[giomasce]

That's not a corner case. Either you defined "triangle" and "angles" to mean a plane triangle and angles, or that is not a theorem. Within the theory you're looking at, the definitions are not part of the context, they are part of the theory itself. So you're not depending on the context.

[ggm]

Like the other response you basically said context is everything. You just prefer to call the context axioms. What is context free here is the arithmetic.

[giomasce]

Why should arithmetic be more or less context free than anything else? It's defined by axioms and definitions as much as the rest.