Nuprl Lemma : prior-classrel
∀[T,Info:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ Prior(X)(e);↓∃e':E. (((last(λe'.0 <z #(X es e')) e) = (inl e') ∈ (E + Top)) ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
es-local-pred: last(P),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
lt_int: i <z j,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
inl: inl x,
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs)
Lemmas :
classrel_wf,
primed-class_wf,
squash_wf,
exists_wf,
top_wf,
es-local-pred_wf,
lt_int_wf,
bag-size_wf,
subtype_rel_sum,
sq_exists_wf,
es-locl_wf,
assert_wf,
all_wf,
not_wf,
or_wf,
es-E_wf,
event-ordering+_subtype,
nat_wf,
event-ordering+_wf,
eclass_wf,
equal_wf,
bag-member_wf,
empty-bag_wf,
bag-member-empty-iff,
sq_stable__bag-member
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. (((last(\mlambda{}e'.0 <z \#(X es e')) e) = (inl e')) \mwedge{} v \mmember{} X(e')))
Date html generated:
2015_07_22-PM-00_14_44
Last ObjectModification:
2015_01_28-AM-10_46_22
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