Nuprl Lemma : pv11_p1_ord_comm
∀Cmd:ValueAllType. ∀accpts:bag(Id). ∀mf:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(mf)). ∀e1,e2:E.
∀b:pv11_p1_Ballot_Num(). ∀s:ℤ. ∀waitfor1,waitfor2:bag(Id).
((e1 <loc e2)
⇒ waitfor1 ∈ pv11_p1_CommanderState(Cmd;accpts;mf) b s(e1)
⇒ waitfor2 ∈ pv11_p1_CommanderState(Cmd;accpts;mf) b s(e2)
⇒ sub-bag(Id;waitfor2;waitfor1))
Proof
Definitions occuring in Statement :
pv11_p1_CommanderState: pv11_p1_CommanderState(Cmd;accpts;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-locl: (e <loc e'),
es-E: E,
Id: Id,
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
int: ℤ,
sub-bag: sub-bag(T;as;bs),
bag: bag(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,
list_wf,
classrel_wf,
squash_wf,
true_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
State1-state-class1,
pv11_p1_on_p2b_wf,
pv11_p1_p2b'base_wf,
State-loc-comb-trans-refl,
sub-bag_wf,
single-bag_wf,
sub-bag_weakening,
sub-bag_transitivity,
pv11_p1_eq_bnums_wf,
bool_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
eq_int_wf,
assert_of_eq_int,
iff_transitivity,
equal-wf-T-base,
assert_wf,
int_subtype_base,
iff_weakening_uiff,
assert_of_band,
sub-bag-remove-if,
id-deq_wf,
bor_wf,
bnot_wf,
or_wf,
not_wf,
bnot_thru_band,
eqff_to_assert,
assert_of_bor,
assert_of_bnot,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
single-valued-bag-single,
es-le_weakening,
pv11_p1_CommanderState_wf,
es-locl_wf,
pv11_p1_Ballot_Num_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
pv11_p1_headers_type_wf,
bag_wf,
Id_wf,
set_wf,
valueall-type_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}accpts:bag(Id). \mforall{}mf:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(mf)).
\mforall{}e1,e2:E. \mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}s:\mBbbZ{}. \mforall{}waitfor1,waitfor2:bag(Id).
((e1 <loc e2)
{}\mRightarrow{} waitfor1 \mmember{} pv11\_p1\_CommanderState(Cmd;accpts;mf) b s(e1)
{}\mRightarrow{} waitfor2 \mmember{} pv11\_p1\_CommanderState(Cmd;accpts;mf) b s(e2)
{}\mRightarrow{} sub-bag(Id;waitfor2;waitfor1))
Date html generated:
2015_07_23-PM-04_31_57
Last ObjectModification:
2015_02_04-AM-07_23_27
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