Changes

Summary

1. merged
2. added lemma refl_lex_prod[simp]
3. added lemmas reflI and reflD
4. added lemmas asym_on_lex_prod[simp] and asym_lex_prod[simp]
5. added lemmas sym_on_lex_prod[simp] and sym_lex_prod[simp]
6. added lemmas irrefl_on_lex_prod[simp] and irrefl_lex_prod[simp]
7. strengthened and renamed lemmas asym_if_irrefl_and_trans and asymp_if_irreflp_and_transp
8. strengthened and renamed lemma antisym_converse and added lemma antisymp_on_conversep
9. added lemmas asym_on_converse[simp] and asymp_on_conversep[simp]
10. strengthened and renamed lemma sym_converse and added lemma symp_on_conversep
11. strengthened and renamed lemmas antisymp_less and antisymp_greater
12. strengthened lemmas antisym_on_if_asym_on and antisymp_on_if_asymp_on
13. tuned naming
14. added lemma asymp_on_asym_on_eq[pred_set_conv]
15. strengthened and renamed asymp_less and asymp_greater
16. added lemmas asym_on_subset and asymp_on_subset
17. added lemmas asym_onI, asymp_onI, asym_onD, and asymp_onD
18. added predicates asym_on and asymp_on and redefined asym and asymp to be abbreviations