Nuprl Lemma : pv11_p1_leq_bnum_linorder
∀ldrs_uid:Id ⟶ ℤ. (Inj(Id;ℤ;ldrs_uid) ⇒ Linorder(pv11_p1_Ballot_Num();b1,b2.↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)))
Proof
Definitions occuring in Statement :
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
linorder: Linorder(T;x,y.R[x; y]),
inject: Inj(A;B;f),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
linorder: Linorder(T;x,y.R[x; y]),
and: P ∧ Q,
order: Order(T;x,y.R[x; y]),
refl: Refl(T;x,y.E[x; y]),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
pv11_p1_leq_bnum': pv11_p1_leq_bnum'(ldrs_uid),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cand: A c∧ B,
trans: Trans(T;x,y.E[x; y]),
bfalse: ff,
anti_sym: AntiSym(T;x,y.R[x; y]),
unit: Unit,
connex: Connex(T;x,y.R[x; y]),
inject: Inj(A;B;f),
le: A ≤ B,
bor: p ∨bq,
bool: 𝔹,
it: ⋅,
sq_type: SQType(T),
bnot: ¬bb,
band: p ∧b q,
nequal: a ≠ b ∈ T
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} Linorder(pv11\_p1\_Ballot\_Num();b1,b2.\muparrow{}(pv11\_p1\_leq\_b\000Cnum(ldrs$_{uid}$) b1 b2)))
Date html generated:
2016_05_17-PM-03_13_32
Last ObjectModification:
2016_01_18-AM-11_20_18
Theory : paxos!synod
Home
Index