Nuprl Lemma : iseg-es-interval
∀[es:EO]. ∀[L:E List]. ∀[e1,e2:E]. (L = [e1, last(L)] ∈ (E List)) supposing ((¬↑null(L)) and L ≤ [e1, e2])
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
last: last(L),
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Lemmas :
iseg_filter,
es-ble_wf,
append_wf,
es-before_wf,
cons_wf,
nil_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
es-E_wf,
top_wf,
iseg_wf,
es-interval_wf,
list_wf,
event_ordering_wf,
l_member_wf,
es-le-before_wf2,
last_wf,
es-le_wf,
set_wf,
filter_wf5,
squash_wf,
true_wf,
bool_wf,
iff_weakening_equal,
assert_functionality_wrt_uiff,
assert_elim,
and_wf,
equal_wf,
not_assert_elim,
btrue_neq_bfalse,
null-filter2,
l_all_wf2,
l_all_not,
l_exists_wf,
assert-bl-exists,
bl-exists_wf,
not-not-assert,
l_exists_iff,
assert-es-ble,
member_null,
decidable__equal_int,
subtract_wf,
length_wf,
es-le-before-ordered,
iseg-l-ordered,
es-locl_wf,
l-ordered-inst,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtract-is-less,
lelt_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
es-locl_transitivity1,
es-le_weakening,
select_wf,
le_wf,
less_than_wf,
list_decomp_last,
list-cases,
length_of_nil_lemma,
nil_member,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
iseg-es-le-before-is-before,
last-filter1
\mforall{}[es:EO]. \mforall{}[L:E List]. \mforall{}[e1,e2:E]. (L = [e1, last(L)]) supposing ((\mneg{}\muparrow{}null(L)) and L \mleq{} [e1, e2])
Date html generated:
2015_07_17-AM-08_44_41
Last ObjectModification:
2015_02_04-AM-07_09_48
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