Nuprl Lemma : consensus-accum-num-property3
∀[V:Type]
∀A:Id List. ∀t:ℕ+. ∀f:(V List) ⟶ V. ∀v0:V. ∀L:consensus-rcv(V;A) List.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in if b
then archive-condition(V;A;t;f;i - 1;v;L)
else ∀v:V. (¬archive-condition(V;A;t;f;i;v;L))
fi
Proof
Definitions occuring in Statement :
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
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+,
ifthenelse: if b then t else f fi ,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s],
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
list_accum: list_accum,
nil: [],
subtract: n - m,
not: ¬A,
archive-condition: archive-condition(V;A;t;f;n;v;L),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
cons: [a / b],
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
consensus-rcv: consensus-rcv(V;A),
consensus-accum-num: consensus-accum-num(num;f;s;r),
cs-initial-rcv: Init[v],
spreadn: spread3,
let: let,
cs-rcv-vote: Vote[a;i;v],
le: A ≤ B,
nat_plus: ℕ+,
iff: P ⇐⇒ Q,
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
rev_implies: P ⇐ Q,
cand: A c∧ B,
decidable: Dec(P),
less_than: a < b,
rev_uimplies: rev_uimplies(P;Q),
values-for-distinct: values-for-distinct(eq;L),
less_than': less_than'(a;b),
votes-from-inning: votes-from-inning(i;L),
squash: ↓T,
rcvd-inning-eq: inning(r) =z i,
rcvd-vote: rcvd-vote(x),
mapfilter: mapfilter(f;P;L),
outr: outr(x),
rcv-vote?: rcv-vote?(x),
band: p ∧b q,
pi1: fst(t),
unzip: unzip(as),
pi2: snd(t)
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}v0:V. \mforall{}L:consensus-rcv(V;A) List.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in if b
then archive-condition(V;A;t;f;i - 1;v;L)
else \mforall{}v:V. (\mneg{}archive-condition(V;A;t;f;i;v;L))
fi
Date html generated:
2016_05_16-PM-00_43_22
Last ObjectModification:
2016_01_17-PM-08_03_19
Theory : event-ordering
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