Nuprl Lemma : member-class-le-before
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
  uiff(v ↓∈ class-le-before(X;es;e);↓∃e':E. (e' ≤loc e  ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement : 
classrel: v ∈ X(e)
, 
class-le-before: class-le-before(X;es;e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-le: e ≤loc e' 
, 
es-E: E
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
exists: ∃x:A. B[x]
, 
squash: ↓T
, 
and: P ∧ Q
, 
universe: Type
, 
bag-member: x ↓∈ bs
Definitions unfolded in proof : 
class-le-before: class-le-before(X;es;e)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
uimplies: b supposing a
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
eclass: EClass(A[eo; e])
, 
so_apply: x[s]
, 
classrel: v ∈ X(e)
, 
squash: ↓T
, 
exists: ∃x:A. B[x]
, 
cand: A c∧ B
, 
rev_uimplies: rev_uimplies(P;Q)
, 
bag-member: x ↓∈ bs
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Latex:
\mforall{}[Info,T:Type].  \mforall{}[X:EClass(T)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:T].
    uiff(v  \mdownarrow{}\mmember{}  class-le-before(X;es;e);\mdownarrow{}\mexists{}e':E.  (e'  \mleq{}loc  e    \mwedge{}  v  \mmember{}  X(e')))
Date html generated:
2016_05_16-PM-01_58_55
Last ObjectModification:
2016_01_17-PM-07_41_08
Theory : event-ordering
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