Nuprl Lemma : primed-class-opt-classrel
∀[T,Info:Type]. ∀[X:EClass(T)]. ∀[init:Id ─→ bag(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ Prior(X)?init(e);↓(∃e':E. ((es-p-local-pred(es;λe'.(↓∃w:T. w ∈ X(e'))) e e') ∧ v ∈ X(e')))
∨ ((∀e':E. ((e' <loc e) ⇒ (∀w:T. (¬w ∈ X(e'))))) ∧ v ↓∈ init loc(e)))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
bag-member_wf,
squash_wf,
or_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
es-p-local-pred_wf,
all_wf,
es-locl_wf,
not_wf,
es-loc_wf,
assert_of_lt_int,
bag-size_wf,
nat_wf,
assert_wf,
bag-member-iff-size,
sq_stable__bag-member,
true_wf,
bag_wf,
es-locl-trichotomy,
empty-bag-iff-no-member,
lt_int_wf,
length_of_nil_lemma
Latex:
\mforall{}[T,Info:Type]. \mforall{}[X:EClass(T)]. \mforall{}[init:Id {}\mrightarrow{} bag(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} Prior(X)?init(
e);\mdownarrow{}(\mexists{}e':E. ((es-p-local-pred(es;\mlambda{}e'.(\mdownarrow{}\mexists{}w:T. w \mmember{} X(e'))) e e') \mwedge{} v \mmember{} X(e')))
\mvee{} ((\mforall{}e':E. ((e' <loc e) {}\mRightarrow{} (\mforall{}w:T. (\mneg{}w \mmember{} X(e'))))) \mwedge{} v \mdownarrow{}\mmember{} init loc(e)))
Date html generated:
2015_07_21-PM-02_31_23
Last ObjectModification:
2015_01_27-PM-09_57_52
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