Nuprl Lemma : Memory-classrel
∀[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)) ∧ iterated_classrel(es;B;A;f;init;X;pred(e);v)))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
sq_stable: SqStable(P),
or: P ∨ Q,
cand: A c∧ B,
true: True,
bag-member: x ↓∈ bs,
squash: ↓T,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
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{} iterated\_classrel(es;B;A;f;init;X;pred(e);v)))
Date html generated:
2016_05_17-AM-09_22_48
Last ObjectModification:
2016_01_17-PM-11_12_45
Theory : classrel!lemmas
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