Nuprl Lemma : cs-ref-map3-ambivalent
∀[V:Type]. ∀[L:ts-reachable(consensus-ts3(V))].
uiff((∀[v:V]. (¬(COMMITED[v] ∈ L))) ∧ (∀[v:V]. (¬(CONSIDERING[v] ∈ L)));cs-ref-map3(L)
= AMBIVALENT
∈ 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-ambivalent: AMBIVALENT,
consensus-state2: consensus-state2(T),
l_member: (x ∈ l),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
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],
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
ts-reachable: ts-reachable(ts),
consensus-ts3: consensus-ts3(T),
ts-type: ts-type(ts),
pi1: fst(t),
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: ⋅,
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),
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B,
nat: ℕ,
ge: i ≥ j ,
cs-decided: Decided[v],
cs-ambivalent: AMBIVALENT,
consensus-state2: consensus-state2(T),
isl: isl(x),
cs-predecided: PREDECIDED[v],
sq_type: SQType(T)
Latex:
\mforall{}[V:Type]. \mforall{}[L:ts-reachable(consensus-ts3(V))].
uiff((\mforall{}[v:V]. (\mneg{}(COMMITED[v] \mmember{} L))) \mwedge{} (\mforall{}[v:V]. (\mneg{}(CONSIDERING[v] \mmember{} L)));cs-ref-map3(L)
= AMBIVALENT)
Date html generated:
2016_05_16-AM-11_53_34
Last ObjectModification:
2016_01_17-PM-03_51_43
Theory : event-ordering
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