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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
causal-class-rel-in-out: if class_out outputs (m) then class_in observed x,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
exists: ∃x:A. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
label: ...$L... t
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[T:Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[m:Id \mtimes{} Message(f)].
\mforall{}[class$_{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:
2016_05_17-AM-08_57_20
Last ObjectModification:
2015_12_29-PM-02_53_09
Theory : messages
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