| 1. | This system is used in Metamath set . mm formal proof database.
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| 2. | Would the expansion into formal proofs raise the expected degree of f?
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| 3. | The outline of a formal proof of the expected time complexity follows.
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| 4. | Since formal proofs in proof theory are purely rules of inference.
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| 5. | "I don't have formal proof that Mr . Dumas intervened, " she said.
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| 6. | "' Euclidean geometry "'is a mathematical system attributed to the Alexandrian formal proof.
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| 7. | Formal proofs are useful because their theorems can be interpreted as true propositions.
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| 8. | We want a formal proof that starts from the expression, ends in zero.
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| 9. | Solutions like a security token give a formal proof answer by constantly shifting password.
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| 10. | The semantic verification is deferred to a separate model and general formal proof tools.
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