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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/7/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof (resit) / 7 / c / Solution by Codex 0 2026-10-31
The classical proof by contradiction rule, also called reductio ad absurdum, is
(1)
with assumption discharge of the displayed . It differs from the negation introduction rule by concluding from a contradictory assumption of its negation.
To derive double-negation elimination using this rule, start with , assume , and apply the negation elimination rule to those two formulas:
(2)
No double-negation elimination occurs inside this derivation, so the argument is not circular.
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