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
Lemmas :
sq_stable__le,
lg-size_wf,
nat_wf,
ldag_wf,
pInTransit_wf,
list_wf,
component_wf,
pMsg_wf,
Id_wf,
strong-type-continuous_wf,
list_accum_wf,
deliver-msg-to-comp_wf,
System_wf,
list_induction,
all_wf,
le_wf,
list_accum_nil_lemma,
le_weakening,
list_accum_cons_lemma,
eq_id_wf,
bool_wf,
eqtt_to_assert,
assert-eq-id,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
Process-apply_wf,
Process_wf,
pExt_wf,
cons_wf,
lg-append_wf_dag,
add-cause_wf,
le_transitivity,
lg-append_wf,
squash_wf,
true_wf,
lg-size-append,
iff_weakening_equal
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:
2015_07_23-AM-11_08_57
Last ObjectModification:
2015_02_04-PM-04_48_57
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