| Rank | Theorem | Name |
| 5 | Thm* strong-subtype(A;A')
Thm* 
Thm* ( B:(A Type), C:(A' Type), eq:EqDecider(A), eq':EqDecider(A'),
Thm* ( f,g:a:A fp-> B(a). ( a:A. B(a) r C(a))  f g  f g) | [fpf-sub-functionality] |
| cites the following: |
| 4 | Thm* eq:EqDecider(Y), f:x:X fp-> Top, x:Y.
Thm* strong-subtype(X;Y)  x dom(f)  x X | [fpf-dom-type2] |
| 1 | Thm* strong-subtype(A;B)  (EqDecider(B) r EqDecider(A)) | [strong-subtype-deq-subtype] |
| 4 | Thm* eq1,eq2:EqDecider(A), f:a:A fp-> Top, x:A. x dom(f)  x dom(f) | [fpf-dom_functionality2] |
| 2 | Thm* B1:(A1 Type), B2:(A2 Type).
Thm* strong-subtype(A1;A2)
Thm* 
Thm* ( a:A1. B1(a) r B2(a))  (a:A1 fp-> B1(a) r a:A2 fp-> B2(a)) | [subtype-fpf3] |