Nuprl Lemma : pred-member-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:{1..||(e1, e2)||-}]. (pred((e1, e2)[n]) = (e1, e2)[n - 1] ∈ E)
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
select: L[n],
length: ||as||,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T
Lemmas :
int_seg_properties,
es-open-interval-ordered-inst,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
decidable__lt,
less-iff-le,
le-add-cancel2,
lelt_wf,
subtract-is-less,
es-pred-locl,
select_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
int_seg_wf,
length_wf,
es-E_wf,
es-open-interval_wf,
event_ordering_wf,
es-locl-trichotomy,
es-pred_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_of_ff,
es-loc-pred,
es-pred_property,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-causl_transitivity2,
es-causle_weakening,
es-causl_irreflexivity,
member-es-open-interval,
le_wf,
less_than_wf,
sq_stable__le,
es-le_weakening,
es-locl_wf,
es-open-interval-ordered-iff
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\{1..||(e1, e2)||\msupminus{}\}]. (pred((e1, e2)[n]) = (e1, e2)[n - 1])
Date html generated:
2015_07_17-AM-08_43_52
Last ObjectModification:
2015_01_27-PM-02_30_48
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