Nuprl Lemma : new_23_sig_voter_start
∀[Cmd:ValueAllType]. ∀[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))]. ∀[e:E]. ∀[n:ℤ]. ∀[c:Cmd].
(<n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)
⇒ (↓∃e':E
∃c':Cmd
(e' ≤loc e
∧ <n, c'> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e')
∧ (¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e'))))))
Proof
Definitions occuring in Statement :
new_23_sig_ReplicaStateFun: new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e),
new_23_sig_Proposal: new_23_sig_Proposal(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-le: e ≤loc e' ,
es-E: E,
list: T List,
vatype: ValueAllType,
assert: ↑b,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom,
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item)
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,
classrel_wf,
new_23_sig_Proposal_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
new_23_sig_headers_type_wf,
set-sig_wf,
list_wf,
set_wf,
valueall-type_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_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,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
decidable__assert,
set-sig-member_wf,
new_23_sig_ReplicaStateFun_wf,
new_23_sig_replica_state_from_proposal_fun,
es-le_weakening,
not_wf,
assert_wf,
exists_wf,
es-le_wf,
es-le-self,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul
Latex:
\mforall{}[Cmd:ValueAllType]. \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))]. \mforall{}[e:E]. \mforall{}[n:\mBbbZ{}].
\mforall{}[c:Cmd].
(<n, c> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e)
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
\mexists{}c':Cmd
(e' \mleq{}loc e
\mwedge{} <n, c'> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e')
\mwedge{} (\mneg{}\muparrow{}(set-sig-member(slots) n
new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e'))))))
Date html generated:
2015_07_23-PM-04_03_08
Last ObjectModification:
2015_02_04-PM-03_54_05
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