Thm* T:Type, eq:{T }, L,M:T List. L (eq)M Type | [is_intersection_wf] |
Thm* eq:{T }, u:T, L:T List, v:T. v( eq) remove(eq;u;L)  v( eq) L | [remove_is_member_lemma] |
Thm* eq:{T }, L,M:T List. Dec(L(~eq)M) | [decidable__list_iso] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. L(~eq)M  (~ eq)(L,M)) | [list_iso_iff_assert_list_iso_2] |
Thm* L1,L2:T List, eq1,eq2,eq3:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  eq2 = eq3  L1(~eq1)L2  L3(~eq2)L4  (L1(~eq3)L3  L2(~eq3)L4) | [list_iso_functionality_wrt_id_list_iso_list_iso] |
Thm* L1,L2:T List, eq1,eq2:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  L1(~eq1)L2  L3 = L4  (L1(~eq2)L3  L2(~eq2)L4) | [list_iso_functionality_wrt_id_list_iso_id] |
Thm* L1,L2:T List, eq1,eq2,eq3,eq4:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  eq2 = eq3  eq3 = eq4  L1(~eq1)L2  L3(~eq2)L4  (L1( eq3)L3  L2( eq4)L4) | [sublist_functionality_wrt_id_list_iso_list_iso] |
Thm* L1,L2:T List, eq1,eq2:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  L1 = L2  L3(~eq1)L4  (L1( eq2)L3  L2( eq2)L4) | [sublist_functionality_wrt_id_id_list_iso] |
Thm* L1,L2:T List, eq1,eq2:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  L1(~eq1)L2  L3 = L4  (L1( eq2)L3  L2( eq2)L4) | [sublist_functionality_wrt_id_list_iso_id] |
Thm* L1,L2:T List, eq1,eq2,eq3:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  eq2 = eq3  L1(~eq1)L2  L3(~eq2)L4  (L1 @ L3)(~eq3)(L2 @ L4) | [append_functionality_wrt_list_iso] |
Thm* Discrete{T}  ( eq1,eq2,eq3:{T }, L1,L2,L3:T List. eq1 = eq2  eq2 = eq3  L1(~eq1)L2  L2(~eq2)L3  L1(~eq3)L3) | [list_iso_transitivity] |
Thm* Discrete{T}  ( eq1,eq2:{T }, L,M:T List. eq1 = eq2  L(~eq1)M  M(~eq2)L) | [list_iso_inversion] |
Thm* eq:{T }, L,M:T List. L(~eq)M  M(~eq)L | [list_iso_commutative] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. L = M  L(~eq)M) | [list_iso_weakening_wrt_identity] |
Thm* eq:{T }, x:T, L:T List. x( eq) L  ( y:T. x( eq) (y.L)) | [is_member_tail] |
Thm* L1,L2:T List, eq1,eq2,eq3:{T }, L3,L4:T List. Discrete{T}  eq1 = eq2  eq2 = eq3  L1( eq1)L2  L3( eq2)L4  (L1 @ L3)( eq3)(L2 @ L4) | [append_functionality_wrt_sublist] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. (L @ M)(~eq)(M @ L)) | [append_commutes_under_list_iso] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. (L @ M)( eq)(M @ L)) | [append_commutes_under_sublist] |
Thm* eq:{T }, L,M:T List, x:T. x( eq) (L @ M)  x( eq) (M @ L) | [append_commutes_under_is_member] |
Thm* eq:{T }, x:T, L,M:T List. x( eq) (L @ M)  x( eq) L x( eq) M | [is_member_append_disjunction_lemma] |
Thm* eq:{T }, L,M:T List, x:T. x( eq) (L @ M)  x( eq) L x( eq) M | [is_member_of_append_lemma] |
Thm* eq:{T }, L:T List, x:T. x( eq) L  ( M,N:T List, y:T. eq(x,y) & L = (M @ (y.N))) | [is_member_append_lemma1] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. L( eq)M  ( eq)(L,M)) | [sublist_iff_assert_sublist_2] |
Thm* Discrete{T}  ( eq1,eq2,eq3:{T }, L1,L2,L3:T List. eq1 = eq2  eq2 = eq3  L1( eq1)L2  L2( eq2)L3  L1( eq3)L3) | [sublist_transitivity] |
Thm* Discrete{T}  ( eq:{T }, L,M:T List. L = M  L( eq)M) | [sublist_weakening_wrt_identity] |
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* Discrete{T}  ( eq:{T }, u:T, v:T List. v( eq)(u.v)) | [sublist_tail] |
Thm* eq:{T }, L,M:T List. Dec(L( eq)M) | [decidable__sublist] |
Thm* T:Type, eq:{T }, L1,L2:T List. L1( eq)L2 Type | [sublist_wf2] |
Thm* eq:{T }, L,M:T List. disjoint(eq;L;M)  disjoint (eq;L;M) | [disjoint_iff_assert_disjoint2] |
Thm* T:Type, eq:{T }, L,M:T List. disjoint (eq;L;M)  | [disjoint2_wf] |
Thm* eq:{T }, x,y:T, L:T List. x( eq) remove(eq;y;L)  x( eq) L | [remove_is_member] |
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* eq:{T }, t:T, L:T List. t( eq) (t.L) | [is_member_cons] |
Thm* eq:{T }, L:T List. L nil  ( x:T. x( eq) L) | [non_nil_is_member] |
Thm* eq:{T }, L:T List. ||L|| 1  hd(L)( eq) L | [hd_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] |