My example with triangles was just that, an example. I was talking about "the nature of proof" and the impossibility to prove something doesn't exist suggested by the parent post.
What I said can be expressed as "once you prove P(X) is true for all X, you can trivially prove that an X for which P(X) is false doesn't exist". Let me repeat that : ONCE YOU PROVE. I wasn't discussing whether or not you CAN prove it, or under what conditions you can prove it (I obviously assumed euclidean axioms), for my example that proof is part of the hypothesis.
My example with triangles (which is valid, BTW, because by saying "once you prove" I automatically implied a set of axioms where you *can* prove it) was supposed to make my point easier to understand by lowering the abstraction level at which I was expressing it, but looks like no matter how low the abstraction level goes, some people go to great lengths to NOT understand it :(