I mean the equivalence / transference proofs. Otherwise you're pulling a theorem out of the air and telling students to just accept it. And by "accessible" I mean easy enough to understand that they don't become a huge distraction (or worse).
You're then discussing math in terms of a set whose properties don't obviously match anything the student has dealt with. It needs to be established, one way or another, that adding infinitesimals etc. is not introducing new behavior.
I don't see why that can't just be stated. Students need somewhere to start from, and there's plenty already that we say "trust us for now, we'll prove it later" - and it's not like the reals actually match anything the student has dealt with, at the corner cases, either...
You're working with strictly _more_ axioms, and the extra axioms don't seem justified unless you use the equivalence proof to show you haven't added undesired behavior.
(If you look at the other axioms, the hardest one to justify is the bounding axiom, and its necessity is reinforced by proof. Every other axiom fits in with the student's understanding of arithmetic.)
