The inductive step of the

The correct answer to Question 1 in logic-knowledge-taken-for-granted is *Choice (iv)*.

The Induction Step of the inductive proof of

(implies (true-listp z) (equal (rev (rev z)) z))

for an induction on the linear list

Induction Step: (implies (and (not (endp z)) (implies (true-listp (cdr z)) (equal (rev (rev (cdr z))) (cdr z)))) (implies (true-listp z) (equal (rev (rev z)) z)))

The second hypothesis above is the *induction hypothesis*. The
conclusion above is the formula we are trying to prove. Each induction
hypothesis is *always* an

If you thought the right answer was

Induction Step -- Choice (i): (implies (not (endp z)) (implies (true-listp z) (equal (rev (rev z)) z)))

then perhaps you didn't understand that we're doing an inductive proof.
Certainly if you prove the Base Case already discussed and you prove *Choice
(i)* above, then you will have proved the goal conjecture, but you would
have done it by simple case analysis: prove it when *Choice (i)* directly because you have no induction hypothesis to work
with.

If you thought the right answer was:

Induction Step -- Choice (ii): (implies (true-listp (cdr z)) (equal (rev (rev (cdr z))) (cdr z)))

then perhaps you misunderstand the difference between the *Induction
Step* and the *Induction Hypothesis*. The Induction *Step* is
the ``other half'' of the main proof, balancing the Base Case. The Induction
*Hypothesis* is just a hypothesis you get to use during the Induction
Step. The question Q1 asked what is the Induction Step.

If you thought the right answer was:

Induction Step -- Choice (iii): (implies (and (not (endp z)) (equal (rev (rev (cdr x))) (cdr x))) ;``induction hyp''(implies (true-listp z) (equal (rev (rev z)) z)))

then you are making the most common mistake newcomers make to induction.
You are giving yourself an ``induction hypothesis'' that is not an instance of
the conjecture you're proving. This alleged induction hypothesis says that
*if*

If this doesn't make sense, perhaps you should read about

When you understand why *Choice (iv)* is the correct answer, use your
browser's **Back Button** to return to logic-knowledge-taken-for-granted and go to question Q2.