Thm* f:(T1![](FONT/dash.png) T2), Q:(T2![](FONT/dash.png) ![](FONT/then_med.png) ), L:T1 List.
Thm* filter(Q;map(f;L)) = map(f;filter(Q o f;L)) | [filter_map] |
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: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* 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* f,as':Top, A:Type, as:A List. map(f;as @ as') ~ (map(f;as) @ map(f;as')) | [map_append_sq] |
Def unzip(as) == <map( p.1of(p);as),map( p.2of(p);as)> | [unzip] |