Nuprl Lemma : primed-class-opt-single-val0
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ⟶ bag(B)].
  ∀e:E. ∀v1,v2:B.
    (single-valued-bag(init loc(e);B)
    
⇒ single-valued-classrel(es;X;B)
    
⇒ v1 ∈ Prior(X)?init(e)
    
⇒ v2 ∈ Prior(X)?init(e)
    
⇒ (v1 = v2 ∈ B))
Proof
Definitions occuring in Statement : 
primed-class-opt: Prior(X)?b
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
classrel: v ∈ X(e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-loc: loc(e)
, 
es-E: E
, 
Id: Id
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
equal: s = t ∈ T
, 
single-valued-bag: single-valued-bag(b;T)
, 
bag: bag(T)
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
squash: ↓T
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
single-valued-bag: single-valued-bag(b;T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
es-p-local-pred: es-p-local-pred(es;P)
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
es-locl: (e <loc e')
, 
not: ¬A
, 
false: False
, 
guard: {T}
, 
single-valued-classrel: single-valued-classrel(es;X;T)
Latex:
\mforall{}[Info,B:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[X:EClass(B)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
    \mforall{}e:E.  \mforall{}v1,v2:B.
        (single-valued-bag(init  loc(e);B)
        {}\mRightarrow{}  single-valued-classrel(es;X;B)
        {}\mRightarrow{}  v1  \mmember{}  Prior(X)?init(e)
        {}\mRightarrow{}  v2  \mmember{}  Prior(X)?init(e)
        {}\mRightarrow{}  (v1  =  v2))
Date html generated:
2016_05_17-AM-09_16_18
Last ObjectModification:
2016_01_17-PM-11_13_41
Theory : classrel!lemmas
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