Nuprl Lemma : pv11_p1_commander_state_fun_eq
∀[Cmd:ValueAllType]. ∀[f:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[accpts:bag(Id)].
∀[b:pv11_p1_Ballot_Num()]. ∀[s:ℤ].
(pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es;e)
= if e ∈b pv11_p1_p2b'base(Cmd;f)
then if first(e)
then pv11_p1_on_p2b() b s loc(e) pv11_p1_p2b'base(Cmd;f)@e accpts
else pv11_p1_on_p2b() b s loc(e) pv11_p1_p2b'base(Cmd;f)@e
pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es;pred(e))
fi
if first(e) then accpts
else pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es;pred(e))
fi
∈ bag(Id))
Proof
Definitions occuring in Statement :
pv11_p1_CommanderStateFun: pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e),
pv11_p1_on_p2b: pv11_p1_on_p2b(),
pv11_p1_p2b'base: pv11_p1_p2b'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),
classfun-res: X@e,
member-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
apply: f a,
int: ℤ,
equal: s = t ∈ T,
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,
pv11_p1_Ballot_Num_wf,
bag_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,
state-class1-fun-eq,
pv11_p1_on_p2b_wf,
pv11_p1_p2b'base_wf,
base-headers-msg-val-single-val,
subtype_rel_weakening,
ext-eq_weakening,
member-eclass_wf,
bool_wf,
eqtt_to_assert,
es-first_wf2,
es-loc_wf,
classfun-res_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
classfun_wf,
state-class1_wf,
loop-class-state-functional,
single-bag_wf,
eclass1_wf,
bag_size_single_lemma,
false_wf,
eclass1-single-val,
single-valued-bag-single,
es-pred_wf
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[f:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E].
\mforall{}[accpts:bag(Id)]. \mforall{}[b:pv11\_p1\_Ballot\_Num()]. \mforall{}[s:\mBbbZ{}].
(pv11\_p1\_CommanderStateFun(Cmd;accpts;f;b;s;es;e)
= if e \mmember{}\msubb{} pv11\_p1\_p2b'base(Cmd;f)
then if first(e)
then pv11\_p1\_on\_p2b() b s loc(e) pv11\_p1\_p2b'base(Cmd;f)@e accpts
else pv11\_p1\_on\_p2b() b s loc(e) pv11\_p1\_p2b'base(Cmd;f)@e
pv11\_p1\_CommanderStateFun(Cmd;accpts;f;b;s;es;pred(e))
fi
if first(e) then accpts
else pv11\_p1\_CommanderStateFun(Cmd;accpts;f;b;s;es;pred(e))
fi )
Date html generated:
2015_07_23-PM-04_47_54
Last ObjectModification:
2015_02_04-AM-08_18_37
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