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