Nuprl Lemma : not-pv11_p1_leq_bnum
∀ldrs_uid:Id ⟶ ℤ. ∀b,b':pv11_p1_Ballot_Num().
(Inj(Id;ℤ;ldrs_uid) ⇒ (¬↑(pv11_p1_leq_bnum(ldrs_uid) b b')) ⇒ (↑(b' < b)))
Proof
Definitions occuring in Statement :
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
inject: Inj(A;B;f),
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
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,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
linorder: Linorder(T;x,y.R[x; y]),
and: P ∧ Q,
connex: Connex(T;x,y.R[x; y]),
or: P ∨ Q,
not: ¬A,
false: False,
uimplies: b supposing a,
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
so_lambda: λ2x.t[x],
so_apply: x[s],
Id: Id,
sq_type: SQType(T),
guard: {T}
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b,b':pv11\_p1\_Ballot\_Num().
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} (\mneg{}\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}\mbackslash{}ff\000C24) b b')) {}\mRightarrow{} (\muparrow{}(b' < b)))
Date html generated:
2016_05_17-PM-03_15_22
Last ObjectModification:
2015_12_29-PM-11_21_38
Theory : paxos!synod
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