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
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
listp: A List+,
name: Name,
CLK_headers: CLK_headers(),
rev_implies: P ⇐ Q,
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
CLK_headers_fun: CLK_headers_fun(MsgType),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
list_ind: list_ind,
cons: [a / b],
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
CLK_ClockFun: CLK_ClockVal(MsgType;f)@e,
CLK_Clock: CLK_Clock(MsgType;f),
CLK_msg'base: CLK_msg'base(MsgType;f),
encodes-msg-type: hdr encodes T,
bool: 𝔹,
unit: Unit,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
CLK_upd_clock: CLK_upd_clock(MsgType),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
pi2: snd(t)
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:
2016_05_17-PM-02_46_12
Last ObjectModification:
2015_12_29-PM-10_19_07
Theory : lamport!s!clocks
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