Nuprl Lemma : pv11_p1_acc_state_from_p2a_fun
∀Cmd:ValueAllType. ∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀ldrs_uid:Id ─→ ℤ.
∀b:pv11_p1_Ballot_Num(). ∀s:ℤ. ∀c:Cmd.
(Inj(Id;ℤ;ldrs_uid)
⇒ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e)))
⇒ (↓∃e':E
∃l:Id
(e' ≤loc e
∧ <l, b, s, c> ∈ pv11_p1_p2a'base(Cmd;f)(e')
∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())
∧ (∀e'':E
(e' ≤loc e'' ⇒ e'' ≤loc e ⇒ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e''))))))))
Proof
Definitions occuring in Statement :
pv11_p1_AcceptorStateFun: pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_p2a'base: pv11_p1_p2a'base(Cmd;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-le: e ≤loc e' ,
es-E: E,
Id: Id,
l_member: (x ∈ l),
inject: Inj(A;B;f),
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: 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,
pv11_p1_AcceptorStateFun_wf,
list_wf,
inject_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_acc_state_from_p2a,
pair-eta,
subtype_rel_product,
top_wf,
subtype_top,
pv11_p1_AcceptorState-classrel
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{}b:pv11\_p1\_Ballot\_Num(). \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
(Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} (<b, s, c> \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e)))
{}\mRightarrow{} (\mdownarrow{}\mexists{}e':E
\mexists{}l:Id
(e' \mleq{}loc e
\mwedge{} <l, b, s, c> \mmember{} pv11\_p1\_p2a'base(Cmd;f)(e')
\mwedge{} (b = (fst(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e'))))
\mwedge{} (\mforall{}e'':E
(e' \mleq{}loc e''
{}\mRightarrow{} e'' \mleq{}loc e
{}\mRightarrow{} (<b, s, c> \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es\000C;e''))))))))
Date html generated:
2015_07_23-PM-04_49_42
Last ObjectModification:
2015_02_04-AM-08_00_43
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