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