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
Lemmas :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
btrue_wf,
nil_wf,
Id_wf,
l_member_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
lt_int_wf,
subtract_wf,
assert_of_lt_int,
bfalse_wf,
less_than_wf,
cons_wf,
let_wf,
list_wf,
length_wf,
remove-repeats_wf,
id-deq_wf,
subtype_rel-deq,
sq_stable__l_member,
decidable__equal_Id,
set_wf,
values-for-distinct_wf,
zip_wf,
append_wf,
consensus-rcv_wf
\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:
2015_07_17-AM-11_48_50
Last ObjectModification:
2015_01_28-AM-00_44_46
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