Nuprl Lemma : consensus-ts4-ref-map
∀[V:Type]
((∃v,v':V. (¬(v = v' ∈ V)))
⇒ (∀v,v':V. Dec(v = v' ∈ V))
⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List.
(two-intersection(A;W) ⇒ (∃f:ConsensusState ⟶ (consensus-state3(V) List). cs-ref-map-constraints(V;A;W;f)))))
Proof
Definitions occuring in Statement :
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
two-intersection: two-intersection(A;W),
consensus-state4: ConsensusState,
consensus-state3: consensus-state3(T),
Id: Id,
l_member: (x ∈ l),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
guard: {T},
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
pi1: fst(t),
uimplies: b supposing a,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
bfalse: ff,
true: True,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
cand: A c∧ B,
sq_stable: SqStable(P),
int_seg: {i..j-},
lelt: i ≤ j < k,
sq_type: SQType(T)
Latex:
\mforall{}[V:Type]
((\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
(two-intersection(A;W)
{}\mRightarrow{} (\mexists{}f:ConsensusState {}\mrightarrow{} (consensus-state3(V) List). cs-ref-map-constraints(V;A;W;f)))))
Date html generated:
2016_05_16-PM-00_07_14
Last ObjectModification:
2016_01_17-PM-03_56_05
Theory : event-ordering
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