Nuprl Lemma : cs-inning-committed-single
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[s:ConsensusState]. ∀[i:ℤ]. ∀[v,v2:V].
(v = v2 ∈ V) supposing
(in state s, inning i has committed v2 and
in state s, inning i could commit v and
two-intersection(A;W))
Proof
Definitions occuring in Statement :
two-intersection: two-intersection(A;W),
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
consensus-state4: ConsensusState,
Id: Id,
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cs-inning-committable: in state s, inning i could commit v ,
exists: ∃x:A. B[x],
cs-inning-committed: in state s, inning i has committed v,
and: P ∧ Q,
prop: ℙ,
two-intersection: two-intersection(A;W),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
not: ¬A,
false: False,
guard: {T}
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[s:ConsensusState]. \mforall{}[i:\mBbbZ{}]. \mforall{}[v,v2:V].
(v = v2) supposing
(in state s, inning i has committed v2 and
in state s, inning i could commit v and
two-intersection(A;W))
Date html generated:
2016_05_16-PM-00_04_15
Last ObjectModification:
2015_12_29-PM-01_23_06
Theory : event-ordering
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