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Exercise 1:

  • look for lemmas supporting contrapositive reasoning
  • use the eqP view to finish the proof.

Exercise 2:

  • it helps to find out what is behind ./2 and .*2 in order to Search
  • any proof would do, but there is one not using implyP

Exercise 3:

  • Prove this view by unfolding maxn and then using leqP

Exercise 4:

  • there is no need to prove reflect with iffP: here just use rewrite and apply
  • check out the definitions and theory of leq and maxn
  • proof sketch:
       n <= m = n - m == 0
              = m + n - m == m + 0
              = maxn m n == m