Nuprl Lemma : es-interval-non-zero
∀es:EO. ∀e,e':E. (e ≤loc e' ⇐⇒ 0 < ||[e, e']||)
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
length: ||as||,
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Lemmas :
es-le_wf,
less_than_wf,
length_wf,
es-interval_wf,
pos_length,
es-E_wf,
decidable__lt,
false_wf,
add_functionality_wrt_le,
add-commutes,
zero-add,
le-add-cancel,
es-le-self,
member-es-interval,
member-implies-null-eq-bfalse,
and_wf,
equal_wf,
list_wf,
null_wf3,
subtype_rel_list,
top_wf,
null_nil_lemma,
btrue_wf,
btrue_neq_bfalse,
equal-wf-T-base,
member_exists,
listp-not-nil,
assert_of_lt_int,
assert_wf,
lt_int_wf,
es-le_transitivity
\mforall{}es:EO. \mforall{}e,e':E. (e \mleq{}loc e' \mLeftarrow{}{}\mRightarrow{} 0 < ||[e, e']||)
Date html generated:
2015_07_17-AM-08_41_52
Last ObjectModification:
2015_01_27-PM-02_39_33
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