Nuprl Lemma : pv11_p1_lt_bnum_trans1
∀ldrs_uid:Id ⟶ ℤ. ∀b1,b2,b3:pv11_p1_Ballot_Num().
((↑(b1 < b2)) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b2 b3)) ⇒ (↑(b1 < b3)))
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,
assert: ↑b,
all: ∀x:A. B[x],
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,
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
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,
rev_uimplies: rev_uimplies(P;Q),
pv11_p1_leq_bnum': pv11_p1_leq_bnum'(ldrs_uid),
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,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
isl: isl(x),
btrue: tt,
unit: Unit,
true: True
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2,b3:pv11\_p1\_Ballot\_Num().
((\muparrow{}(b1 < b2)) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b2 b3)) {}\mRightarrow{} (\muparrow{}(b1 < b3)))
Date html generated:
2016_05_17-PM-03_12_40
Last ObjectModification:
2016_01_18-AM-11_20_01
Theory : paxos!synod
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