Nuprl Lemma : member-votes-from-inning
∀[V:Type]
∀A:Id List. ∀L:consensus-rcv(V;A) List. ∀i:ℕ. ∀b:{b:Id| (b ∈ A)} . ∀v:V.
((<b, v> ∈ votes-from-inning(i;L)) ⇐⇒ (Vote[b;i;v] ∈ L))
Proof
Definitions occuring in Statement :
votes-from-inning: votes-from-inning(i;L),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
l_member: (x ∈ l),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
pair: <a, b>,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
votes-from-inning: votes-from-inning(i;L),
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
cand: A c∧ B,
nat: ℕ,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
rcvd-inning-eq: inning(r) =z i,
rcv-vote?: rcv-vote?(x),
uimplies: b supposing a,
consensus-rcv: consensus-rcv(V;A),
or: P ∨ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
true: True,
bfalse: ff,
false: False,
spreadn: spread3,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
rcvd-vote: rcvd-vote(x),
outr: outr(x),
uiff: uiff(P;Q),
top: Top,
pi1: fst(t),
pi2: snd(t),
cs-rcv-vote: Vote[a;i;v],
squash: ↓T,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}L:consensus-rcv(V;A) List. \mforall{}i:\mBbbN{}. \mforall{}b:\{b:Id| (b \mmember{} A)\} . \mforall{}v:V.
((<b, v> \mmember{} votes-from-inning(i;L)) \mLeftarrow{}{}\mRightarrow{} (Vote[b;i;v] \mmember{} L))
Date html generated:
2016_05_16-PM-00_35_23
Last ObjectModification:
2016_01_17-PM-03_57_11
Theory : event-ordering
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