L:T List, a,b:T. a before b 
L 
(b L)x:T, L:T List. (x L) 
[x] 
LL1,L2,L3:T List. L1 L2 L2 L3 L1 L3L1,L2:T List. 
null(L2) L1 tl(L2) L1 L2L1,L2:T List. L1 = L2 L1 L2| Rank | Theorem | Name |
| 3 | L:T List, a,b:T. a before b L (b L) | [l_before_member] |
| cites the following: | ||
| 0 | x:T, L:T List. (x L) [x] L | [member_iff_sublist] |
| 2 | L1,L2,L3:T List. L1 L2 L2 L3 L1 L3 | [sublist_transitivity] |
| 2 | L1,L2:T List. null(L2) L1 tl(L2) L1 L2 | [sublist_tl] |
| 1 | L1,L2:T List. L1 = L2 L1 L2 | [sublist_weakening] |