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This is sometimes described as a constructive version of https://us.metamath.org/mpeuni/sbth.html
We would:
- Figure out what notation to use.
- We might define notation for reductions or maybe the definition of a reduction can be expanded inline
- I suppose expressing reductions however we choose and combining with
-->
,-1-1->
, and-1-1-onto->
may suffice for the analogues to ≼ and ≈ used in expressing the Myhill property - Perhaps
X e. Myhill
would be suitable notation for "X has the Myhill property"? Then_om e. Myhill
would express the usual Myhill isomorphism theorem and we could pose questions likeNN+oo e. Myhill
or the strength ofA. x x e. Myhill
.
- Show that NN (or _om) has the Myhill property
- Wikipedia has a sketch of the proof which would resemble the https://us.metamath.org/mpeuni/sbth.html proof apparently.
- Show that a set satisfying https://us.metamath.org/ileuni/df-fin.html has the Myhill property
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