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
Home
Index