Thm* eq:{T= }, L,M:T List. L (eq)M  ( x:{x:T| x( eq) L }. x( eq) M) | [is_intersection_implies_exists_element] |
Thm* eq:{T= }, x,y:T, L:T List. x( eq) L  eq(x,y)  x( eq) remove(eq;y;L) | [not_is_member_remove_lemma] |
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* eq:{T= }, L:T List, x:T. x( eq) L  ( M,N:T List. L = (M @ (x.N)) & remove(eq;x;L) = (M @ N)) | [is_member_remove_lemma] |
Thm* eq:{T= }, u:T, L:T List. u( eq) L  ( v:T, M:T List. L = v.M) | [is_member_non_nil] |
Thm* eq:{T= }, L:T List, x:T. ( M,N:T List. L = (M @ (x.N)))  x( eq) L | [append_is_member_lemma] |
Thm* eq:{T= }, L:T List, x:T. x( eq) L  ( M,N:T List. L = (M @ (x.N))) | [is_member_append_lemma] |
Thm* eq:{T= }, L:T List. L( eq)nil  L = nil | [sublist_of_nil_iff_nil] |
Thm* L,M:T List, eq:{T= }. L( eq)M  ( eq)(L,M) | [sublist_iff_assert_sublist_2_x] |
Thm* eq:{T= }, x:T, L,M:T List. x( eq) L  L( eq)M  x( eq) M | [is_member_sublist_lemma] |
Thm* eq:{T= }, L:T List. L( eq)L | [sublist_reflexive] |
Thm* EQ:{T= }, eq:{T }, L,M:T List. L( eq)M  ( z:T. z( EQ) L  z( eq) M) | [sublist_list_all_lemma] |
Thm* eq:{T= }, u:T, v:T List. v( eq)(u.v) | [sublist_tail1] |
Thm* T:Type, eq:{T= }, L1,L2:T List. L1( eq)L2 Type | [sublist_wf1] |
Thm* eq:{T= }, L,M:T List. disjoint(eq;L;M)  ( x:T. x( eq) L & x( eq) M) | [not_disjoint_is_member_lemma] |
Thm* eq:{T= }, P:(T Type), L:T List. x L.P(x)  ( x:{x:T| x( eq) L }. P(x)) | [list_all_all] |
Thm* eq:{T= }, P:(T Type), L:T List. x L.P(x)  ( x:{x:T| x( eq) L }. P(x)) | [list_exists_exists] |
Thm* eq:{T= }, P:(T Prop), x:T, L:T List. x( eq) L  P(x)  y L.P(y) | [list_exists_is_member_lemma1] |
Thm* eq:{T= }, P:(T Prop), L:T List. ( x:T. x( eq) L & P(x))  y L.P(y) | [list_exists_is_member_lemma] |
Thm* eq:{T= }, P:(T Prop), L:T List. x L.P(x)  ( z:T. z( eq) L  P(z)) | [list_all_is_member_lemma] |
Thm* equiv:{T }, eq:{T= }, u:T, L:T List. u( equiv) L  ( v:T. equiv(u,v) & v( eq) L) | [is_member_equality_strengthening_lemma] |
Thm* eq:{T= }, u:T, L:T List. u( eq) L  ( f:{T }. u( f) L) | [is_member_equalities_lemma] |