Nuprl Lemma : new_23_sig_round_info_classrel2
∀[Cmd:ValueAllType]
∀propose:Atom List
∀[notify:Atom List]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀es:EO+(Message(f)). ∀e:E.
∀[nrc:ℤ × ℤ × Cmd]
uiff(nrc ∈ new_23_sig_RoundInfo(Cmd;notify;propose;f)(e);((header(e) = ``new_23_sig retry`` ∈ Name)
∧ nrc = body(e))
∨ (has-es-info-type(es;e;f;ℤ × ℤ × Cmd × Id)
∧ (header(e) = ``new_23_sig vote`` ∈ Name)
∧ ((fst(fst(nrc))) = (fst(fst(fst(msgval(e))))) ∈ ℤ)
∧ ((snd(fst(nrc))) = (snd(fst(fst(msgval(e))))) ∈ ℤ)
∧ ((snd(nrc)) = (snd(fst(msgval(e)))) ∈ Cmd)))
Proof
Definitions occuring in Statement :
new_23_sig_RoundInfo: new_23_sig_RoundInfo(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
equal-info-body: v = body(e),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
name: Name,
cons: [a / b],
nil: [],
list: T List,
vatype: ValueAllType,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
product: x:A × B[x],
int: ℤ,
token: "$token",
atom: Atom,
equal: s = t ∈ T
Definitions :
assert: ↑b,
ifthenelse: if b then t else f fi ,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
cons: [a / b],
band: p ∧b q,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
bfalse: ff,
false: False
Lemmas :
sq_stable__and,
equal_wf,
vatype_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
Id_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,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
new_23_sig_headers_type_wf,
list_wf,
set_wf,
valueall-type_wf,
classrel_wf,
new_23_sig_RoundInfo_wf,
or_wf,
equal-wf-T-base,
es-header_wf,
equal-info-body_wf,
has-es-info-type_wf,
es-info-body_wf,
parallel-classrel,
new_23_sig_retry'base_wf,
eclass0_wf,
new_23_sig_vote'base_wf,
new_23_sig_vote2retry_wf,
decidable__equal_name,
sq_stable__has-es-info-type,
base-noloc-classrel,
subtype_rel_weakening,
ext-eq_weakening,
eclass0-classrel,
bag-member-single,
and_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
pi2_wf,
subtype_rel_wf,
pair-eta,
bag-member_wf,
es-loc_wf
Latex:
\mforall{}[Cmd:ValueAllType]
\mforall{}propose:Atom List
\mforall{}[notify:Atom List]. \mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)].
\mforall{}es:EO+(Message(f)). \mforall{}e:E.
\mforall{}[nrc:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd]
uiff(nrc \mmember{} new\_23\_sig\_RoundInfo(Cmd;notify;propose;f)(e);((header(e)
= ``new\_23\_sig retry``)
\mwedge{} nrc = body(e))
\mvee{} (has-es-info-type(es;e;f;\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id)
\mwedge{} (header(e) = ``new\_23\_sig vote``)
\mwedge{} ((fst(fst(nrc))) = (fst(fst(fst(msgval(e))))))
\mwedge{} ((snd(fst(nrc))) = (snd(fst(fst(msgval(e))))))
\mwedge{} ((snd(nrc)) = (snd(fst(msgval(e)))))))
Date html generated:
2015_07_23-PM-03_59_04
Last ObjectModification:
2015_02_04-PM-03_57_17
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