Thm* eq:{T= }, P:(T  ), L:T List, x:T. x( eq) L  P(x)  x( eq) filter(( x.P(x));L) | [filter_is_member_lemma] |
Thm* eq:{T= }, P:(T  ), L:T List, x:T. x( eq) filter(( x.P(x));L)  P(x) | [is_member_filter_lemma] |
Thm* T:Type, L,M:T List, eq:(T T  ). ( eq)(L,M)  | [apply_wf_sublist_2] |
Thm* T:Type, L,M:T List, eq:(T T  ). ( eq)(L,M)  | [apply_sublist_2_wf] |
Thm* T:Type, eq:(T T  ), L1,L2:T List. L1( eq)L2 Type | [sublist_wf] |
Thm* T:Type, eq:{T }, L,M:T List. disjoint (eq;L;M)  | [disjoint2_wf] |
Thm* eq:(T T  ), L1,L2:T List, x:T. disjoint(eq;(x.L1);L2)  disjoint(eq;L1;L2) | [disjoint_tail] |
Thm* eq:(T T  ), L1,L2:T List. Dec(disjoint(eq;L1;L2)) | [decidable__disjoint] |
Thm* T:Type, P:(T  ), L:T List. x L.P(x)  | [list_exists_2_wf] |
Thm* P:(T  ), L:T List. x L.P(x)  x L.P(x) | [list_all_2_all] |
Thm* eq:(T T  ), L:T List. x L.x( eq) nil  nil = L | [list_all_is_member_nil_lemma] |
Thm* L:T List, P:(T  ). x L.P(x)  x L.P(x) | [list_all_iff_assert_list_all_2] |
Thm* eq:{T }, P:(T  ), L:T List.  x L.P(x)  ( x:{x:T| x( eq) L }. P(x)) | [not_list_all_2_implies_exists_not] |
Thm* T:Type, P:(T  ), L:T List. x L.P(x)  | [list_all_2_wf] |
Thm* eq:(T T  ), x:T, L:T List. Dec(x( eq) L) | [decidable__is_member] |
Thm* eq:(T T  ), x:T, L:T List. SqStable(x( eq) L) | [sq_stable__is_member] |
Thm* T:Type, eq:(T T  ), x:T, L:T List. x( eq) L  | [is_member_wf] |
Thm* T:Type, eq:(T T  ), u:T. u( eq) nil  | [is_member_wf_nil] |
Thm* T:Type, f:(T  ), L:T List. filter(f;L) {x:T| f(x) } List | [filter_wf_subtype] |
Thm* T:Type, f:(T  ), L:T List. filter(f;L) T List | [filter_wf] |
Thm* T:Type, eq:(T T  ), x:T, L:T List. remove(eq;x;L) T List | [remove_wf] |
Thm* L:T List. null(L) = false  ( h:T, t:T List. L = h.t) | [null_false_lemma] |
Thm* L:T List. null(L) = true  L = nil | [null_true_lemma] |