Thm* P:(T Prop), L:T List. x L.P(x)  ( M,N:T List, x:T. P(x) & L = (M @ (x.N))) | [list_exists_is_member_append_lemma] |
Thm* P:(T Prop), L,M:T List. x (L @ M).P(x)  x L.P(x) x M.P(x) | [list_exists_append_lemma] |
Thm* P:(T Prop), L,M:T List. x (L @ M).P(x)  x L.P(x) & x M.P(x) | [list_all_append_lemma] |
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* eq:{T }, L,M:T List. L(~eq)M  M(~eq)L | [list_iso_commutative] |
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. 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* Discrete{T}  ( eq:{T }, L,M:T List. L( eq)M  ( eq)(L,M)) | [sublist_iff_assert_sublist_2] |
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 }, L,M:T List. disjoint(eq;L;M)  disjoint (eq;L;M) | [disjoint_iff_assert_disjoint2] |
Thm* P:(T Prop). ( x:T. Dec(P(x)))  ( L:T List.  x L.( P(x))  x L.P(x)) | [not_list_all_not_iff_list_exists] |
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), L:T List. ( x:T. x( eq) L & P(x))  y L.P(y) | [list_exists_is_member_lemma] |
Thm* eq:(T T  ), L:T List. x L.x( eq) nil  nil = L | [list_all_is_member_nil_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* L:T List, P:(T  ). x L.P(x)  x L.P(x) | [list_all_iff_assert_list_all_2] |
Thm* L:T List, x:T. x (x.L).False  False | [list_all_of_false_false] |
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] |