| Rank | Theorem | Name |
| 9 | Thm* L:MsgA List, M:MsgA. ( A,B L.A ||+ B)  (M L)  M (L) | [ma-sub-join-list] |
| cites the following: |
| 1 | Thm* l:T List, a,x:T. (x [a / l])  x = a (x l) | [cons_member] |
| 1 | Thm* T:Type{i}, x:T, L:T List, P:(T T Prop{i'}).
Thm* ( x,y [x / L].P(x,y))  ( x,y L.P(x,y)) & ( y L.P(x,y)) | [pairwise-cons] |
| 6 | Thm* M1,M2:MsgA. M1 M1 M2 | [ma-sub-join-left] |
| 7 | Thm* M1,M2,M3:MsgA. M1 M2  M2 M3  M1 M3 | [ma-sub_transitivity] |
| 6 | Thm* M1,M2:MsgA. M1 || M2  M2 M1 M2 | [ma-sub-join-right] |
| 8 | Thm* L:MsgA List.
Thm* ( A,B L.A ||+ B)  (L) MsgA & ( M:MsgA. ( B L.M ||+ B)  M ||+ (L)) | [ma-join-list-property] |