Level 1. Given an explicit object x and an explicit property p(x),prove that p(x) is true.
Level 2. Given an explicit set X and an explicit property p(x),prove that p(x) is true for all x in X.
Level 3. Given an explicit set X and an explicit property p(x),prove or disprove that p(x) is true for all x in X.
Level 4. Given an explicit set X and an explicit property p(x),find a necessary and sufficient condition q(x) that p(x) is true.
Level 5. Given an explicit set X , find an interesting property p(x) of its elements.