Nuprl Lemma : Accum-classrel-Memory
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
(v ∈ Accum-class(f;init;X)(e) ⇐⇒ ↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Memory-class(f;init;X)(e) ∧ (v = (f a b) ∈ B)))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
Accum-class: Accum-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
Accum-classrel-Memory-sq,
squash_wf,
exists_wf,
classrel_wf,
Memory-class_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
bag-member_wf,
lifting-2_wf,
iff_wf,
Accum-class_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
bag-member-lifting-2
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{} Accum-class(f;init;X)(e)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Memory-class(f;init;X)(e) \mwedge{} (v = (f a b))))
Date html generated:
2015_07_22-PM-00_11_27
Last ObjectModification:
2015_01_28-AM-11_41_06
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