Nuprl Lemma : nysiad_on_input_message_bag_wf
∀[M:ValueAllType]. ∀[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. ∀[deqM:EqDecider(M)].
∀[inputmsghdr,kdeliverhdr,readyhdr:Atom List]. ∀[senders:bag(Id)]. ∀[tooarcasthdr:Atom List].
∀[waitingmap:map-sig{i:l}(Id;M)].
∀[mf:nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr)].
∀[msg2m:Message(mf) ⟶ M].
(nysiad_on_input_message_bag(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;...;readyhdr;...;...;...;mf;...)
∈ Id
⟶ (Message(mf) × Id? × Id + (Message(mf) × Id? × Id))
⟶ ((M × Id? × Id) List × map-sig-map(waitingmap))
⟶ bag(Interface))
Proof
Definitions occuring in Statement :
nysiad_on_input_message_bag: nysiad_on_input_message_bag(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;...;mf;...),
nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
msg-interface: Interface,
Message: Message(f),
Id: Id,
list: T List,
deq: EqDecider(T),
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
atom: Atom,
bag: bag(T)
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nysiad_headers_type: nysiad_headers_type{i:l}(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
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,
nysiad_headers: nysiad_headers(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
uimplies: b supposing a,
nysiad_headers_fun: nysiad_headers_fun(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr;mf),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
cand: A c∧ B,
nysiad_headers_no_rep: nysiad_headers_no_rep(add2baghdr;addwaitinghdr;adeliverhdr;inputmsghdr;kdeliverhdr;readyhdr;tooarcasthdr),
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,
nysiad_on_input_message_bag: nysiad_on_input_message_bag(M;add2baghdr;addwaitinghdr;adeliverhdr;deqM;inputmsghdr;kdeliverhdr;...;...;...;...;mf;...),
outr: outr(x),
isl: isl(x),
outl: outl(x)
Latex:
\mforall{}[M:ValueAllType]. \mforall{}[add2baghdr,addwaitinghdr,adeliverhdr:Atom List]. \mforall{}[deqM:EqDecider(M)].
\mforall{}[inputmsghdr,kdeliverhdr,readyhdr:Atom List]. \mforall{}[senders:bag(Id)]. \mforall{}[tooarcasthdr:Atom List].
\mforall{}[waitingmap:map-sig\{i:l\}(Id;M)].
\mforall{}[...
Date html generated:
2016_05_17-PM-01_25_56
Last ObjectModification:
2016_01_18-AM-07_29_53
Theory : event-logic-applications
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