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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
not: ¬A,
uall: ∀[x:A]. B[x],
false: False,
prop: ℙ,
guard: {T},
es-locl: (e <loc e'),
or: P ∨ Q
Latex:
\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:
2016_05_16-AM-09_23_51
Last ObjectModification:
2015_12_28-PM-09_51_33
Theory : new!event-ordering
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