Nuprl Lemma : new_23_sig_validity
∀[Cmd:ValueAllType]. ∀[eq:EqDecider(Cmd)]. ∀[reps,clients:bag(Id)]. ∀[coeff:{2...}]. ∀[flrs:ℕ].
∀[propose,notify:Atom List]. ∀[slots:set-sig{i:l}(ℤ)]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀[es:EO+(Message(f))].
(new_23_sig_message-constraint{i:l}(Cmd;clients;eq;coeff;flrs;notify;propose;reps;slots;f)
⇒ for every p1 in new_23_sig_decided'base(Cmd;notify;propose;f) there is an
earlier event with info=m such that
(msg-header(m) = propose ∈ Name) ∧ (p1 = msg-body(m) ∈ (ℤ × Cmd)))
Proof
Definitions occuring in Statement :
new_23_sig_message-constraint: new_23_sig_message-constraint{i:l}(Cmd;clients;cmdeq;coeff;flrs;notify;propose;reps;slots;f),
new_23_sig_decided'base: new_23_sig_decided'base(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
msg-body: msg-body(msg),
msg-header: msg-header(m),
Message: Message(f),
causal-class-relation: causal-class-relation,
event-ordering+: EO+(Info),
Id: Id,
name: Name,
deq: EqDecider(T),
list: T List,
int_upper: {i...},
nat: ℕ,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
atom: Atom,
equal: s = t ∈ T,
bag: bag(T),
set-sig: set-sig{i:l}(Item)
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,
base-noloc-classrel,
subtype_rel_weakening,
ext-eq_weakening,
es-causl_wf,
event-ordering+_subtype,
equal-wf-T-base,
msg-header_wf,
es-info_wf,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
classrel_wf,
new_23_sig_decided'base_wf,
es-E_wf,
new_23_sig_message-constraint_wf,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
new_23_sig_headers_type_wf,
set-sig_wf,
list_wf,
nat_wf,
int_upper_wf,
bag_wf,
Id_wf,
deq_wf,
set_wf,
valueall-type_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
new_23_sig_vote'base_wf,
new_23_sig_retry'base_wf,
new_23_sig_QuorumStateFun_wf,
eo-forward_wf,
member-eo-forward-E,
es-loc_wf,
es-causle_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
zero-le-nat,
lelt_wf,
base-noloc-classrel-make-Msg2,
hdrmkmsg_lemma,
new_23_sig_headers_internal_wf,
exists_wf,
msg-interface_wf,
new_23_sig_main_wf,
make-msg-interface_wf,
es-causle-le,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
msg-authentic_wf,
new_23_sig-decided,
new_23_sig-vote,
new_23_sig-retry,
es-info-body_wf,
new_23_sig_propose'base_wf,
poss-maj-unanimous,
poss-maj_wf,
length_of_cons_lemma,
and_wf,
le_transitivity,
l_all_cons,
es-causl_transitivity2,
es-causle_weakening,
eo-forward-E-subtype,
es-causl_transitivity1,
es-causle_weakening_locl,
eclass_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
pi2_wf,
poss-maj-member,
new_23_sig_assert_newvote,
new_23_sig_quorum_invariant_fun,
new_23_sig_quorum_inv_vote_fun,
le_antisymmetry_iff,
select_wf,
eo-forward-locl,
eo-forward-base-classrel,
event-ordering+_cumulative,
es-causl_weakening,
es-le_weakening
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[eq:EqDecider(Cmd)]. \mforall{}[reps,clients:bag(Id)]. \mforall{}[coeff:\{2...\}]. \mforall{}[flrs:\mBbbN{}].
\mforall{}[propose,notify:Atom List]. \mforall{}[slots:set-sig\{i:l\}(\mBbbZ{})].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)]. \mforall{}[es:EO+(Message(f))].
(new\_23\_sig\_message-constraint\{i:l\}(Cmd;clients;eq;coeff;flrs;notify;propose;reps;slots;f)
{}\mRightarrow{} for every p1 in new\_23\_sig\_decided'base(Cmd;notify;propose;f) there is an
earlier event with info=m such that
(msg-header(m) = propose) \mwedge{} (p1 = msg-body(m)))
Date html generated:
2015_07_23-PM-04_00_48
Last ObjectModification:
2015_02_04-PM-04_03_44
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