>>491-492
整列定理から選択公理が導けるのは当然
選択公理から整列定理が導ける↓の証明は分かるかい？

Proof from axiom of choice
The well-ordering theorem follows from the axiom of choice as follows.[9]

Let the set we are trying to well-order be
A, and let f be a choice function for the family of non-empty subsets of A.
For every ordinal α, define an element aα that is in A by setting
aα = f(A∖{aξ∣ξ<α}) if this complement A∖{aξ∣ξ<α} is nonempty,
or leave aα undefined if it is.
That is, aα is chosen from the set of elements of A
that have not yet been assigned a place in the ordering
(or undefined if the entirety of A has been successfully enumerated).
Then the order < on A defined by aα<aβ if and only if α<β
(in the usual well-order of the ordinals)
is a well-order of A as desired, of order type sup{α∣aα is defined}.