Thm* F:(A![](FONT/dash.png) Prop), L:A List. ( k:A. Dec(F(k))) ![](FONT/eq.png) Dec(( k L.F(k))) | [decidable__l_all] |
Thm* L1,L2:T List, P:(T![](FONT/dash.png) ![](FONT/then_med.png) ). L2 filter(P;L1) ![](FONT/if_big.png) L2 L1 & ( x L2.P(x)) | [sublist_filter] |
Thm* L:T List, P:(T![](FONT/dash.png) ![](FONT/then_med.png) ). ( x L.P(x)) ![](FONT/if_big.png) reduce( x,y. P(x)![](FONT/and.png) y;true ;L) | [l_all_reduce] |
Thm* P:(T![](FONT/dash.png) Prop). ( x nil.P(x)) | [l_all_nil] |
Thm* f:(A![](FONT/dash.png) B), L:A List, P:(B![](FONT/dash.png) Prop). ( x map(f;L).P(x)) ![](FONT/if_big.png) ( x L.P(f(x))) | [l_all_map] |
Thm* L:T List, P:(T![](FONT/dash.png) Prop). ( x L.P(x)) ![](FONT/eq.png) L {x:T| P(x) } List | [list_set_type] |
Thm* P:(T![](FONT/dash.png) ![](FONT/then_med.png) ), L:T List. ( x L. P(x)) ![](FONT/eq.png) (filter(P;L) ~ nil) | [filter_is_nil] |
Thm* P:(T![](FONT/dash.png) ![](FONT/then_med.png) ), L:T List. ( x L.P(x)) ![](FONT/eq.png) filter(P;L) = L | [filter_trivial2] |
Thm* P:(T![](FONT/dash.png) ![](FONT/then_med.png) ), L:T List. ( x L.P(x)) ![](FONT/eq.png) (filter(P;L) ~ L) | [filter_trivial] |
Thm* P:(T![](FONT/dash.png) Prop), x:T, L:T List. ( y [x / L].P(y)) ![](FONT/if_big.png) P(x) & ( y L.P(y)) | [l_all_cons] |