Nuprl Lemma : lg-size-deliver-msg
∀[M:Type ⟶ Type]
∀[t:ℕ]. ∀[x:Id]. ∀[m:pMsg(P.M[P])]. ∀[Cs:component(P.M[P]) List]. ∀[G:LabeledDAG(pInTransit(P.M[P]))].
(lg-size(G) ≤ lg-size(snd(deliver-msg(t;m;x;Cs;G))))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
deliver-msg: deliver-msg(t;m;x;Cs;L),
pInTransit: pInTransit(P.M[P]),
component: component(P.M[P]),
pMsg: pMsg(P.M[P]),
ldag: LabeledDAG(T),
lg-size: lg-size(g),
Id: Id,
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
le: A ≤ B,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
ldag: LabeledDAG(T),
subtype_rel: A ⊆r B,
nat: ℕ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
System: System(P.M[P]),
all: ∀x:A. B[x],
deliver-msg: deliver-msg(t;m;x;Cs;L)
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[t:\mBbbN{}]. \mforall{}[x:Id]. \mforall{}[m:pMsg(P.M[P])]. \mforall{}[Cs:component(P.M[P]) List].
\mforall{}[G:LabeledDAG(pInTransit(P.M[P]))].
(lg-size(G) \mleq{} lg-size(snd(deliver-msg(t;m;x;Cs;G))))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_38_53
Last ObjectModification:
2016_01_18-AM-00_15_21
Theory : process-model
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