Thm* l:T List, x,y,z:T.
Thm* no_repeats(T;l)  x before y l  y before z l  x before z l | [l_before_transitivity] |
Thm* L1,L2,L:T List, x:T.
Thm* no_repeats(T;L)  L1 @ [x] L  [x / L2] L  L1 @ [x / L2] L | [append_overlapping_sublists] |
Thm* l:T List. no_repeats(T;l)  ( x,y:T. x before y l  x = y) | [no_repeats_iff] |
Thm* as:T1 List, bs:T2 List. ||as|| = ||bs||  unzip(zip(as;bs)) = <as,bs> | [unzip_zip] |
Thm* as:T1 List, bs:T2 List. ||as|| = ||bs||  ||zip(as;bs)|| = ||as||  | [length_zip] |
Thm* as:T1 List, bs:T2 List, i: .
Thm* i<||zip(as;bs)||  zip(as;bs)[i] = <as[i],bs[i]> | [select_zip] |
Thm* L_1,L_2:T List. L_1 L_2  L_1 L_2 | [iseg_is_sublist] |
Thm* l1,l2:T List. l1 l2  ||l1|| ||l2|| | [iseg_length] |
Thm* P:(T  ), L2,L1:T List. L1 L2  filter(P;L1) filter(P;L2) | [filter_iseg] |
Thm* l1,l2:T List, x:T. l1 l2  (x l1)  (x l2) | [iseg_member] |
Thm* l1,l2:T List. l1 l2  ||l1|| ||l2|| & ( i: . i<||l1||  l1[i] = l2[i]) | [iseg_select] |
Thm* l1,l2,l3:T List. l2 l3  l1 l2  l1 l3 | [iseg_transitivity2] |
Thm* l1,l2,l3:T List. l1 l2  l1 l2 @ l3 | [iseg_append] |
Thm* l1,l2,l3:T List. l1 l2  l2 l3  l1 l3 | [iseg_transitivity] |
Thm* L:A List, f1,f2:(A  ). f1 = f2  (filter(f1;L) ~ filter(f2;L)) | [filter_functionality] |
Thm* L:T List, a,b:T. a before b L  (a L) | [l_before_member2] |
Thm* L:T List, a,b:T. a before b L  (b L) | [l_before_member] |
Thm* x,y:T, L:T List.
Thm* (x L)  (y L)  x = y x before y L y before x L | [l_tricotomy] |
Thm* L:T List, i,j: ||L||. i<j  [L[i]; L[j]] L | [sublist_pair] |
Thm* L1,L2:T List. null(L2)  L1 tl(L2)  L1 L2 | [sublist_tl] |
Thm* L1,L2:T List. L1 = L2  L1 L2 | [sublist_weakening] |
Thm* L1,L2:T List. L1 L2  L2 L1  L1 = L2 | [sublist_antisymmetry] |
Thm* L1,L2:T List. L1 L2  ||L1|| = ||L2||  L1 = L2 | [proper_sublist_length] |
Thm* L1,L2:T List. L1 L2  ||L1|| ||L2|| | [length_sublist] |
Thm* L1,L2,L3:T List. L1 L2  L2 L3  L1 L3 | [sublist_transitivity] |
Thm* L:T List, x:T. null(L)  last([x / L]) = last(L) | [last_cons] |
Thm* T:Type, L:T List. null(L)  last(L) T | [last_wf] |
Thm* x:T, l:T List. ( y:T. Dec(x = y))  Dec((x l)) | [l_member_decidable] |
Thm* L:T List, x:T. (x L)  null(L) | [member_null] |
Thm* L:T List, x:T. null(L)  (x L) | [null_member] |
Thm* as:T List, x:T. 0<||as||  (x tl(as))  (x as) | [member_tl] |
Thm* a:T List, f:(T T). ( x:T. (x a)  f(x) = x)  map(f;a) = a | [trivial_map] |
Thm* a:T List, f,g:(T T').
Thm* ( x:T. (x a)  f(x) = g(x))  map(f;a) = map(g;a) | [map_equal2] |
Thm* L:T List. L = nil  ( x:T. (x L)) | [member_exists] |
Thm* z:T List. ||z|| = 2  z = [z[0]; z[1]] | [list_2_decomp] |
Thm* Q:((T List) Prop).
Thm* Q(nil)  ( ys:T List, x:T. Q(ys)  Q(ys @ [x]))  ( zs:T List. Q(zs)) | [list_append_singleton_ind] |
Thm* L:T List. 0<||L||  ( x:T, L':T List. L = (L' @ [x])) | [list_decomp_reverse] |
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] |
Thm* L:T List. 0<||L||  (L ~ [hd(L) / tl(L)]) | [list_decomp] |
Thm* L:T List. L = nil  0<||L|| | [non_nil_length] |
Thm* L:T List, P:( ||L|| Prop).
Thm* ( x: ||L||. Dec(P(x)))
Thm* 
Thm* ( i,j: ||L||. P(i)  i<j  P(j))
Thm* 
Thm* ( L_1,L_2:T List. L = (L_1 @ L_2) & ( i: ||L||. P(i)  ||L_1|| i)) | [append_split2] |
Def no_repeats(T;l) == i,j: . i<||l||  j<||l||  i = j  l[i] = l[j] T | [no_repeats] |