Nuprl Lemma : lg-label-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]))].
∀[i:ℕlg-size(G)].
(lg-label(snd(deliver-msg(t;m;x;Cs;G));i) = lg-label(G;i) ∈ pInTransit(P.M[P]))
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-label: lg-label(g;x),
lg-size: lg-size(g),
Id: Id,
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
deliver-msg: deliver-msg(t;m;x;Cs;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
pi2: snd(t),
ldag: LabeledDAG(T),
subtype_rel: A ⊆r B,
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,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
nat: ℕ,
System: System(P.M[P]),
le: A ≤ B,
less_than': less_than'(a;b),
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla)
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]))]. \mforall{}[i:\mBbbN{}lg-size(G)].
(lg-label(snd(deliver-msg(t;m;x;Cs;G));i) = lg-label(G;i))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_39_03
Last ObjectModification:
2016_01_18-AM-00_21_23
Theory : process-model
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