Nuprl Lemma : lg-size-deliver-msg-general
∀[M:Type ⟶ Type]
∀[t:ℕ]. ∀[x:Id]. ∀[m:pMsg(P.M[P])]. ∀[Cs,X:component(P.M[P]) List]. ∀[G:LabeledDAG(pInTransit(P.M[P]))].
(lg-size(G) ≤ lg-size(snd(accumulate (with value S and list item C):
deliver-msg-to-comp(t;m;x;S;C)
over list:
Cs
with starting value:
<X, G>))))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
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_accum: list_accum,
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],
pair: <a, b>,
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,
so_lambda: λ2x y.t[x; y],
System: System(P.M[P]),
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
pi2: snd(t),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
component: component(P.M[P]),
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[t:\mBbbN{}]. \mforall{}[x:Id]. \mforall{}[m:pMsg(P.M[P])]. \mforall{}[Cs,X:component(P.M[P]) List].
\mforall{}[G:LabeledDAG(pInTransit(P.M[P]))].
(lg-size(G) \mleq{} lg-size(snd(accumulate (with value S and list item C):
deliver-msg-to-comp(t;m;x;S;C)
over list:
Cs
with starting value:
<X, G>))))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_38_48
Last ObjectModification:
2016_01_18-AM-00_19_41
Theory : process-model
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