Nuprl Lemma : cs-ref-map3-predecided
∀[V:Type]
∀L:ts-reachable(consensus-ts3(V)). ∀v:V.
((∀v':V. (¬(COMMITED[v'] ∈ L))) ∧ (CONSIDERING[v] ∈ L) ⇐⇒ cs-ref-map3(L) = PREDECIDED[v] ∈ consensus-state2(V))
Proof
Definitions occuring in Statement :
cs-ref-map3: cs-ref-map3(L),
consensus-ts3: consensus-ts3(T),
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
cs-predecided: PREDECIDED[v],
consensus-state2: consensus-state2(T),
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
ts-reachable: ts-reachable(ts),
consensus-ts3: consensus-ts3(T),
ts-type: ts-type(ts),
pi1: fst(t),
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
cs-ref-map3: cs-ref-map3(L),
let: let,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
true: True,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
l_member: (x ∈ l),
cand: A c∧ B,
nat: ℕ,
le: A ≤ B,
cons: [a / b],
less_than': less_than'(a;b),
ge: i ≥ j ,
cs-decided: Decided[v],
cs-predecided: PREDECIDED[v],
consensus-state2: consensus-state2(T),
isl: isl(x),
sq_type: SQType(T),
cs-ambivalent: AMBIVALENT,
outl: outl(x)
Latex:
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}v:V.
((\mforall{}v':V. (\mneg{}(COMMITED[v'] \mmember{} L))) \mwedge{} (CONSIDERING[v] \mmember{} L) \mLeftarrow{}{}\mRightarrow{} cs-ref-map3(L) = PREDECIDED[v])
Date html generated:
2016_05_16-AM-11_53_16
Last ObjectModification:
2016_01_17-PM-03_51_35
Theory : event-ordering
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