Nuprl Lemma : decidable__archive-condition
∀[V:Type]
(V
⇒ (∀A:Id List. ∀t:ℕ+. ∀f:(V List) ⟶ V. ∀L:consensus-rcv(V;A) List.
Dec(∃n:ℕ. ∃v:V. archive-condition(V;A;t;f;n;v;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+,
nat: ℕ,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
nat_plus: ℕ+,
so_apply: x[s1;s2],
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
and: P ∧ Q,
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
uimplies: b supposing a,
top: Top,
le: A ≤ B,
not: ¬A,
false: False,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
bfalse: ff,
pi1: fst(t),
pi2: snd(t),
decidable: Dec(P),
exists: ∃x:A. B[x],
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
cand: A c∧ B,
true: True,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb
Latex:
\mforall{}[V:Type]
(V
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}L:consensus-rcv(V;A) List.
Dec(\mexists{}n:\mBbbN{}. \mexists{}v:V. archive-condition(V;A;t;f;n;v;L))))
Date html generated:
2016_05_16-PM-00_43_52
Last ObjectModification:
2016_01_17-PM-07_59_38
Theory : event-ordering
Home
Index