I think I had to do something similar to this in my "Elements of Artificial Intelligence" class, but the terminology and symbolism were slightly different.
I am glad to be of help. You probably have it figured out. Explaining notation over the web in a forum without explicit support for symbols is difficult.
It seems like the Axioms of HJ are equivalent to the use of CP, Reit, and Hyp.
I'd imagine the part that makes the proof difficult is remembering the exact definitions and following the steps in tedious detail.
But it seems like CP (after more googling) is like the second axiom. I don't know what Reit and Hyp are.
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