Nuprl Lemma : new_23_sig_quorum_state_fun_eq
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e:E. ∀nr:ℤ × ℤ.
(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;nr;es;e)
= if first(e) then <[], []>
if pred(e) ∈b new_23_sig_vote'base(Cmd;notify;propose;f)
then new_23_sig_add_to_quorum(Cmd) nr loc(e) new_23_sig_vote'base(Cmd;notify;propose;f)@pred(e)
new_23_sig_QuorumStateFun(Cmd;notify;propose;f;nr;es;pred(e))
else new_23_sig_QuorumStateFun(Cmd;notify;propose;f;nr;es;pred(e))
fi
∈ (Cmd List × (Id List)))
Proof
Definitions occuring in Statement :
new_23_sig_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e),
new_23_sig_add_to_quorum: new_23_sig_add_to_quorum(Cmd),
new_23_sig_vote'base: new_23_sig_vote'base(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
classfun-res: X@e,
member-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
nil: [],
list: T List,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
new_23_sig_headers_fun_wf,
cons_member,
cons_wf,
cons_wf_listp,
listp_wf,
nil_wf,
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,
squash_wf,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
Id_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
new_23_sig_headers_type_wf,
list_wf,
set_wf,
valueall-type_wf,
loop-class-memory-fun-eq,
eclass1_wf,
new_23_sig_vote'base_wf,
new_23_sig_add_to_quorum_wf,
single-bag_wf,
bag_size_single_lemma,
false_wf,
single-valued-bag-single,
eclass1-single-val,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
es-first_wf2,
member-eclass_wf,
es-pred_wf,
es-loc_wf,
classfun-res_wf,
classfun_wf,
loop-class-memory_wf,
loop-class-memory-functional,
sv_bag_only_single_lemma,
member-eclass-eclass1,
loop-class-memory-member,
classfun-res-eclass1,
es-loc-pred
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}nr:\mBbbZ{} \mtimes{} \mBbbZ{}.
(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;nr;es;e)
= if first(e) then <[], []>
if pred(e) \mmember{}\msubb{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)
then new\_23\_sig\_add\_to\_quorum(Cmd) nr loc(e)
new\_23\_sig\_vote'base(Cmd;notify;propose;f)@pred(e)
new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;nr;es;pred(e))
else new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;nr;es;pred(e))
fi )
Date html generated:
2015_07_23-PM-03_59_07
Last ObjectModification:
2015_02_04-PM-03_57_37
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