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* 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* P:(T  ), L:T List. x L.P(x)  x L.P(x) | [list_all_2_all] |
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 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* P:(T Prop), L:T List. ( x:T. Dec(P(x)))  Dec( x L.P(x)) | [decidable__list_all] |
Thm* P:(T Prop), L:T List. ( x:T. SqStable(P(x)))  SqStable( x L.P(x)) | [sq_stable__list_all] |
Thm* P:(T Prop), L:T List, x:T. x (x.L).P(x)  x L.P(x) | [list_all_tail] |
Def L1( eq)L2 == x L1. x( eq) L2 | [sublist] |
Def disjoint(eq;L1;L2) == x L1.  x( eq) L2 | [disjoint] |