Nuprl Lemma : assert-rcvd-inning-gt
∀[V:Type]
∀A:Id List. ∀r:consensus-rcv(V;A). ∀i:ℤ.
(↑i <z inning(r) ⇐⇒ ∃a:{b:Id| (b ∈ A)} . ∃v:V. ∃j:ℕ. (i < j ∧ (r = Vote[a;j;v] ∈ consensus-rcv(V;A))))
Proof
Definitions occuring in Statement :
rcvd-inning-gt: i <z inning(r),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
l_member: (x ∈ l),
list: T List,
nat: ℕ,
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
rcvd-inning-gt: i <z inning(r),
rcvd-vote: rcvd-vote(x),
rcv-vote?: rcv-vote?(x),
outr: outr(x),
bfalse: ff,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
spreadn: spread3,
btrue: tt,
uiff: uiff(P;Q),
cand: A c∧ B,
cs-rcv-vote: Vote[a;i;v],
rev_uimplies: rev_uimplies(P;Q),
isl: isl(x),
not: ¬A,
bnot: ¬bb,
true: True,
top: Top,
pi1: fst(t),
pi2: snd(t),
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}r:consensus-rcv(V;A). \mforall{}i:\mBbbZ{}.
(\muparrow{}i <z inning(r) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:\{b:Id| (b \mmember{} A)\} . \mexists{}v:V. \mexists{}j:\mBbbN{}. (i < j \mwedge{} (r = Vote[a;j;v])))
Date html generated:
2016_05_16-PM-00_34_30
Last ObjectModification:
2016_01_17-PM-03_57_22
Theory : event-ordering
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