Nuprl Lemma : pv11_p1_valid-proposal-transitivity-forward
∀[Cmd:{T:Type| valueall-type(T)} ]
∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀p:ℤ × Cmd. ∀e':{e':E| e' ≤loc e } . ∀e1:{e1:E|
e1 ≤loc e' } .
(pv11_p1_valid-proposal(Cmd;es.e1;e';p;f) ⇒ pv11_p1_valid-proposal(Cmd;es;e;p;f))
Proof
Definitions occuring in Statement :
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
Message: Message(f),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
product: x:A × B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
subtype_rel: A ⊆r B,
listp: A List+,
name: Name,
vatype: ValueAllType,
prop: ℙ,
and: P ∧ Q,
sq_stable: SqStable(P),
l_all: (∀x∈L.P[x]),
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
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,
pv11_p1_headers: pv11_p1_headers(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
subtract: n - m,
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
pv11_p1_headers_fun: pv11_p1_headers_fun(Cmd),
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,
bfalse: ff,
btrue: tt,
null: null(as),
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
exists: ∃x:A. B[x],
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
pv11_p1_propose'base: pv11_p1_propose'base(Cmd;mf),
encodes-msg-type: hdr encodes T,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
equal-info-body: v = body(e),
es-header: header(e),
top: Top
Latex:
\mforall{}[Cmd:\{T:Type| valueall-type(T)\} ]
\mforall{}f:pv11\_p1\_headers\_type\{i:l\}(Cmd). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}p:\mBbbZ{} \mtimes{} Cmd. \mforall{}e':\{e':E| e' \mleq{}loc e \} .
\mforall{}e1:\{e1:E| e1 \mleq{}loc e' \} .
(pv11\_p1\_valid-proposal(Cmd;es.e1;e';p;f) {}\mRightarrow{} pv11\_p1\_valid-proposal(Cmd;es;e;p;f))
Date html generated:
2016_05_17-PM-04_14_24
Last ObjectModification:
2016_01_18-AM-11_14_56
Theory : paxos!synod
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