Nuprl Lemma : member-es-before
∀the_es:EO. ∀e',e:E. ((e ∈ before(e')) ⇐⇒ (e <loc e'))
Proof
Definitions occuring in Statement :
es-before: before(e),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
es-before: before(e),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
iff: P ⇐⇒ Q,
not: ¬A,
false: False,
rev_implies: P ⇐ Q,
or: P ∨ Q
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e',e:E. ((e \mmember{} before(e')) \mLeftarrow{}{}\mRightarrow{} (e <loc e'))
Date html generated:
2016_05_16-AM-09_29_59
Last ObjectModification:
2015_12_28-PM-09_50_21
Theory : new!event-ordering
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