Nuprl Lemma : pv11_p1_valid-proposal-transitivity
∀[Cmd:{T:Type| valueall-type(T)} ]
∀f:pv11_p1_headers_type{i:l}(Cmd). ∀es:EO+(Message(f)). ∀e:E. ∀p:ℤ × Cmd.
(pv11_p1_valid-proposal(Cmd;es;e;p;f) ⇒ (∀e':E. (e c≤ e' ⇒ 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),
event-ordering+: EO+(Info),
es-causle: e c≤ 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],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
pv11_p1_valid-proposal: pv11_p1_valid-proposal(Cmd;es;e;p;f),
squash: ↓T,
exists: ∃x:A. B[x],
and: P ∧ Q,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
cand: A c∧ B,
vatype: ValueAllType,
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
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.
(pv11\_p1\_valid-proposal(Cmd;es;e;p;f)
{}\mRightarrow{} (\mforall{}e':E. (e c\mleq{} e' {}\mRightarrow{} pv11\_p1\_valid-proposal(Cmd;es;e';p;f))))
Date html generated:
2016_05_17-PM-04_14_07
Last ObjectModification:
2016_01_18-AM-11_14_08
Theory : paxos!synod
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