Nuprl Lemma : loop-class-state-prior
∀[Info,B:Type]. ∀[X:EClass(B ⟶ B)]. ∀[init:Id ⟶ bag(B)].
∀es:EO+(Info). ∀e:E.
∀[v:B]
uiff(v ∈ Prior(loop-class-state(X;init))?init(e);((↑first(e)) ∧ v ↓∈ init loc(e))
∨ ((¬↑first(e)) ∧ v ∈ loop-class-state(X;init)(pred(e))))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
primed-class-opt: Prior(X)?b,
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,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
cand: A c∧ B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
prop: ℙ,
not: ¬A,
false: False,
guard: {T},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
es-p-local-pred: es-p-local-pred(es;P),
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
es-locl: (e <loc e'),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
Id: Id,
sq_type: SQType(T)
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]
uiff(v \mmember{} Prior(loop-class-state(X;init))?init(e);((\muparrow{}first(e)) \mwedge{} v \mdownarrow{}\mmember{} init loc(e))
\mvee{} ((\mneg{}\muparrow{}first(e)) \mwedge{} v \mmember{} loop-class-state(X;init)(pred(e))))
Date html generated:
2016_05_16-PM-11_35_14
Last ObjectModification:
2016_01_17-PM-07_09_01
Theory : event-ordering
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