Nuprl Lemma : causal-class-rel-in-out_wf
∀[f:Name ─→ Type]. ∀[T:Type]. ∀[es:EO+(Message(f))]. ∀[m:Id × Message(f)]. ∀[class_out:EClass(Id × Message(f))]. ∀[x:T].
∀[class_in:EClass(T)].
(if class_out outputs (m) then class_in observed x ∈ ℙ')
Proof
Definitions occuring in Statement :
causal-class-rel-in-out: if class_out outputs (m) then class_in observed x,
Message: Message(f),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
name: Name,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
all_wf,
es-E_wf,
event-ordering+_subtype,
classrel_wf,
squash_wf,
exists_wf,
es-causle_wf,
eclass_wf3,
subtype_rel_dep_function,
name_wf,
Id_wf,
Message_wf,
event-ordering+_wf
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[T:Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[m:Id \mtimes{} Message(f)].
\mforall{}[class$_{out}$:EClass(Id \mtimes{} Message(f))]. \mforall{}[x:T]. \mforall{}[class$_{in}\mbackslash{}\000Cff24:EClass(T)].
(if class$_{out}$ outputs (m) then class$_{in}$ observed x\000C \mmember{} \mBbbP{}')
Date html generated:
2015_07_21-PM-04_53_13
Last ObjectModification:
2015_01_28-AM-08_43_13
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