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EDIT: Let me add the following properties that you can assume to. too:

No Format
  (booleanp z) => (andp z t) = z
  (booleanp z) => (andp t z) = z
  (booleanp z) => (orp z nil) = z
  (booleanp z) => (orp nil z) = z

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These may come in handy in the proofs of the next theorems.

For *EDIT*: note that proving the above gives you that the following two theorems are true:

  • (and-foldp (app x y)) = (andp (and-foldp x) (and-foldp y))
  • (or-foldp (app x y)) = (orp (of-foldp x) (or-foldp y))

These may come in handy in the proofs of the next theorems.

the next few theorems, you will want to prove the following lemma first:

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