theory Exercises4 = Main: text {* Proof (in single steps:) *} lemma "(\x. \y. R x y) = (\y. \x. R x y)" oops lemma "((\x. P x) \ (\x. Q x)) = (\x. (P x \ Q x))" oops lemma "((\x. P x) \ (\x. Q x)) = (\x. (P x \ Q x))" oops lemma "(\(\x. P x)) = (\x. \ P x)" oops text {* Prove or disprove: If every poor person has a rich mother then there is a rich person with a rich grandmother. *} theorem "\person. \rich person \ rich (mother_of person) \ \person. rich (mother_of (mother_of person)) \ rich person" oops end