Why can't I assign to an lambda-syntax read-only property in the constructor?

Question

My case:

public class A
{
    public string _prop { get; }
    public A(string prop)
    {
        _prop = prop; // allowed
    }
}

Another case:

public class A
{
    public string _prop => string.Empty;
    public A(string prop)
    {
        // Property or indexer 'A._prop' cannot be assigned to -- it is read only
        _prop = prop;
    }
}

Both syntax:

public string _prop { get; }

and

 public string _prop => string.Empty;

create a read only property. But why coundn't I assign it in the second case?

Answer 1

public string _prop => string.Empty;

is equal to:

public string _prop { get { return string.Empty; } }

So, string.Empty is like method code in method get.

public string _prop { get; }

is equal to:

private readonly string get_prop;
public string _prop { get { return get_prop;} }

So, you can assign get_prop a value from constructor;

More information in the article.