Nuprl Lemma : member-es-hist
∀[Info:Type]. ∀es:EO+(Info). ∀e1,e2:E. ∀t:Info. ((t ∈ es-hist(es;e1;e2)) ⇐⇒ ∃e∈[e1,e2].t = info(e) ∈ Info)
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
es-info: info(e),
event-ordering+: EO+(Info),
existse-between2: ∃e∈[e1,e2].P[e],
es-E: E,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
existse-between2: ∃e∈[e1,e2].P[e],
es-hist: es-hist(es;e1;e2),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
cand: A c∧ B,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e1,e2:E. \mforall{}t:Info. ((t \mmember{} es-hist(es;e1;e2)) \mLeftarrow{}{}\mRightarrow{} \mexists{}e\mmember{}[e1,e2].t = info(e))
Date html generated:
2016_05_16-PM-01_18_53
Last ObjectModification:
2015_12_29-PM-01_57_38
Theory : event-ordering
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