Nuprl Lemma : return-loc-bag-class-classrel
∀[Info,A:Type]. ∀[x:Id ─→ bag(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A].
(v ∈ return-loc-bag-class(x)(e) ⇐⇒ v ↓∈ x loc(e) ∧ (↑first(e)))
Proof
Definitions occuring in Statement :
return-loc-bag-class: return-loc-bag-class(x),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
es-first_wf2,
bool_wf,
eqtt_to_assert,
bag-member_wf,
es-loc_wf,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag-member-empty-iff,
event-ordering+_subtype,
classrel_wf,
return-loc-bag-class_wf,
assert_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf
Latex:
\mforall{}[Info,A:Type]. \mforall{}[x:Id {}\mrightarrow{} bag(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A].
(v \mmember{} return-loc-bag-class(x)(e) \mLeftarrow{}{}\mRightarrow{} v \mdownarrow{}\mmember{} x loc(e) \mwedge{} (\muparrow{}first(e)))
Date html generated:
2015_07_22-PM-00_06_25
Last ObjectModification:
2015_01_28-AM-11_42_47
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