Nuprl Lemma : cs-inning-committable-step
∀V:Type
((∀v,v':V. Dec(v = v' ∈ V))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List. ∀x,y:ts-reachable(consensus-ts4(V;A;W)). ∀i:ℕ. ∀v:V.
((x ts-rel(consensus-ts4(V;A;W)) y)
⇒ in state y, inning i could commit v
⇒ in state x, inning i could commit v )))
Proof
Definitions occuring in Statement :
cs-inning-committable: in state s, inning i could commit v ,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
l_member: (x ∈ l),
list: T List,
nat: ℕ,
decidable: Dec(P),
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts)
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
ts-reachable: ts-reachable(ts),
infix_ap: x f y,
uimplies: b supposing a,
ts-type: ts-type(ts),
pi1: fst(t),
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
nat: ℕ,
ts-rel: ts-rel(ts),
pi2: snd(t),
consensus-rel: CR[x,y],
cs-inning-committable: in state s, inning i could commit v ,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
decidable: Dec(P),
guard: {T},
not: ¬A,
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
false: False,
Id: Id,
sq_type: SQType(T),
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
fpf-domain: fpf-domain(f),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
fpf-single: x : v,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y]),
le: A ≤ B,
fpf-sub: f ⊆ g
Latex:
\mforall{}V:Type
((\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}x,y:ts-reachable(consensus-ts4(V;A;W)). \mforall{}i:\mBbbN{}. \mforall{}v:V\000C.
((x ts-rel(consensus-ts4(V;A;W)) y)
{}\mRightarrow{} in state y, inning i could commit v
{}\mRightarrow{} in state x, inning i could commit v )))
Date html generated:
2016_05_16-PM-00_08_12
Last ObjectModification:
2016_01_17-PM-03_54_26
Theory : event-ordering
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