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Exercise 6

[1XP]Prerequisites:[26H],[1XS].Difficulty:*.

Assume that a (partial) order \(≤\) associated to \(ℕ\) satisfies [26H]. Use the strong induction principle [1XS] to show that every non-empty \(A⊆ ℕ\) contains a minimal element, i.e.

\[ ∃ a∈ A~ ,~ ∀ b∈ A~ ,~ ¬(b{\lt}a)\quad . \]

Solution 1

[1XZ]

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