Nuprl Lemma : pv11_p1_max_bnum_comm
∀[ldrs_uid:Id ⟶ ℤ]. ∀[b1,b2:pv11_p1_Ballot_Num()].
(pv11_p1_max_bnum(ldrs_uid) b1 b2) = (pv11_p1_max_bnum(ldrs_uid) b2 b1) ∈ pv11_p1_Ballot_Num()
supposing Inj(Id;ℤ;ldrs_uid)
Proof
Definitions occuring in Statement :
pv11_p1_max_bnum: pv11_p1_max_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_leq_bnum': pv11_p1_leq_bnum'(ldrs_uid),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: ℙ,
and: P ∧ Q,
top: Top,
true: True,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
squash: ↓T,
guard: {T},
not: ¬A,
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
inject: Inj(A;B;f),
decidable: Dec(P),
le: A ≤ B,
cand: A c∧ B,
less_than: a < b
Latex:
\mforall{}[ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}]. \mforall{}[b1,b2:pv11\_p1\_Ballot\_Num()].
(pv11\_p1\_max\_bnum(ldrs$_{uid}$) b1 b2) = (pv11\_p1\_max\_bnum(ldrs$_{\000Cuid}$) b2 b1) supposing Inj(Id;\mBbbZ{};ldrs$_{uid}$)
Date html generated:
2016_05_17-PM-03_16_17
Last ObjectModification:
2016_01_18-AM-11_18_34
Theory : paxos!synod
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