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Everywhere I have read about it, the conservation of energy have been expressly confirmed in experiments and observations, but there is no way to prove this conclusion.

I would like to hear your thought on this subject (aside from that digging deep enough, all scientific facts are based on theories that have been sucessful in predicting experimental results, in some sense.)

My point is that conservation of energy is an assumption that cannot be rigorously proved, while he implies it is completely justified, and keeps referring to the above theorem, no matter what arguments are presented.

Thanks :)