Nuprl Lemma : new_23_sig_when_quorum_wf
∀[Cmd:ValueAllType]. ∀[cmdeq:EqDecider(Cmd)]. ∀[coeff,flrs:ℤ]. ∀[notify,propose:Atom List]. ∀[reps:bag(Id)].
∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
(new_23_sig_when_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f) ∈ (ℤ × ℤ)
─→ Id
─→ (ℤ × ℤ × Cmd × Id)
─→ (Cmd List × (Id List))
─→ bag(Interface))
Proof
Definitions occuring in Statement :
new_23_sig_when_quorum: new_23_sig_when_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
msg-interface: Interface,
Id: Id,
deq: EqDecider(T),
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
atom: Atom,
bag: bag(T)
Lemmas :
sq_stable__and,
equal_wf,
vatype_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
new_23_sig_headers_fun_wf,
cons_member,
equal-wf-base,
list_subtype_base,
atom_subtype_base,
iff_weakening_equal,
name_eq_wf,
bool_wf,
eqtt_to_assert,
assert-name_eq,
sq_stable__no_repeats,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
subtype_rel_dep_function,
new_23_sig_newvote_wf,
new_23_sig_roundout_wf,
empty-bag_wf,
msg-interface_wf,
list_wf,
new_23_sig_headers_type_wf,
bag_wf,
Id_wf,
deq_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[cmdeq:EqDecider(Cmd)]. \mforall{}[coeff,flrs:\mBbbZ{}]. \mforall{}[notify,propose:Atom List].
\mforall{}[reps:bag(Id)]. \mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)].
(new\_23\_sig\_when\_quorum(Cmd;cmdeq;coeff;flrs;notify;propose;reps;f) \mmember{} (\mBbbZ{} \mtimes{} \mBbbZ{})
{}\mrightarrow{} Id
{}\mrightarrow{} (\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id)
{}\mrightarrow{} (Cmd List \mtimes{} (Id List))
{}\mrightarrow{} bag(Interface))
Date html generated:
2015_07_23-PM-03_50_38
Last ObjectModification:
2015_02_04-PM-01_59_47
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