Thm* 'a,'b:S.
Thm* all
Thm* ( e:'b. equal
Thm* ( e:'b. (inr(e)
Thm* ( e:'b. ,abs_sum( b:hbool. x:'a. y:'b. and(equal(y,e),not(b))))) | [hinr_def] |
Thm* 'b,'a:S.
Thm* all
Thm* ( e:'a. equal(inl(e),abs_sum( b:hbool. x:'a. y:'b. and(equal(x,e),b)))) | [hinl_def] |
Thm* 'a,'b:S.
Thm* ( x:'a+'b. abs_sum(rep_sum(x)) = x 'a+'b)
Thm* & ( x:(  'a 'b  ). is_sum_rep(x) = ((rep_sum(abs_sum(x))) = x)) | [sum_iso] |
Thm* 'a,'b:S.
Thm* and
Thm* (all( a:hsum('a; 'b). equal(abs_sum(rep_sum(a)),a))
Thm* ,all
Thm* ,( r:hbool  'a  'b  hbool. equal
Thm* ,( r:hbool  'a  'b  hbool. (is_sum_rep(r)
Thm* ,( r:hbool  'a  'b  hbool. ,equal(rep_sum(abs_sum(r)),r)))) | [hsum_iso_def] |