Nuprl Lemma : State-comb-classrel-mem3
∀[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)
⇐⇒ ((↑first(e)) ∧ v ↓∈ init loc(e)) ∨ ((¬↑first(e)) ∧ v ∈ State-comb(init;f;X)(pred(e))))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
Memory-class: Memory-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
classrel_wf,
Memory-class_wf,
or_wf,
assert_wf,
es-first_wf2,
event-ordering+_subtype,
bag-member_wf,
es-loc_wf,
not_wf,
State-comb_wf,
es-pred_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
Memory-classrel,
State-comb-classrel,
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{} ((\muparrow{}first(e)) \mwedge{} v \mdownarrow{}\mmember{} init loc(e)) \mvee{} ((\mneg{}\muparrow{}first(e)) \mwedge{} v \mmember{} State-comb(init;f;X)(pred(e))))
Date html generated:
2015_07_22-PM-00_21_27
Last ObjectModification:
2015_01_28-AM-10_12_47
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