Nuprl Lemma : Memory-class-single-val2
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)].
  ∀es:EO+(Info). ∀e:E. ∀s1,s2:S.
    (single-valued-classrel(es;X;A)
    
⇒ single-valued-bag(init loc(e);S)
    
⇒ s1 ∈ Memory-class(f;init;X)(e)
    
⇒ s2 ∈ Memory-class(f;init;X)(e)
    
⇒ (s1 = s2 ∈ S))
Proof
Definitions occuring in Statement : 
Memory-class: Memory-class(f;init;X)
, 
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
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
single-valued-bag: single-valued-bag(b;T)
, 
not: ¬A
, 
false: False
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
squash: ↓T
, 
prop: ℙ
, 
es-E: E
, 
es-base-E: es-base-E(es)
, 
true: True
, 
guard: {T}
, 
rev_implies: P 
⇐ Q
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,S:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(S)].  \mforall{}[f:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S].  \mforall{}[X:EClass(A)].
    \mforall{}es:EO+(Info).  \mforall{}e:E.  \mforall{}s1,s2:S.
        (single-valued-classrel(es;X;A)
        {}\mRightarrow{}  single-valued-bag(init  loc(e);S)
        {}\mRightarrow{}  s1  \mmember{}  Memory-class(f;init;X)(e)
        {}\mRightarrow{}  s2  \mmember{}  Memory-class(f;init;X)(e)
        {}\mRightarrow{}  (s1  =  s2))
Date html generated:
2016_05_17-AM-09_23_41
Last ObjectModification:
2016_01_17-PM-11_10_42
Theory : classrel!lemmas
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