x:T, l:T List. (y:T. Dec(x = y)) 
Dec((x 
l))x:T. (x nil) 
Falsel:T List, a,x:T. (x [a / l]) x = a 
(x l)| Rank | Theorem | Name |
| 2 | x:T, l:T List. (y:T. Dec(x = y)) Dec((x l)) | [l_member_decidable] |
| cites the following: | ||
| 0 | x:T. (x nil) False | [nil_member] |
| 1 | l:T List, a,x:T. (x [a / l]) x = a (x l) | [cons_member] |