Nuprl Lemma : consensus-ts3-invariant0
∀[V:Type]
∀L:ts-reachable(consensus-ts3(V)). ∀i:ℕ||L||.
∀j:ℕ||L||. (L[j] = INITIAL ∈ consensus-state3(V)) ∨ (L[j] = WITHDRAWN ∈ consensus-state3(V)) supposing i < j
supposing L[i] = INITIAL ∈ consensus-state3(V)
Proof
Definitions occuring in Statement :
consensus-ts3: consensus-ts3(T),
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
select: L[n],
length: ||as||,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
or: P ∨ Q,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
uimplies: b supposing a,
guard: {T},
ts-reachable: ts-reachable(ts),
consensus-ts3: consensus-ts3(T),
ts-type: ts-type(ts),
pi1: fst(t),
ts-init: ts-init(ts),
pi2: snd(t),
select: L[n],
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
ts-rel: ts-rel(ts),
infix_ap: x f y,
or: P ∨ Q,
decidable: Dec(P),
squash: ↓T,
cand: A c∧ B,
le: A ≤ B,
less_than: a < b,
subtype_rel: A ⊆r B,
list: T List,
label: ...$L... t,
cons: [a / b],
nat: ℕ,
ge: i ≥ j ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
sq_type: SQType(T)
Latex:
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}i:\mBbbN{}||L||.
\mforall{}j:\mBbbN{}||L||. (L[j] = INITIAL) \mvee{} (L[j] = WITHDRAWN) supposing i < j supposing L[i] = INITIAL
Date html generated:
2016_05_16-AM-11_51_44
Last ObjectModification:
2016_01_17-PM-03_57_32
Theory : event-ordering
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