Nuprl Lemma : class-opt-class-classrel2
∀[Info,T:Type]. ∀[X,Y:EClass(T)]. ∀[v:T]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(v ∈ X?Y(e);((↑bag-null(X es e)) ⇒ v ∈ Y(e)) ∧ ((¬↑bag-null(X es e)) ⇒ v ∈ X(e)))
Proof
Definitions occuring in Statement :
class-opt-class: X?Y,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
bag-null: bag-null(bs)
Lemmas :
assert_wf,
bag-null_wf,
not_wf,
classrel_wf,
class-opt-class_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bag-null,
eqff_to_assert,
iff_transitivity,
bnot_wf,
equal-wf-T-base,
bag_wf,
iff_weakening_uiff,
assert_of_bnot,
uiff_transitivity
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[v:T]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(v \mmember{} X?Y(e);((\muparrow{}bag-null(X es e)) {}\mRightarrow{} v \mmember{} Y(e)) \mwedge{} ((\mneg{}\muparrow{}bag-null(X es e)) {}\mRightarrow{} v \mmember{} X(e)))
Date html generated:
2015_07_22-PM-00_08_21
Last ObjectModification:
2015_01_28-AM-11_42_34
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