prove more algebraic version of functorial properties; retain old properties for convenience
use "../settings.ML";
use_thy "Tree";
use_thy "Tree2";
use_thy "Plus";
use_thy "case_exprs";
use_thy "fakenat";
use_thy "natsum";
use_thy "pairs";
use_thy "Option2";
use_thy "types";
use_thy "prime_def";
use_thy "simp";
use_thy "Itrev";
use_thy "AdvancedInd";
use_thy "appendix";