# Theorem 5.7 is already proved there, what else do you need to prove

in it? please let me know. Well here is the final question, in the proof of theorem 5.7, it was proven that C(2z) is less than or equal to 0 and 0 < C(0). Therefore, the reasoning goes that by the intermediate value theorem C(w)= 0 for some w in (0, 2z). But the IMT only applies when the real number (in this case 0) is strictly in between the functional values. Here it was only proven that 0 is greater than or equal to C(2z). This is the final piece to the solution of this problem. By logical reasoning, you can reason from p to (p ∨ q) or q to (p ∨ q) but you cannot do the converse reasoning. So you can reason from a strict inequality to a nonstrict inequality by the valid inference of disjunction but the converse is invalid reasoning.

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