Nuprl Lemma : es-pred-exists-between2
∀es:EO. ∀e1,e2:E. ((e1 <loc e2) ⇒ (∃e:{e:E| ¬↑first(e)} . ((e1 = pred(e) ∈ E) ∧ e ≤loc e2 )))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
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,
and: P ∧ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Lemmas :
es-pred-exists-between,
es-pred_property,
assert_elim,
es-first_wf2,
es-locl-first,
btrue_neq_bfalse,
assert_wf,
es-causl_weakening,
es-pred_wf,
not_assert_elim,
es-le_wf,
es-locl_wf,
es-E_wf,
event_ordering_wf,
equal_wf,
es-pred-one-one,
es-le-self,
and_wf,
es-causl_wf,
es-loc_wf,
es-loc-pred,
es-pred-locl-implies-le,
es-pred-locl,
es-locl_transitivity1,
es-le_weakening
\mforall{}es:EO. \mforall{}e1,e2:E. ((e1 <loc e2) {}\mRightarrow{} (\mexists{}e:\{e:E| \mneg{}\muparrow{}first(e)\} . ((e1 = pred(e)) \mwedge{} e \mleq{}loc e2 )))
Date html generated:
2015_07_17-AM-08_39_20
Last ObjectModification:
2015_01_27-PM-02_42_20
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