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Exercise 1:

  • Write a recursive function taking a natural number to a boolean value. That value is true iff the number if even

Exercise 2:

  • State and prove the following boolean formulas: b1 && (~~ b2 || b3) = (b1 && ~~ b2) || (b1 && b3)

Exercise 3 :

Prove Peirce's law using only the rewrite command.

  • Hint: use Search to find relevant lemmas about ==> and ~~
  • Hint: use the lemma that says (a || b) && a = a

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