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)
Lemmas :
Memory-classrel,
not_wf,
assert_wf,
es-first_wf2,
event-ordering+_subtype,
iterated-classrel_wf,
es-pred_wf,
iterated-classrel-iff,
bag-member_wf,
es-loc_wf,
sq_stable__classrel,
Memory-class_wf,
iterated_classrel_wf
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:
2015_07_22-PM-00_12_36
Last ObjectModification:
2015_01_28-AM-11_39_51
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