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Lecture14MechanicalLogic - Lecture 14 CS 2603 Applied Logic...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 14 — CS 2603 Applied Logic for Hardware and Software Induction and Mechanical Logic
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9 Proved: L(0) 9 Proved: n. (L(n) L(n+1)) 9 Conclusion: n. L(n) — by the principle of induction qed Theorem {++ additive}. n. L(n) where L(n) ((length([x 1 , x 2 … x n ] ++ ys) = (n + (length ys))) Additive Property of Concatenation proven by the principle of induction (x: xs) ++ ys = x: (xs ++ ys) (++) : [ ] ++ ys = ys (++) [ ] (++) axioms review Proof of this theorems confirms that this equation is always true TESTING COULD NEVER CONFIRM THIS FACT Another way to say it: xs. ys.((length(xs ++ ys) = ((length xs) + (length ys))) CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2
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