Nuprl Lemma : only_value_of_sv_class_in_classrel
∀[Info,T:Type].
∀eo:EO+(Info). ∀[e:E]. ∀[v:T]. ∀[X:EClass(T)]. ((v ∈ X(e) ∧ Singlevalued(X)) ⇒ (v = only(X eo e) ∈ T))
Proof
Definitions occuring in Statement :
sv-class: Singlevalued(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs)
Lemmas :
event_in_sv_classrel_is_in_class,
es-E-interface-property,
es-interface-subtype_rel2,
top_wf,
es-E_wf,
event-ordering+_subtype,
assert_of_eq_int,
bag-size_wf,
nat_wf,
bag-size-one,
bag-member-single,
bag-only_wf2,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
classrel_wf,
sv-class_wf,
event-ordering+_wf,
eclass_wf,
single-valued-bag-if-le1,
le_weakening
Latex:
\mforall{}[Info,T:Type].
\mforall{}eo:EO+(Info)
\mforall{}[e:E]. \mforall{}[v:T]. \mforall{}[X:EClass(T)]. ((v \mmember{} X(e) \mwedge{} Singlevalued(X)) {}\mRightarrow{} (v = only(X eo e)))
Date html generated:
2015_07_22-PM-00_14_40
Last ObjectModification:
2015_01_28-AM-10_45_30
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