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* 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 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* P:(T Prop), L:T List. ( x:T. Dec(P(x)))  Dec( x L.P(x)) | [decidable__list_exists] |
Thm* T:Type, P:(T Prop), L:T List. x L.P(x) Type | [list_exists_wf] |
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* 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] |
Thm* T:Type, P:(T Prop), L:T List. x L.P(x) Type | [list_all_wf] |