Nuprl Lemma : new_23_sig_QuorumState-classrel
∀[Cmd:ValueAllType]. ∀[notify,propose:Atom List]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀es:EO+(Message(f)). ∀e:E. ∀x:ℤ × ℤ. ∀v:Cmd List × (Id List).
(v ∈ new_23_sig_QuorumState(Cmd;notify;propose;f) x(e)
⇐⇒ v = new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e) ∈ (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_QuorumState: new_23_sig_QuorumState(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
list: T List,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ 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,
classrel-classfun,
new_23_sig_QuorumState-functional,
classrel_wf,
list_wf,
Id_wf,
new_23_sig_QuorumState_wf,
new_23_sig_QuorumStateFun_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
new_23_sig_headers_type_wf,
set_wf,
valueall-type_wf
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{}x:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}v:Cmd List \mtimes{} (Id List).
(v \mmember{} new\_23\_sig\_QuorumState(Cmd;notify;propose;f) x(e)
\mLeftarrow{}{}\mRightarrow{} v = new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;x;es;e))
Date html generated:
2015_07_23-PM-03_50_44
Last ObjectModification:
2015_02_04-PM-01_59_24
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