Nuprl Lemma : consensus-refinement2
∀[V:Type]. ts-refinement(consensus-ts2(V);consensus-ts3(V);λL.cs-ref-map3(L))
Proof
Definitions occuring in Statement :
cs-ref-map3: cs-ref-map3(L),
consensus-ts3: consensus-ts3(T),
consensus-ts2: consensus-ts2(T),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
ts-refinement: ts-refinement(ts1;ts2;f)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ts-refinement: ts-refinement(ts1;ts2;f),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
infix_ap: x f y,
ts-reachable: ts-reachable(ts),
subtype_rel: A ⊆r B,
consensus-ts3: consensus-ts3(T),
ts-init: ts-init(ts),
cs-ref-map3: cs-ref-map3(L),
consensus-ts2: consensus-ts2(T),
ts-type: ts-type(ts),
pi1: fst(t),
pi2: snd(t),
top: Top,
let: let,
ifthenelse: if b then t else f fi ,
btrue: tt,
uimplies: b supposing a,
null: null(as),
filter: filter(P;l),
reduce: reduce(f;k;as),
list_ind: list_ind,
nil: [],
it: ⋅,
cs-ambivalent: AMBIVALENT,
or: P ∨ Q,
consensus-state2: consensus-state2(T),
exists: ∃x:A. B[x],
ts-rel: ts-rel(ts),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
cs-initial: INITIAL,
cs-commited: COMMITED[v],
isl: isl(x),
consensus-state3: consensus-state3(T),
l_member: (x ∈ l),
nat: ℕ,
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
le: A ≤ B,
squash: ↓T,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
cs-considering: CONSIDERING[v],
cs-is-considering: cs-is-considering(x),
assert: ↑b,
true: True,
ts-final: ts-final(ts),
listp: A List+,
list: T List,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
select: L[n],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_type: SQType(T),
cons: [a / b],
less_than: a < b,
cs-committed-val: cs-committed-val(x),
cs-is-committed: cs-is-committed(x),
bfalse: ff,
outl: outl(x)
Latex:
\mforall{}[V:Type]. ts-refinement(consensus-ts2(V);consensus-ts3(V);\mlambda{}L.cs-ref-map3(L))
Date html generated:
2016_05_16-AM-11_54_16
Last ObjectModification:
2016_01_17-PM-04_01_03
Theory : event-ordering
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