Nuprl Lemma : Memory-classrel2
∀[Info,B,A:Type]. ∀[f:A ⟶ B ⟶ B]. ∀[init:Id ⟶ bag(B)].
  ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
    ∀[v:B]. (v ∈ Memory-class(f;init;X)(e) 
⇐⇒ ↓prior-iterated-classrel(es;A;B;v;X;f;init;e))
Proof
Definitions occuring in Statement : 
Memory-class: Memory-class(f;init;X)
, 
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e)
, 
classrel: v ∈ X(e)
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-E: E
, 
Id: Id
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
squash: ↓T
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
bag: bag(T)
Definitions unfolded in proof : 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
rev_implies: P 
⇐ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
classrel: v ∈ X(e)
, 
bag-member: x ↓∈ bs
, 
or: P ∨ Q
, 
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e)
, 
cand: A c∧ B
, 
uimplies: b supposing a
, 
not: ¬A
, 
false: False
, 
uiff: uiff(P;Q)
, 
guard: {T}
, 
sq_stable: SqStable(P)
, 
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[f: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].  (v  \mmember{}  Memory-class(f;init;X)(e)  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}prior-iterated-classrel(es;A;B;v;X;f;init;e))
Date html generated:
2016_05_17-AM-09_22_52
Last ObjectModification:
2016_01_17-PM-11_11_46
Theory : classrel!lemmas
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