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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/8/c/i/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) / 8 / c / i / Solution by Codex 0 2026-10-31
The equality introduction rule is reflexivity, with no premise. The equality elimination rule is substitution of equal first-order terms into a first-order formula:
(1)
The indicated substitution must be capture-avoiding substitution in first-order logic: the first-order terms must be free for the replaced variable. One can designate a particular argument occurrence by choosing appropriately; the rule does not demand replacing every occurrence of an identical-looking term in a formula.
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