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
Lemmas :
false_wf,
exists_wf,
l_member_wf,
nat_wf,
less_than_wf,
subtype_rel_sum,
cs-rcv-vote_wf,
assert_of_lt_int,
assert_wf,
lt_int_wf,
assert_witness,
consensus-rcv_wf,
list_wf,
Id_wf,
btrue_wf,
and_wf,
equal_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
outr_wf,
set_wf,
le_wf,
less_than_transitivity1,
le_weakening
\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:
2015_07_17-AM-11_47_32
Last ObjectModification:
2015_01_28-AM-01_31_17
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