Challenge 2: Deriving a Domain Before Labeling — Possible Solution
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derive_demo.pl:

:- use_module(library(clpfd)).

Query:

    ?- Y in 3..8, X #= Y * 2.
    X in 6..16,
    Y in 3..8.

-- Why would the equivalent is/2 version raise an error here? --
--
-- X is Y * 2 demands that its right-hand side, Y * 2, already be
-- fully ground arithmetic at the moment is/2 runs -- Y has to
-- already be bound to a specific number, or Prolog cannot evaluate
-- Y * 2 at all and raises an "Arguments are not sufficiently
-- instantiated" error. Here, Y is only a domain variable ranging
-- over 3..8, with no single value chosen yet -- is/2 has no way to
-- multiply an entire RANGE by 2. #=, in contrast, doesn't need
-- either side to be a concrete number -- it works directly over
-- domains, propagating the multiplication across Y's whole 3..8
-- range to derive X's own domain, 6..16, immediately, with neither
-- variable committed to any specific value yet. This is exactly the
-- bidirectional, domain-level behavior the chapter names as #='s
-- real difference from is/2.

WHY THIS WORKS AS AN ANSWER
------------------------------
This uses a fresh multiplication example (rather than reusing the
chapter's own X #= Y + 1) to show domain propagation happening before
either variable is labeled, then explicitly ties the failure of the
is/2 equivalent back to is/2's requirement for already-ground
arithmetic, matching the chapter's own stated distinction.