Nuprl Lemma : archive-condition-one-one
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ⟶ V]. ∀[L:consensus-rcv(V;A) List]. ∀[n1,n2:ℤ]. ∀[v1,v2:V].
({(n1 = n2 ∈ ℤ) ∧ (v1 = v2 ∈ V)}) supposing
(archive-condition(V;A;t;f;n2;v2;L) and
archive-condition(V;A;t;f;n1;v1;L))
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
list: T List,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
archive-condition: archive-condition(V;A;t;f;n;v;L),
exists: ∃x:A. B[x],
guard: {T},
and: P ∧ Q,
or: P ∨ Q,
top: Top,
cand: A c∧ B,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
cons: [a / b],
nat: ℕ,
nat_plus: ℕ+,
le: A ≤ B,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
listp: A List+,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b,
assert: ↑b,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
ifthenelse: if b then t else f fi ,
btrue: tt,
values-for-distinct: values-for-distinct(eq;L),
map: map(f;as),
list_ind: list_ind,
remove-repeats: remove-repeats(eq;L),
votes-from-inning: votes-from-inning(i;L),
mapfilter: mapfilter(f;P;L),
filter: filter(P;l),
reduce: reduce(f;k;as),
nil: [],
it: ⋅,
consensus-rcv: consensus-rcv(V;A),
cs-initial-rcv: Init[v],
outl: outl(x),
isl: isl(x),
cs-rcv-vote: Vote[a;i;v],
sq_type: SQType(T),
outr: outr(x),
pi1: fst(t),
pi2: snd(t),
ge: i ≥ j ,
rcvd-inning-eq: inning(r) =z i,
band: p ∧b q,
rcv-vote?: rcv-vote?(x),
bfalse: ff,
rcvd-vote: rcvd-vote(x),
spreadn: spread3,
squash: ↓T
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
(\{(n1 = n2) \mwedge{} (v1 = v2)\}) supposing
(archive-condition(V;A;t;f;n2;v2;L) and
archive-condition(V;A;t;f;n1;v1;L))
Date html generated:
2016_05_16-PM-00_39_40
Last ObjectModification:
2016_01_17-PM-08_03_56
Theory : event-ordering
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