Konrad and Rob have already answered Bill very thoroughly, but I'll add
two additional comments:
1. I guess Bill was dicombobulated by the "..._AX" name, which does
suggest an axiom. This name is for historical reasons and compatibility
with other HOLs. BOOL_CASES_AX was traditionally a
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On 17 Mar 2014, at 00:52, Konrad Slind wrote:
> RE: type bool. I think BOOL_CASES_AX can be derived from choice.
> There's a topos-flavoured proof (due to Diaconescu?) in Lambek and Scott,
> which I think John ported to HOL-Light.
Yes. I don’t know the right reference: the comment in the HOL Li