Nuprl Lemma : eo-forward-causle
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e,e1,e2:E].
e1 c≤ e2 ⇐⇒ e1 c≤ e2 supposing ((loc(e1) = loc(e) ∈ Id) ⇒ e ≤loc e1 ) ∧ ((loc(e2) = loc(e) ∈ Id) ⇒ e ≤loc e2 )
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-causle: e c≤ e',
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
label: ...$L... t,
guard: {T},
es-causle: e c≤ e',
or: P ∨ Q,
member: t ∈ T,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q)
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e,e1,e2:E].
e1 c\mleq{} e2 \mLeftarrow{}{}\mRightarrow{} e1 c\mleq{} e2
supposing ((loc(e1) = loc(e)) {}\mRightarrow{} e \mleq{}loc e1 ) \mwedge{} ((loc(e2) = loc(e)) {}\mRightarrow{} e \mleq{}loc e2 )
Date html generated:
2016_05_16-PM-01_05_56
Last ObjectModification:
2015_12_29-PM-01_48_08
Theory : event-ordering
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