Nuprl Lemma : iseg-filter-es-interval
∀[es:EO]. ∀[L:E List]. ∀[e1,e2:E]. ∀[P:{x:E| (x ∈ [e1, e2])} ─→ 𝔹].
(L = filter(P;[e1, last(L)]) ∈ (E List)) supposing ((¬↑null(L)) and L ≤ filter(P;[e1, e2]))
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
last: last(L),
l_member: (x ∈ l),
filter: filter(P;l),
null: null(as),
list: T List,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
last_member,
iseg_member,
last_wf,
member_filter_2,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
es-E_wf,
top_wf,
iseg_wf,
filter_wf5,
es-interval_wf,
l_member_wf,
bool_wf,
list_wf,
event_ordering_wf,
l-ordered-equality,
es-locl_wf,
es-locl-antireflexive,
es-locl_transitivity2,
es-le_weakening,
es-locl_irreflexivity,
member-es-interval,
es-le_transitivity,
subtype_rel_self,
set_wf,
subtype_rel_dep_function,
subtype_rel_sets,
l-ordered-filter2,
es-interval-ordered,
iseg-l-ordered,
before_last_or,
es-le-self,
es-le_wf,
l-ordered-is-sorted-by,
l_before-sorted-by,
equal_wf,
member-iseg-sorted-by
\mforall{}[es:EO]. \mforall{}[L:E List]. \mforall{}[e1,e2:E]. \mforall{}[P:\{x:E| (x \mmember{} [e1, e2])\} {}\mrightarrow{} \mBbbB{}].
(L = filter(P;[e1, last(L)])) supposing ((\mneg{}\muparrow{}null(L)) and L \mleq{} filter(P;[e1, e2]))
Date html generated:
2015_07_17-AM-08_44_49
Last ObjectModification:
2015_01_27-PM-02_30_54
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