| 11. | For a formal proof of the powerset construction, please see the Powerset construction article.
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| 12. | A formal proof is written in a formal language instead of a natural language.
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| 13. | "' Proof theory "'is the study of formal proofs in various logical deduction systems.
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| 14. | In the 1960s formal proofs were presented under different assumptions by continuum of agents.
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| 15. | If so, I would like to see the formal proof.
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| 16. | Having a definition of formal proof makes the concept of proof amenable to study.
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| 17. | While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.
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| 18. | The interactive applet conveys a good intuition of the idea behind the formal proof.
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| 19. | One example of such a formal proof is as follows.
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| 20. | Formal proofs often are constructed with the help of computers in interactive theorem proving.
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