Nuprl Lemma : OARcast_deliverer_for_sender_seq_output_wf
∀[M:ValueAllType]. ∀[deliverhdr:Atom List]. ∀[flrs:ℤ]. ∀[oarcasthdr,orderedhdr,orderhdr:Atom List].
∀[mf:OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
(OARcast_deliverer_for_sender_seq_output(M;deliverhdr;flrs;oarcasthdr;orderedhdr;orderhdr;mf) ∈ Id
⟶ ℤ
⟶ Id
⟶ (bag(Id) × ((M × ℕ) List))
⟶ bag(Interface))
Proof
Definitions occuring in Statement :
OARcast_deliverer_for_sender_seq_output: OARcast_deliverer_for_sender_seq_output(M;deliverhdr;flrs;oarcasthdr;orderedhdr;orderhdr;mf),
OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
msg-interface: Interface,
Id: Id,
list: T List,
nat: ℕ,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
atom: Atom,
bag: bag(T)
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
OARcast_headers_type: OARcast_headers_type{i:l}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
name: Name,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
OARcast_headers: OARcast_headers(deliverhdr;oarcasthdr;orderedhdr;orderhdr),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
OARcast_headers_fun: OARcast_headers_fun(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
OARcast_headers_no_rep: OARcast_headers_no_rep(deliverhdr;oarcasthdr;orderedhdr;orderhdr),
squash: ↓T,
no_repeats: no_repeats(T;l),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
less_than: a < b,
true: True,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
select: L[n],
subtract: n - m,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
OARcast_deliverer_for_sender_seq_output: OARcast_deliverer_for_sender_seq_output(M;deliverhdr;flrs;oarcasthdr;orderedhdr;orderhdr;mf),
outl: outl(x),
isl: isl(x)
Latex:
\mforall{}[M:ValueAllType]. \mforall{}[deliverhdr:Atom List]. \mforall{}[flrs:\mBbbZ{}]. \mforall{}[oarcasthdr,orderedhdr,orderhdr:Atom List].
\mforall{}[mf:OARcast\_headers\_type\{i:l\}(M;deliverhdr;oarcasthdr;orderedhdr;orderhdr)].
(OARcast\_deliverer\_for\_sender\_seq\_output(M;deliverhdr;flrs;oarcasthdr;orderedhdr;orderhdr;mf) \mmember{} Id
{}\mrightarrow{} \mBbbZ{}
{}\mrightarrow{} Id
{}\mrightarrow{} (bag(Id) \mtimes{} ((M \mtimes{} \mBbbN{}) List))
{}\mrightarrow{} bag(Interface))
Date html generated:
2016_05_17-PM-01_09_10
Last ObjectModification:
2016_01_18-AM-07_36_16
Theory : event-logic-applications
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