| 31. | A formal proof of the lemma relies on taking the limit of a sequence of random variables.
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| 32. | The realizer, however, usually gives more information about the formula than a formal proof would directly provide.
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| 33. | John Cowles developed a formal proof that Knuth's generalized function was total, using the ACL2 theorem prover.
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| 34. | The FBI estimated the cost at dlrs 250, 000, although no formal proof was provided in court.
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| 35. | In other formal proof systems, the deduction theorem is sometimes taken as a primitive rule of inference.
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| 36. | For most mathematicians, writing a fully formal proof is too pedantic and long-winded to be in common use.
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| 37. | The military frustrated from not having received formal proof of Chavez's resignation withdrew their support of Carmona's presidency.
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| 38. | We will present the applicable result from ( Wald, 1984 eq 11.2 . 10 ) without a formal proof.
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| 39. | For the formal proof, algorithms are presumed to define partial functions over strings and are themselves represented by strings.
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| 40. | On 10 August 2014 Hales announced the completion of a formal proof using automated proof checking, removing any doubt.
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