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> Equality should at least have the property that ∀ f, x = y ⇒ f(x) = f(y)

My impression was that even that might be a bit contentious[1]. Well, maybe not contentious, but maybe... disputable? It also requires a theory of functions, or at least a syntax to derivation rules.

That was just to be absurdly nitpicky, I think I understand what you're saying here, and it's much appreciated.

[1] https://pdfs.semanticscholar.org/806a/92153c4b8d344edec45eec...



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