Nuprl Lemma : es-causl-max-list
∀es:EO. ∀L:E List. (0 < ||L|| ⇒ (¬(∀e:{e:E| (e ∈ L)} . ∃e':{e:E| (e ∈ L)} . (e < e'))))
Proof
Definitions occuring in Statement :
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
natural_number: $n
Lemmas :
all_wf,
es-E_wf,
l_member_wf,
exists_wf,
es-causl_wf,
less_than_wf,
length_wf,
list_wf,
event_ordering_wf,
sorted-by_wf,
equal-wf-T-base,
length_wf_nat,
int_subtype_base,
int_seg_wf,
select_wf,
sq_stable__le,
set_wf,
primrec-wf2,
nat_wf,
nil_wf,
length_of_nil_lemma,
stuck-spread,
base_wf,
false_wf,
le_wf,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
decidable__equal_int,
subtype_base_sq,
cons_wf,
hd_wf,
decidable__le,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
sorted-by-single,
zero-le-nat,
length-singleton,
iff_weakening_equal,
length_of_cons_lemma,
hd_member,
list-cases,
null_nil_lemma,
product_subtype_list,
null_cons_lemma,
decidable__lt,
not-equal-2,
le_antisymmetry_iff,
subtract_wf,
minus-minus,
le-add-cancel,
lelt_wf,
sorted-by-cons,
minus-zero,
es-causl_transitivity2,
less_than_transitivity2,
es-causle_weakening,
length_cons,
non_neg_length,
sq_stable__l_member,
decidable__es-E-equal,
squash_wf,
true_wf,
select_cons_tl,
not-le-2,
le-add-cancel-alt,
sorted-by-strict-no_repeats,
es-causal-antireflexive,
l_contains-no_repeats-length
\mforall{}es:EO. \mforall{}L:E List. (0 < ||L|| {}\mRightarrow{} (\mneg{}(\mforall{}e:\{e:E| (e \mmember{} L)\} . \mexists{}e':\{e:E| (e \mmember{} L)\} . (e < e'))))
Date html generated:
2015_07_17-AM-08_38_32
Last ObjectModification:
2015_02_04-AM-07_08_16
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