Nuprl Lemma : pv11_p1_A2
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
∀bnum1,bnum2:pv11_p1_Ballot_Num(). ∀accepted1,accepted2:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀b:pv11_p1_Ballot_Num().
∀pv:ℤ × Cmd. ∀loc:Id.
(Inj(Id;ℤ;ldrs_uid)
⇒ (¬↑first(e))
⇒ <bnum2, accepted2> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(e)
⇒ <bnum1, accepted1> ∈ pv11_p1_AcceptorState(Cmd;ldrs_uid;f)(pred(e))
⇒ (<b, pv> ∈ accepted2)
⇒ (¬(<b, pv> ∈ accepted1))
⇒ (b = bnum2 ∈ pv11_p1_Ballot_Num()))
Proof
Definitions occuring in Statement :
pv11_p1_AcceptorState: pv11_p1_AcceptorState(Cmd;ldrs_uid;mf),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
Id: Id,
l_member: (x ∈ l),
list: T List,
inject: Inj(A;B;f),
vatype: ValueAllType,
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
pv11_p1_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
pv11_p1_headers_fun_wf,
cons_wf_listp,
nil_wf,
listp_wf,
cons_member,
cons_wf,
equal-wf-base,
iff_weakening_equal,
not_wf,
classrel_wf,
es-pred_wf,
pv11_p1_AcceptorState_wf,
assert_wf,
es-first_wf2,
inject_wf,
list_wf,
pv11_p1_Ballot_Num_wf,
Id_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
set_wf,
valueall-type_wf,
pv11_p1_inc_acc,
es-pred-locl,
squash_wf,
true_wf,
eclass_wf,
member_append,
pv11_p1_AcceptorState-classrel,
append_wf,
pv11_p1_acc_state_fun_eq,
member-disjoint-union-comb-bool,
pv11_p1_p1a'base_wf,
pv11_p1_p2a'base_wf,
member-eclass_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
classfun-res-disjoint-union-comb-as-parallel-eclass1,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
base-disjoint-classrel,
iff_transitivity,
name_eq_wf,
bnot_wf,
assert-name_eq,
iff_weakening_uiff,
assert_of_bnot,
classfun-res-parallel-class-left,
eclass1_wf,
pv11_p1_on_p1a_wf,
pv11_p1_on_p2a_wf,
member-eclass-eclass1,
eclass1-disjoint-classrel,
disjoint-classrel-symm,
classfun-res-eclass1,
classfun-res-member-base,
member-base-class,
has-es-info-type-is-msg-has-type,
subtype_rel-equal,
pair-eta,
es-info-body_wf,
subtype_rel_product,
top_wf,
subtype_rel_transitivity,
es-info-type_wf,
pv11_p1_AcceptorStateFun_wf,
subtype_top,
pv11_p1_max_bnum_wf,
append_cancel_nil,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
classfun-res-parallel-class-right,
pv11_p1_leq_bnum_wf,
pv11_p1_add_if_new_wf,
pv11_p1_same_pvalue_wf,
bool_cases,
bl-exists_wf,
l_exists_wf,
assert-bl-exists,
and_wf,
null_wf3,
subtype_rel_list,
member_singleton,
pv11_p1_max_bnum_comm,
pv11_p1_max_bnum_if_leq,
append-cancellation
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}ldrs$_\mbackslash{}ff7\000Cbuid}$:Id {}\mrightarrow{} \mBbbZ{}.
\mforall{}bnum1,bnum2:pv11\_p1\_Ballot\_Num(). \mforall{}accepted1,accepted2:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List.
\mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}pv:\mBbbZ{} \mtimes{} Cmd. \mforall{}loc:Id.
(Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} (\mneg{}\muparrow{}first(e))
{}\mRightarrow{} <bnum2, accepted2> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(e)
{}\mRightarrow{} <bnum1, accepted1> \mmember{} pv11\_p1\_AcceptorState(Cmd;ldrs$_{uid}$;f)(pred(e))
{}\mRightarrow{} (<b, pv> \mmember{} accepted2)
{}\mRightarrow{} (\mneg{}(<b, pv> \mmember{} accepted1))
{}\mRightarrow{} (b = bnum2))
Date html generated:
2015_07_23-PM-04_49_53
Last ObjectModification:
2015_02_04-AM-08_01_03
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