Nuprl Lemma : CLK_ClockFun-eq2
∀[MsgType:ValueAllType]. ∀[f:CLK_headers_type{i:l}(MsgType)]. ∀[es:EO+(Message(f))]. ∀[e:E].
(CLK_ClockVal(MsgType;f)@e
= if e ∈b CLK_msg'base(MsgType;f)
then if first(e)
then imax(snd(CLK_msg'base(MsgType;f)@e);0) + 1
else imax(snd(CLK_msg'base(MsgType;f)@e);CLK_ClockVal(MsgType;f)@pred(e)) + 1
fi
if first(e) then 0
else CLK_ClockVal(MsgType;f)@pred(e)
fi
∈ ℤ)
Proof
Definitions occuring in Statement :
CLK_ClockFun: CLK_ClockVal(MsgType;f)@e,
CLK_msg'base: CLK_msg'base(MsgType;f),
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
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-E: E,
imax: imax(a;b),
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
pi2: snd(t),
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
CLK_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
CLK_headers_fun_wf,
cons_wf_listp,
cons_wf,
nil_wf,
listp_wf,
cons_member,
iff_weakening_equal,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
CLK_headers_type_wf,
set_wf,
valueall-type_wf,
state-class1-fun-eq,
Id_wf,
CLK_upd_clock_wf,
CLK_msg'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,
imax_wf,
pi2_wf,
classfun-res_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
CLK_ClockFun_wf,
es-pred_wf,
pair-eta,
es-interface-subtype_rel2,
subtype_rel_product,
subtype_top,
subtype_rel_wf,
top_wf
Latex:
\mforall{}[MsgType:ValueAllType]. \mforall{}[f:CLK\_headers\_type\{i:l\}(MsgType)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E].
(CLK\_ClockVal(MsgType;f)@e
= if e \mmember{}\msubb{} CLK\_msg'base(MsgType;f)
then if first(e)
then imax(snd(CLK\_msg'base(MsgType;f)@e);0) + 1
else imax(snd(CLK\_msg'base(MsgType;f)@e);CLK\_ClockVal(MsgType;f)@pred(e)) + 1
fi
if first(e) then 0
else CLK\_ClockVal(MsgType;f)@pred(e)
fi )
Date html generated:
2015_07_23-PM-04_10_27
Last ObjectModification:
2015_02_04-PM-02_01_21
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