| Rank | Theorem | Name |
| 3 | Thm* the_es:ES, e',e:E. (e before(e'))  (e <loc e') | [member-es-before] |
| cites the following: |
| 0 | Thm* the_es:ES, j,e:E. first(j)  (e <loc j) | [es-first-implies] |
| 0 | Thm* x:T. (x nil)  False | [nil_member] |
| 1 | Thm* l:T List, a,x:T. (x [a / l])  x = a (x l) | [cons_member] |
| 2 | Thm* x:T, l1,l2:T List. (x l1 @ l2)  (x l1) (x l2) | [member_append] |
| 1 | Thm* the_es:ES, e,e':E.
Thm* (e <loc e')  first(e') & e = pred(e') E (e <loc pred(e')) | [es-locl-iff] |
| 0 | Thm* the_es:ES, j:E. first(j)  (pred(j) <loc j) | [es-pred-locl] |