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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