Nuprl Lemma : new_23_sig_increasing_max
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀slots:set-sig{i:l}(ℤ).
∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)). ∀e1,e2:E. ∀slots1,slots2:set-sig-set(slots).
((e1 <loc e2)
⇒ slots1 ∈ new_23_sig_ReplicaState(Cmd;notify;propose;slots;f)(e1)
⇒ slots2 ∈ new_23_sig_ReplicaState(Cmd;notify;propose;slots;f)(e2)
⇒ (∀x:ℤ. ((↑(set-sig-member(slots) x slots1)) ⇒ (↑(set-sig-member(slots) x slots2)))))
Proof
Definitions occuring in Statement :
new_23_sig_ReplicaState: new_23_sig_ReplicaState(Cmd;notify;propose;slots;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,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
int: ℤ,
atom: Atom,
set-sig-member: set-sig-member(s),
set-sig-set: set-sig-set(s),
set-sig: set-sig{i:l}(Item)
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,
set-sig-set_wf,
Memory1-memory-class1,
set-sig-empty_wf,
new_23_sig_update_replica_wf,
new_23_sig_Proposal_wf,
Memory-loc-class-trans-refl,
all_wf,
assert_wf,
set-sig-member_wf,
single-bag_wf,
sq_stable__all,
sq_stable__assert,
set-sig-add-prop,
int_subtype_base,
parallel-class-single-val,
new_23_sig_propose'base_wf,
eclass0_wf,
new_23_sig_vote'base_wf,
new_23_sig_vote2prop_wf,
disjoint-classrel-symm,
eclass0-disjoint-classrel,
base-disjoint-classrel,
length_of_cons_lemma,
length_of_nil_lemma,
false_wf,
le_wf,
not_wf,
less_than_wf,
nat_wf,
sq_stable__encodes-msg-type,
l_all_fwd,
list_wf,
valueall-type_wf,
subtype_rel_weakening,
ext-eq_weakening,
top_wf,
eclass0-single-val,
single-valued-bag-single,
base-headers-msg-val-single-val,
es-le_weakening,
assert_witness,
new_23_sig_ReplicaState_wf,
es-locl_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
new_23_sig_headers_type_wf,
set-sig_wf,
set_wf
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose: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{}e1,e2:E.
\mforall{}slots1,slots2:set-sig-set(slots).
((e1 <loc e2)
{}\mRightarrow{} slots1 \mmember{} new\_23\_sig\_ReplicaState(Cmd;notify;propose;slots;f)(e1)
{}\mRightarrow{} slots2 \mmember{} new\_23\_sig\_ReplicaState(Cmd;notify;propose;slots;f)(e2)
{}\mRightarrow{} (\mforall{}x:\mBbbZ{}. ((\muparrow{}(set-sig-member(slots) x slots1)) {}\mRightarrow{} (\muparrow{}(set-sig-member(slots) x slots2)))))
Date html generated:
2015_07_23-PM-03_52_19
Last ObjectModification:
2015_02_04-PM-01_53_14
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