Nuprl Lemma : archive-consensus-accum-num
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ⟶ V]. ∀[v0:V]. ∀[L:consensus-rcv(V;A) List]. ∀[v:V]. ∀[i:ℤ].
  ↑(fst(consensus-accum-num-state(t;f;v0;L))) supposing archive-condition(V;A;t;f;i;v;L)
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
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
pi1: fst(t)
, 
function: x:A ⟶ B[x]
, 
int: ℤ
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
so_apply: x[s]
, 
top: Top
, 
guard: {T}
, 
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
pi1: fst(t)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
false: False
, 
archive-condition: archive-condition(V;A;t;f;n;v;L)
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
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]
, 
sq_type: SQType(T)
, 
true: True
, 
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e]
, 
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]
, 
nat_plus: ℕ+
, 
subtract: n - m
, 
btrue: tt
, 
le: A ≤ B
, 
iff: P 
⇐⇒ Q
, 
pi2: snd(t)
, 
not: ¬A
, 
nat: ℕ
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
uiff: uiff(P;Q)
, 
rev_implies: P 
⇐ Q
, 
decidable: Dec(P)
, 
votes-from-inning: votes-from-inning(i;L)
, 
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
, 
values-for-distinct: values-for-distinct(eq;L)
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].  \mforall{}[v:V].
\mforall{}[i:\mBbbZ{}].
    \muparrow{}(fst(consensus-accum-num-state(t;f;v0;L)))  supposing  archive-condition(V;A;t;f;i;v;L)
Date html generated:
2016_05_16-PM-00_42_37
Last ObjectModification:
2016_01_17-PM-08_04_08
Theory : event-ordering
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