Nuprl Lemma : es-pred-exists-between
∀es:EO. ∀e1,e2:E. ((e1 <loc e2) ⇒ (∃e:{e:E| ¬↑first(e)} . (e1 = pred(e) ∈ E)))
Proof
Definitions occuring in Statement :
es-locl: (e <loc e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
less_than_wf,
decidable__lt,
subtract_wf,
false_wf,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
less-iff-le,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
es-causl_wf,
es-locl-trichotomy,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
es-loc-pred,
not_wf,
equal_wf,
not_assert_elim,
es-locl_wf,
all_wf,
nat_wf,
exists_wf,
set_wf,
primrec-wf2,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
add-zero,
es-E_wf,
event_ordering_wf,
es-pred-causl,
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
\mforall{}es:EO. \mforall{}e1,e2:E. ((e1 <loc e2) {}\mRightarrow{} (\mexists{}e:\{e:E| \mneg{}\muparrow{}first(e)\} . (e1 = pred(e))))
Date html generated:
2015_07_17-AM-08_38_34
Last ObjectModification:
2015_01_27-PM-02_43_09
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