İs constraining the expression holder after assigning to it a cvx variable is equivalent to constraining the cvx variable?

If I constrain an expression holder after we assign to it a chunk of the CVX variable, will it be equivalent to constraining that chunk ?

Your question is not very clear. You need to be more specific.

Is that what you are asking?

variable x
y = x
0 <= y <= 3

constrains x to satisfy 0 <= x <= 3

is the following equivalent:

variable x(n)
expression h(n)
minimize norm(Ax-b)+lambda*norm(x,1)

and

variable x(n)
expression h (n)
h=x;
minimize norm(Ax-b)+lambda*norm(h,1)

Yes, equivalent …