| Rank | Theorem | Name |
| 5 | Thm* eq:EqDecider(A), B:(A Type), f,g,h:a:A fp-> B(a).
Thm* h || f  h || g  h || f g | [fpf-compatible-join] |
| cites the following: |
| 4 | Thm* B:(A Type), eq:EqDecider(A), f,g:a:A fp-> B(a), x:A.
Thm* x dom(f g)  f g(x) = if x dom(f) f(x) else g(x) fi B(x) | [fpf-join-ap] |
| 3 | Thm* B:(A Type), eq:EqDecider(A), f,g:a:A fp-> B(a), x:A.
Thm* x dom(f g)  x dom(f) x dom(g) | [fpf-join-dom] |