Nuprl Lemma : Memory-loc-classrel-single-val
∀[Info,B,A:Type].
  ∀f:Id ⟶ A ⟶ B ⟶ B. ∀init:Id ⟶ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
    (uiff(v ∈ Memory-loc-class(f;init;X)(e);prior-iterated-classrel(es;A;B;v;X;f loc(e);init;e))) supposing 
       (single-valued-classrel(es;X;A) and 
       single-valued-bag(init loc(e);B))
Proof
Definitions occuring in Statement : 
Memory-loc-class: Memory-loc-class(f;init;X)
, 
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e)
, 
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
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
single-valued-bag: single-valued-bag(b;T)
, 
bag: bag(T)
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
single-valued-bag: single-valued-bag(b;T)
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
single-valued-classrel: single-valued-classrel(es;X;T)
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
, 
squash: ↓T
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,B,A:Type].
    \mforall{}f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B.  \mforall{}init:Id  {}\mrightarrow{}  bag(B).  \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.  \mforall{}v:B.
        (uiff(v  \mmember{}  Memory-loc-class(f;init;X)(
                            e);prior-iterated-classrel(es;A;B;v;X;f  loc(e);init;e)))  supposing 
              (single-valued-classrel(es;X;A)  and 
              single-valued-bag(init  loc(e);B))
Date html generated:
2016_05_17-AM-09_23_11
Last ObjectModification:
2016_01_17-PM-11_11_14
Theory : classrel!lemmas
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