Thm* as:T1 List, bs:T2 List, i: .
Thm* i<||zip(as;bs)||  zip(as;bs)[i] = <as[i],bs[i]> | [select_zip] |
Thm* l1,l2:T List. l1 l2  ||l1|| ||l2|| & ( i: . i<||l1||  l1[i] = l2[i]) | [iseg_select] |
Thm* L:T List, i,j: ||L||. i<j  [L[i]; L[j]] L | [sublist_pair] |
Thm* L:T List, i: ||L||. (L[i] L) | [select_member] |
Thm* n: , f:( n T), i: n. mklist(n;f)[i] = f(i) | [mklist_select] |
Thm* z:T List. ||z|| = 2  z = [z[0]; z[1]] | [list_2_decomp] |
Thm* a:T List, f,g:(T T').
Thm* ( i: . i<||a||  f(a[i]) = g(a[i]))  map(f;a) = map(g;a) | [map_equal] |
Thm* a,b:T List. ||a|| = ||b||  ( i: . i<||a||  a[i] = b[i])  a = b | [list_extensionality] |
Thm* m: , L:T List. m<||L||  (nth_tl(m;L) ~ [L[m] / nth_tl(1+m;L)]) | [nth_tl_decomp] |
Def no_repeats(T;l) == i,j: . i<||l||  j<||l||  i = j  l[i] = l[j] T | [no_repeats] |
Def L1 L2
Def == f:( ||L1||  ||L2||).
Def == increasing(f;||L1||) & ( j: ||L1||. L1[j] = L2[(f(j))] T) | [sublist] |
Def last(L) == L[(||L||-1)] | [last] |
Def (x l) == i: . i<||l|| & x = l[i] T | [l_member] |