

public abstract class Array : ICloneable, IList

> противоположного указания тоже нигде нет или поверить гуру на слово

The base interfaces of an interface are the explicit base interfaces and
their base interfaces. In other words, the set of base interfaces is the
complete transitive closure of the explicit base interfaces, their explicit
base interfaces, and so on. An interface inherits all members of its base
interfaces. [Example: In the example

interface IControl
{
   void Paint();
}

interface ITextBox: IControl
{
   void SetText(string text);
}

interface IListBox: IControl
{
   void SetItems(string[] items);
}

interface IComboBox: ITextBox, IListBox {}

the base interfaces of IComboBox are IControl, ITextBox, and IListBox. In
other words, the IComboBox interface above inherits members SetText and
SetItems as well as Paint. end example]

A class or struct that implements an interface also implicitly implements
all of the interface’s base interfaces.

When a class implements an interface, it implicitly also implements all
of that interface’s base interfaces. Likewise, a re-implementation of an
interface is also implicitly a re-implementation of all of the interface’s
base interfaces.

N>Приведите пример.

namespace ConsoleApplication1
{
    
    interface IBase
    {
        int A();
    }
    
    interface IDerived: IBase
    {
        new int A();
    }
    
    class Test: IBase, IDerived
    {
        int IBase.A()
        {
            return 1;   
        }
        
        int IDerived.A()
        {
            return 2;
        }
        
    }
    
    class Test2: IDerived
    {
        public int A()
        {
            return 2;
        }
    }
    
    class Program
    {
        static void Main(string[] args)
        {
            IDerived d = new Test();
            IBase b = d;
            Console.WriteLine(b.A());
            Console.WriteLine(d.A());
            d = new Test2();
            b = d;
            Console.WriteLine(b.A());
            Console.WriteLine(d.A());
        }
    }
}

N>>Приведите пример.

O>    class Test: IBase, IDerived
O>    {
O>        int IBase.A()
O>        {
O>            return 1;   
O>        }
        
O>        int IDerived.A()
O>        {
O>            return 2;
O>        }
        
O>    }
    
O>    class Test2: IDerived
O>    {
O>        public int A()
O>        {
O>            return 2;
O>        }
O>    }
O>

using System;

namespace ConsoleApplication1
{
    interface IBase
    {
        int A();
    }

    interface IDerived : IBase
    {
        new int A();
    }

    class Test : IBase, IDerived
    {
        int IBase.A()
        {
            return 1;
        }

        int IDerived.A()
        {
            return 2;
        }

    }

    class Test2 : IDerived
    {
        int IBase.A()
        {
            return 1;
        }

        int IDerived.A()
        {
            return 2;
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            IDerived d = new Test();
            IBase b = d;
            Console.WriteLine(b.A());
            Console.WriteLine(d.A());
            d = new Test2();
            b = d;
            Console.WriteLine(b.A());
            Console.WriteLine(d.A());
        }
    }
}

1
2
1
2

O>    class Test: IBase, IDerived
O>    {
O>        int IBase.A()
O>        {
O>            return 1;   
O>        }
        
O>        int IDerived.A()
O>        {
O>            return 2;
O>        }
        
O>    }
    
O>    class Test2: IDerived
O>    {
O>        public int A()
O>        {
O>            return 2;
O>        }
O>    }
O>