Thm* and
Thm* (all( a:hnum. equal(abs_num(rep_num(a)),a))
Thm* ,all( r:hind. equal(is_num_rep(r),equal(rep_num(abs_num(r)),r)))) | [hnum_iso_def] |
Thm* exists( rep:hnum  hind. type_definition(is_num_rep,rep)) | [hnum_ty_def] |
Thm* all
Thm* ( m:hind. equal
Thm* ( m:hind. (is_num_rep(m)
Thm* ( m:hind. ,all
Thm* ( m:hind. ,( P:hind  hbool. implies
Thm* ( m:hind. ,( P:hind  hbool. (and
Thm* ( m:hind. ,( P:hind  hbool. ((P(zero_rep)
Thm* ( m:hind. ,( P:hind  hbool. (,all( n:hind. implies(P(n),P(suc_rep(n)))))
Thm* ( m:hind. ,( P:hind  hbool. ,P(m))))) | [his_num_rep_wd] |
Thm* equal(zero_rep,select( x:hind. all( y:hind. not(equal(x,suc_rep(y)))))) | [hzero_rep_def] |
Thm* equal(suc_rep,select( f:hind  hind. and(one_one(f),not(onto(f))))) | [hsuc_rep_def] |
Thm* abs_num (hind  hnum) | [habs_num_wf] |