Thm* f:(  (T List)), t,t': .
Thm* t<t'  concat(map(f;upto(t))) @ (f(t)) concat(map(f;upto(t'))) | [concat_map_upto] |
Thm* n,m: . firstn(n;upto(m)) ~ if n m upto(n) else upto(m) fi | [firstn_upto] |
Thm* f:(Top Top), n: , l:Top List. firstn(n;map(f;l)) ~ map(f;firstn(n;l)) | [firstn_map] |
Thm* t',m: , T:Type, f:(  T), P:(T  ).
Thm* m+1 ||filter(P;map(f;upto(t')))||
Thm* 
Thm* ( t: . P(f(t)) & ||filter(P;map(f;upto(t)))|| = m ) | [filter_map_upto2] |
Thm* i,j: .
Thm* i<j
Thm* 
Thm* ( f:(  T), P:(T  ).
Thm* (P(f(i))  ||filter(P;map(f;upto(i)))||<||filter(P;map(f;upto(j)))||) | [filter_map_upto] |
Thm* n: , x,y: n. x before y upto(n)  x<y | [before-upto] |
Thm* n,i: . i<n  (i upto(n)) | [member_upto2] |
Thm* n,i: . (i upto(n))  i<n | [member_upto] |
Thm* m: , n: m. upto(m)[n] = n | [select_upto] |
Thm* i,j: . i j  upto(i) upto(j) | [upto_iseg] |
Thm* m: , n: (m+1). upto(m) ~ (upto(n) @ map( x.x+n;upto(m-n))) | [upto_decomp] |
Thm* n: . ||upto(n)|| ~ n | [length_upto] |
Thm* n: . upto(n) n List | [upto_wf] |
Thm* f:(   ). ( n: . f(n))  f(mu(f)) & ( i: . i<mu(f)  f(i)) | [mu-property] |
Thm* f:(   ). ( n: . f(n))  mu(f)  | [mu_wf] |
Thm* r: , L:Top List. ||nth_tl(r;L)|| = if r< ||L|| ||L||-r else 0 fi | [general_length_nth_tl] |
Thm* n,m: , f,i:Top. (f^n+m(i)) ~ (f^n(f^m(i))) | [fun_exp_add_sq] |
Def IdLnk == Id Id  | [IdLnk] |
Def Id == Atom  | [Id] |
Def finite-type(T) == n: , f:( n T). Surj( n; T; f) | [finite-type] |