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One cannot have a theory (theorem) without proof. Theories are explanations (models with uses such as predicting on outcome of an experiment or event) for scientific laws, which only describe the phenomenon. Proof is anything that backs up a hypothesis. When a significant amount of proof is shown, the hypothesis becomes a theory due to it being accepting by the scientific community.

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Q: What is the difference between theorem and proof?

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An axiom is a self-evident statement that is assumed to be true. A theorem is proved to be true.

A postulate is something that is accepted as true without proof. A theorem, on the other hand, is something that has been proven and is now being accepted as true.

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Parts of formal proof of theorem?

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A theorem is a statement that has been proven on the basis of previously established statements. Property is something that needs no proof, such as a variable "a" in an equation will be equal to all other "a"s in the equation.

A postulate is assumed to be true while a theorem is proven to be true. The truth of a theorem will be based on postulates.

Theory_of_BPT_theorem

Then there is a proof for it.

Then there is a proof for it.

No. A corollary goes a little bit further than a theorem and, while most of the proof is based on the theorem, the extra bit needs additional proof.

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