Nuprl Lemma : consensus-accum-num-archives
∀[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 archive-condition(V;A;t;f;i - 1;v;L) supposing ↑b
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+,
assert: ↑b,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
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],
uimplies: b supposing a,
so_apply: x[s],
guard: {T},
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
list_accum: list_accum,
nil: [],
it: ⋅,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
false: False,
top: Top,
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],
btrue: tt,
true: True,
and: P ∧ Q,
le: A ≤ B,
nat_plus: ℕ+,
nat: ℕ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
not: ¬A,
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
cons: [a / b],
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
cand: A c∧ B,
decidable: Dec(P),
less_than: a < b,
ge: i ≥ j ,
rev_uimplies: rev_uimplies(P;Q),
sq_type: SQType(T),
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 archive-condition(V;A;t;f;i - 1;v;L)
supposing \muparrow{}b
Date html generated:
2016_05_16-PM-00_41_55
Last ObjectModification:
2016_01_17-PM-08_03_32
Theory : event-ordering
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