Nuprl Lemma : new_23_sig_rounds_mem
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e1,e2:E. ∀n,round1,round2:ℤ. ∀z:ℤ × ℤ × Cmd.
((e1 <loc e2)
⇒ z ∈ new_23_sig_RoundInfo(Cmd;notify;propose;f)(e1)
⇒ round1 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e1)
⇒ round2 ∈ new_23_sig_NewRoundsState(Cmd;notify;propose;f) n(e2)
⇒ let z,cmd = z
in let n',round' = z
in (n = n' ∈ ℤ) ⇒ (round' ≤ round2))
Proof
Definitions occuring in Statement :
new_23_sig_NewRoundsState: new_23_sig_NewRoundsState(Cmd;notify;propose;f),
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),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
list: T List,
vatype: ValueAllType,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
spread: spread def,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
new_23_sig_headers_fun_wf,
cons_member,
cons_wf,
cons_wf_listp,
listp_wf,
nil_wf,
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,
squash_wf,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
Id_wf,
classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Memory1-memory-class1,
new_23_sig_update_round_wf,
new_23_sig_RoundInfo_wf,
Memory-loc-class-mem,
int_subtype_base,
le_wf,
single-bag_wf,
eq_int_wf,
assert_of_eq_int,
lt_int_wf,
assert_of_lt_int,
less_than_wf,
neg_assert_of_eq_int,
parallel-class-single-val,
new_23_sig_retry'base_wf,
eclass0_wf,
new_23_sig_vote'base_wf,
new_23_sig_vote2retry_wf,
disjoint-classrel-symm,
eclass0-disjoint-classrel,
base-disjoint-classrel,
iff_transitivity,
not_wf,
assert_wf,
bnot_wf,
iff_weakening_uiff,
assert_of_bnot,
sq_stable__encodes-msg-type,
l_all_fwd,
list_wf,
valueall-type_wf,
subtype_rel_weakening,
ext-eq_weakening,
eclass0-single-val,
single-valued-bag-single,
base-headers-msg-val-single-val,
new_23_sig_NewRoundsState_wf,
es-locl_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
new_23_sig_headers_type_wf,
set_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e1,e2:E. \mforall{}n,round1,round2:\mBbbZ{}. \mforall{}z:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd.
((e1 <loc e2)
{}\mRightarrow{} z \mmember{} new\_23\_sig\_RoundInfo(Cmd;notify;propose;f)(e1)
{}\mRightarrow{} round1 \mmember{} new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f) n(e1)
{}\mRightarrow{} round2 \mmember{} new\_23\_sig\_NewRoundsState(Cmd;notify;propose;f) n(e2)
{}\mRightarrow{} let z,cmd = z
in let n',round' = z
in (n = n') {}\mRightarrow{} (round' \mleq{} round2))
Date html generated:
2015_07_23-PM-03_51_29
Last ObjectModification:
2015_02_04-PM-01_57_08
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