Thm* as:T1 List, bs:T2 List, i: .
Thm* i<||zip(as;bs)|| ![](FONT/eq.png) zip(as;bs)[i] = <as[i],bs[i]> | [select_zip] |
Thm* l1,l2:T List. l1 l2 ![](FONT/if_big.png) ||l1|| ||l2|| & ( i: . i<||l1|| ![](FONT/eq.png) l1[i] = l2[i]) | [iseg_select] |
Thm* n: , f:( n![](FONT/dash.png) T), i: n. mklist(n;f)[i] = f(i) | [mklist_select] |
Thm* n: , f:( n![](FONT/dash.png) T). ||mklist(n;f)|| = n ![](FONT/int.png) | [mklist_length] |
Thm* z:T List. ||z|| = 2 ![](FONT/eq.png) z = [z[0]; z[1]] | [list_2_decomp] |
Thm* f:(A![](FONT/dash.png) B), as:A List. ||map(f;as)|| = ||as|| ![](FONT/nat.png) | [map_length_nat] |
Thm* a:T List, f,g:(T![](FONT/dash.png) T').
Thm* ( i: . i<||a|| ![](FONT/eq.png) f(a[i]) = g(a[i])) ![](FONT/eq.png) map(f;a) = map(g;a) | [map_equal] |
Thm* a,b:T List. ||a|| = ||b|| ![](FONT/eq.png) ( i: . i<||a|| ![](FONT/eq.png) a[i] = b[i]) ![](FONT/eq.png) a = b | [list_extensionality] |
Thm* m: , L:T List. m<||L|| ![](FONT/eq.png) (nth_tl(m;L) ~ [L[m] / nth_tl(1+m;L)]) | [nth_tl_decomp] |
Def no_repeats(T;l) == i,j: . i<||l|| ![](FONT/eq.png) j<||l|| ![](FONT/eq.png) i = j ![](FONT/eq.png) l[i] = l[j] T | [no_repeats] |
Def (x l) == i: . i<||l|| & x = l[i] T | [l_member] |