Nuprl Lemma : assert-rcvd-inning-eq
∀[V:Type]
∀A:Id List. ∀r:consensus-rcv(V;A). ∀i:ℕ.
(↑inning(r) =z i ⇐⇒ ∃a:{b:Id| (b ∈ A)} . ∃v:V. (r = Vote[a;i;v] ∈ consensus-rcv(V;A)))
Proof
Definitions occuring in Statement :
rcvd-inning-eq: inning(r) =z i,
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Lemmas :
false_wf,
exists_wf,
l_member_wf,
equal_wf,
subtype_rel_sum,
nat_wf,
cs-rcv-vote_wf,
assert_of_eq_int,
assert_wf,
eq_int_wf,
assert_witness,
consensus-rcv_wf,
list_wf,
Id_wf,
btrue_wf,
and_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
sq_stable__le,
le_wf,
outr_wf,
set_wf
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}r:consensus-rcv(V;A). \mforall{}i:\mBbbN{}.
(\muparrow{}inning(r) =\msubz{} i \mLeftarrow{}{}\mRightarrow{} \mexists{}a:\{b:Id| (b \mmember{} A)\} . \mexists{}v:V. (r = Vote[a;i;v]))
Date html generated:
2015_07_17-AM-11_47_44
Last ObjectModification:
2015_01_28-AM-01_30_39
Home
Index