Nuprl Lemma : prior-classrel-p-local-pred
∀[T,Info:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ Prior(X)(e);↓∃e':E. ((es-p-local-pred(es;λe'.(↓∃w:T. w ∈ X(e'))) e e') ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
universe: Type
Lemmas :
prior-classrel,
es-p-local-pred_wf,
event-ordering+_subtype,
squash_wf,
exists_wf,
classrel_wf,
es-E_wf,
primed-class_wf,
top_wf,
es-local-pred_wf,
lt_int_wf,
bag-size_wf,
subtype_rel_sum,
sq_exists_wf,
es-locl_wf,
assert_wf,
nat_wf,
all_wf,
not_wf,
or_wf,
es-local-pred-iff-es-p-local-pred
Latex:
\mforall{}[T,Info:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} Prior(X)(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')))
Date html generated:
2015_07_22-PM-00_14_54
Last ObjectModification:
2015_01_28-AM-10_46_32
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