Nuprl Lemma : consensus-accum-num_wf
∀[V:Type]. ∀[A:Id List]. ∀[num:ℤ]. ∀[f:(V List) ⟶ V]. ∀[s:𝔹 × ℤ × {a:Id| (a ∈ A)} List × V List × V].
∀[r:consensus-rcv(V;A)].
(consensus-accum-num(num;f;s;r) ∈ 𝔹 × ℤ × {a:Id| (a ∈ A)} List × V List × V)
Proof
Definitions occuring in Statement :
consensus-accum-num: consensus-accum-num(num;f;s;r),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
l_member: (x ∈ l),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
consensus-accum-num: consensus-accum-num(num;f;s;r),
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
consensus-rcv: consensus-rcv(V;A),
all: ∀x:A. B[x],
implies: P ⇒ Q,
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,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
spreadn: spread3,
nat: ℕ,
not: ¬A,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[num:\mBbbZ{}]. \mforall{}[f:(V List) {}\mrightarrow{} V].
\mforall{}[s:\mBbbB{} \mtimes{} \mBbbZ{} \mtimes{} \{a:Id| (a \mmember{} A)\} List \mtimes{} V List \mtimes{} V]. \mforall{}[r:consensus-rcv(V;A)].
(consensus-accum-num(num;f;s;r) \mmember{} \mBbbB{} \mtimes{} \mBbbZ{} \mtimes{} \{a:Id| (a \mmember{} A)\} List \mtimes{} V List \mtimes{} V)
Date html generated:
2016_05_16-PM-00_37_24
Last ObjectModification:
2015_12_29-PM-01_34_21
Theory : event-ordering
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