Thm* 'c,'b,'a:S.
Thm* all
Thm* ( f:'a  'c. all
Thm* ( f:'a  'c. ( g:'b  'c. exists_unique
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. and
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (all
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. equal
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. (h(inl(x))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. ,f(x)))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,all
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. equal
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. (h(inr(x))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. ,g(x))))))) | [hsum_axiom_2] |
Thm* 'c,'b,'a:S.
Thm* all
Thm* ( f:'a  'c. all
Thm* ( f:'a  'c. ( g:'b  'c. exists_unique
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. and
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (equal(o(h,inl),f)
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,equal(o(h,inr),g))))) | [hsum_axiom] |