Nuprl Lemma : archive-condition-append-init
∀[V:Type]
∀A:Id List. ∀t:ℕ. ∀f:(V List) ⟶ V. ∀L:consensus-rcv(V;A) List. ∀n:ℤ. ∀v,v2:V.
(archive-condition(V;A;t;f;n;v;L @ [Init[v2]])
⇐⇒ {(L = [] ∈ (consensus-rcv(V;A) List)) ∧ (n = 0 ∈ ℤ) ∧ (v2 = v ∈ V)})
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
cs-initial-rcv: Init[v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
archive-condition: archive-condition(V;A;t;f;n;v;L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
top: Top,
nat: ℕ,
so_apply: x[s],
exists: ∃x:A. B[x],
or: P ∨ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
less_than: a < b,
le: A ≤ B,
assert: ↑b,
rev_implies: P ⇐ Q,
cand: A c∧ B,
cons: [a / b],
uiff: uiff(P;Q),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
listp: A List+,
cs-initial-rcv: Init[v],
consensus-rcv: consensus-rcv(V;A),
outl: outl(x),
isl: isl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
cs-rcv-vote: Vote[a;i;v],
votes-from-inning: votes-from-inning(i;L),
rcvd-inning-eq: inning(r) =z i,
mapfilter: mapfilter(f;P;L),
rcv-vote?: rcv-vote?(x),
bfalse: ff,
band: p ∧b q,
squash: ↓T,
values-for-distinct: values-for-distinct(eq;L),
map: map(f;as),
list_ind: list_ind,
remove-repeats: remove-repeats(eq;L),
filter: filter(P;l),
reduce: reduce(f;k;as),
nil: [],
it: ⋅,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}t:\mBbbN{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}L:consensus-rcv(V;A) List. \mforall{}n:\mBbbZ{}. \mforall{}v,v2:V.
(archive-condition(V;A;t;f;n;v;L @ [Init[v2]]) \mLeftarrow{}{}\mRightarrow{} \{(L = []) \mwedge{} (n = 0) \mwedge{} (v2 = v)\})
Date html generated:
2016_05_16-PM-00_36_29
Last ObjectModification:
2016_01_17-PM-08_01_40
Theory : event-ordering
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