Nuprl Lemma : pv11_p1_lt_bnum_implies_not2
∀ldrs_uid:Id ⟶ ℤ. ∀b1,b2:pv11_p1_Ballot_Num(). ((↑(b1 < b2)) ⇒ (↑(b2 < b1)) ⇒ False)
Proof
Definitions occuring in Statement :
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
pv11_p1_lt_bnum': pv11_p1_lt_bnum'(ldrs_uid),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
isl: isl(x)
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num(). ((\muparrow{}(b1 < b2)) {}\mRightarrow{} (\muparrow{}(b2 < \000Cb1)) {}\mRightarrow{} False)
Date html generated:
2016_05_17-PM-03_13_03
Last ObjectModification:
2016_01_18-AM-11_19_17
Theory : paxos!synod
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