Exercise 2: Rewriting "not any(order.total < 0 ...)" as an ALL Statement — Possible Solution
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IDENTIFYING THE ORIGINAL STATEMENT'S SHAPE
------------------------------
"any(order.total < 0 for order in orders)" is exactly Chapter 3's own
∃x P(x) pattern, where the domain is `orders` and P(order) is
"order.total < 0". The full original expression, "not any(...)", is
therefore ¬(∃x P(x)).

APPLYING DE MORGAN'S LAW FOR QUANTIFIERS
------------------------------
Per this chapter, "¬(∃x P(x)) ≡ ∀x ¬P(x)" - negating an existence
claim becomes a universal claim about the negated predicate. Applying
this directly:

  not any(order.total < 0 for order in orders)
  ==
  all(not (order.total < 0) for order in orders)

Simplifying "not (order.total < 0)" to its more natural form,
"order.total >= 0", gives the final rewrite:

  all(order.total >= 0 for order in orders)

PLAIN ENGLISH FOR THE REWRITTEN VERSION
------------------------------
"Every order has a non-negative total" - equivalently, "no order has
a negative total." Both phrasings describe the same underlying ∀
statement; the second is just the negated-∃ framing restated in
ordinary English rather than formal ∀ notation.

WHY THE TWO VERSIONS ARE GUARANTEED TO BEHAVE IDENTICALLY
------------------------------
This isn't a stylistic rewrite - it's the same logical equivalence
Chapter 3 establishes explicitly as a "genuinely useful real refactor"
in its own worked example (not all(...) == any(not ...)), applied
here in its ∃-to-∀ direction instead. For any possible collection of
orders, the two expressions will always evaluate to the same boolean
result.

WHY THIS REWRITE IS GENUINELY USEFUL, NOT JUST EQUIVALENT
------------------------------
The rewritten version reads more directly as a positive assertion
about what should be true ("every total is non-negative") rather than
a negated statement about what should NOT exist ("there's no negative
total") - often easier to reason about correctly, especially once
further conditions get added to the check later.

WHY THIS WORKS AS AN ANSWER
------------------------------
It identifies the original expression's exact quantifier shape,
applies the specific De Morgan's-for-quantifiers rule named in this
chapter, shows the resulting code, and translates the result into
plain English confirming it expresses the same underlying claim.