Nuprl Lemma : pv11_p1_leq_bnum_or
∀ldrs_uid:Id ⟶ ℤ. ∀b1,b2:pv11_p1_Ballot_Num().
((↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)) ∨ (↑(pv11_p1_leq_bnum(ldrs_uid) b2 b1)))
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,
assert: ↑b,
all: ∀x:A. B[x],
or: P ∨ Q,
apply: f a,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
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,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
assert: ↑b,
or: P ∨ Q,
true: True,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
not: ¬A,
band: p ∧b q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
nequal: a ≠ b ∈ T
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num().
((\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b1 b2)) \mvee{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$\mbackslash{}ff5\000Cf{uid}$) b2 b1)))
Date html generated:
2016_05_17-PM-03_15_49
Last ObjectModification:
2016_01_18-AM-11_18_44
Theory : paxos!synod
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