Nuprl Lemma : pv11_p1_max_bnum_if_leq
∀ldrs_uid:Id ⟶ ℤ. ∀b1,b2:pv11_p1_Ballot_Num().
((↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)) ⇒ ((pv11_p1_max_bnum(ldrs_uid) b1 b2) = b2 ∈ pv11_p1_Ballot_Num()))
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],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
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],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num().
((\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b1 b2)) {}\mRightarrow{} ((pv11\_p1\_max\_bnum(ldrs$\mbackslash{}ff5\000Cf{uid}$) b1 b2) = b2))
Date html generated:
2016_05_17-PM-03_15_59
Last ObjectModification:
2015_12_29-PM-11_21_04
Theory : paxos!synod
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