Nuprl Lemma : CLK_Clock-classrel
∀[MsgType:ValueAllType]. ∀[f:CLK_headers_type{i:l}(MsgType)].
∀es:EO+(Message(f)). ∀e:E. ∀v:ℤ. (v ∈ CLK_Clock(MsgType;f)(e) ⇐⇒ v = CLK_ClockVal(MsgType;f)@e ∈ ℤ)
Proof
Definitions occuring in Statement :
CLK_ClockFun: CLK_ClockVal(MsgType;f)@e,
CLK_Clock: CLK_Clock(MsgType;f),
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
Message: Message(f),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-E: E,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
l_all: (∀x∈L.P[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,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
CLK_headers: CLK_headers(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
CLK_headers_fun: CLK_headers_fun(MsgType),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
null: null(as),
uiff: uiff(P;Q),
CLK_ClockFun: CLK_ClockVal(MsgType;f)@e,
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs
Latex:
\mforall{}[MsgType:ValueAllType]. \mforall{}[f:CLK\_headers\_type\{i:l\}(MsgType)].
\mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}v:\mBbbZ{}. (v \mmember{} CLK\_Clock(MsgType;f)(e) \mLeftarrow{}{}\mRightarrow{} v = CLK\_ClockVal(MsgType;f)@e)
Date html generated:
2016_05_17-PM-02_44_40
Last ObjectModification:
2016_01_18-AM-09_50_18
Theory : lamport!s!clocks
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