Thm* l:T List, x:T. no_repeats(T;[x / l]) ![](FONT/if_big.png) no_repeats(T;l) & (x l) | [no_repeats_cons] |
Thm* P:(T![](FONT/dash.png) ![](FONT/then_med.png) ), as:T List, d:T.
Thm* ((first a as s.t. P(a) else d) as)
Thm* (first a as s.t. P(a) else d) = d | [find_property] |
Thm* l1,l2:T List, x:T. l1 l2 ![](FONT/eq.png) (x l1) ![](FONT/eq.png) (x l2) | [iseg_member] |
Thm* P:(T![](FONT/dash.png) ![](FONT/then_med.png) ), L:T List, x:T. (x filter(P;L)) ![](FONT/if_big.png) (x L) & P(x) | [member_filter] |
Thm* l:T List, a,x,y:T.
Thm* x before y [a / l] ![](FONT/if_big.png) x = a & (y l) x before y l | [cons_before] |
Thm* L:T List, a,b:T. a before b L ![](FONT/eq.png) (a L) | [l_before_member2] |
Thm* L:T List, a,b:T. a before b L ![](FONT/eq.png) (b L) | [l_before_member] |
Thm* x,y:T, L:T List.
Thm* (x L) ![](FONT/eq.png) (y L) ![](FONT/eq.png) x = y x before y L y before x L | [l_tricotomy] |
Thm* x:T, L:T List. (x L) ![](FONT/if_big.png) [x] L | [member_iff_sublist] |
Thm* a:T List, x:T', f:(T![](FONT/dash.png) T'). (x map(f;a)) ![](FONT/if_big.png) ( y:T. (y a) & x = f(y)) | [member_map] |
Thm* a,x:T. (x [a]) ![](FONT/if_big.png) x = a | [member_singleton] |
Thm* L:T List, i: ||L||. (L[i] L) | [select_member] |
Thm* x:T, l1,l2:T List. (x l1 @ l2) ![](FONT/if_big.png) (x l1) (x l2) | [member_append] |
Thm* x:T, l:T List. ( y:T. Dec(x = y)) ![](FONT/eq.png) Dec((x l)) | [l_member_decidable] |
Thm* l:T List, a,x:T. (x [a / l]) ![](FONT/if_big.png) x = a (x l) | [cons_member] |
Thm* L:T List, x:T. (x L) ![](FONT/eq.png) null(L) | [member_null] |
Thm* L:T List, x:T. null(L) ![](FONT/eq.png) (x L) | [null_member] |
Thm* x:T. (x nil) ![](FONT/if_big.png) False | [nil_member] |
Thm* as:T List, x:T. 0<||as|| ![](FONT/eq.png) (x tl(as)) ![](FONT/eq.png) (x as) | [member_tl] |
Thm* a:T List, f:(T![](FONT/dash.png) T). ( x:T. (x a) ![](FONT/eq.png) f(x) = x) ![](FONT/eq.png) map(f;a) = a | [trivial_map] |
Thm* a:T List, f,g:(T![](FONT/dash.png) T').
Thm* ( x:T. (x a) ![](FONT/eq.png) f(x) = g(x)) ![](FONT/eq.png) map(f;a) = map(g;a) | [map_equal2] |
Thm* L:T List. L = nil ![](FONT/eq.png) ( x:T. (x L)) | [member_exists] |