Nuprl Lemma : archive-condition-innings
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ⟶ V]. ∀[L1,L2:consensus-rcv(V;A) List]. ∀[n1,n2:ℤ]. ∀[v1,v2:V].
(n1 < n2) supposing (archive-condition(V;A;t;f;n2;v2;L2) and L1 < L2 and archive-condition(V;A;t;f;n1;v1;L1))
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
proper-iseg: L1 < L2,
list: T List,
nat_plus: ℕ+,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
archive-condition: archive-condition(V;A;t;f;n;v;L),
exists: ∃x:A. B[x],
and: P ∧ Q,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
false: False,
cons: [a / b],
top: Top,
bfalse: ff,
decidable: Dec(P),
nat_plus: ℕ+,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
cand: A c∧ B,
cs-rcv-vote: Vote[a;i;v],
rcvd-inning-gt: i <z inning(r),
rcvd-vote: rcvd-vote(x),
outr: outr(x),
spreadn: spread3,
rcv-vote?: rcv-vote?(x),
band: p ∧b q,
uiff: uiff(P;Q),
le: A ≤ B,
sq_type: SQType(T),
votes-from-inning: votes-from-inning(i;L),
consensus-rcv: consensus-rcv(V;A),
rcvd-inning-eq: inning(r) =z i,
values-for-distinct: values-for-distinct(eq;L),
pi1: fst(t)
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[L1,L2:consensus-rcv(V;A) List]. \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
(n1 < n2) supposing
(archive-condition(V;A;t;f;n2;v2;L2) and
L1 < L2 and
archive-condition(V;A;t;f;n1;v1;L1))
Date html generated:
2016_05_16-PM-00_40_00
Last ObjectModification:
2016_01_17-PM-08_03_07
Theory : event-ordering
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