Nuprl Lemma : pv11_p1_leq_bnum_max
∀ldrs_uid:Id ⟶ ℤ. ∀b,b':pv11_p1_Ballot_Num(). (↑(pv11_p1_leq_bnum(ldrs_uid) b (pv11_p1_max_bnum(ldrs_uid) b' b)))
Proof
Definitions occuring in Statement :
pv11_p1_max_bnum: pv11_p1_max_bnum(ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
assert: ↑b,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
pv11_p1_max_bnum: pv11_p1_max_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
all: ∀x:A. B[x],
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
pv11_p1_leq_bnum': pv11_p1_leq_bnum'(ldrs_uid),
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
guard: {T},
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
true: True
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b,b':pv11\_p1\_Ballot\_Num().
(\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b (pv11\_p1\_max\_bnum(ldrs$_{uid\mbackslash{}f\000Cf7d$) b' b)))
Date html generated:
2016_05_17-PM-03_15_39
Last ObjectModification:
2016_01_18-AM-11_18_48
Theory : paxos!synod
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