Nuprl Lemma : es-open-interval-ordered-iff
∀es:EO. ∀e1,e2:E. ∀n1,n2:ℕ||(e1, e2)||. (n1 < n2 ⇐⇒ ((e1, e2)[n1] <loc (e1, e2)[n2]))
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
select: L[n],
length: ||as||,
int_seg: {i..j-},
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Lemmas :
es-open-interval-ordered-inst,
less_than_wf,
decidable__lt,
or_wf,
equal_wf,
false_wf,
decidable__equal_int,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-commutes,
le-add-cancel,
add-swap,
subtype_base_sq,
int_subtype_base,
es-locl_irreflexivity,
select_wf,
es-locl_wf,
es-open-interval_wf,
sq_stable__le,
int_seg_wf,
length_wf,
es-locl_transitivity
\mforall{}es:EO. \mforall{}e1,e2:E. \mforall{}n1,n2:\mBbbN{}||(e1, e2)||. (n1 < n2 \mLeftarrow{}{}\mRightarrow{} ((e1, e2)[n1] <loc (e1, e2)[n2]))
Date html generated:
2015_07_17-AM-08_43_46
Last ObjectModification:
2015_01_27-PM-02_30_02
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