How to search and replace with a counter-based expression in Vim?

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It is possible to have a counter using the substitute-with-an-expression
feature (see :help sub-replace-\=). Unfortunately, since the
\= construct allows only expressions, the :let command cannot
be used, and therefore, a variable cannot not be set the usual way.

However, there is a simple trick to change the value of a variable in
expression if that variable is a list or a dictionary. In that case,
its contents could be modified by the map() function.

In such a manner, substitution for the case described in the question
would look as follows:

:let n=[0] | %s/Id="F"/\='Id="'.map(n,'v:val+1')[0].'"'/g

The tricky part here is in the substitute part of the replacement.
Since it starts with \=, the rest of it is interpreted
as an expression by Vim. Thus, 'Id="'.map(n, 'v:val+1').'"'
is an ordinary expression. Here a string literal 'Id="'
is concatenated (using the . operator) with return value
of the function call map(n, 'v:val+1'), and with another
string, '"'. The map function expects two arguments:
a list (as in this case) or a dictionary, and a string containing
expression that should be evaluated for each of the items in the given
list or dictionary. Special variable v:val denotes an individual
list item. So the 'v:val+1' string will be evaluated to a list item
incremented by one.

In this case, we can even simplify the command further:

:let n=[0] | %s/Id="\zsF\ze"/\=map(n,'v:val+1')[0]/g

The \zs and \ze pattern atoms are used to set the start and
the end of the pattern to replace, respectively (see :help /\zs
and :help /\ze). That way the whole search part of the substitute
command is matched, but only the part between \zs and \ze is
replaced. This avoids clumsy concatenations in the substitute
expression.

Either of these two short one-liners completely solves the issue.

For frequent replacements, one can even define an auxiliary function

function! Inc(x)
    let a:x[0] += 1
    return a:x[0]
endfunction

and make substitution commands even shorter:

:let n=[0] | %s/Id="\zsF\ze"/\=Inc(n)/g

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