Nuprl Lemma : pv11_p1_pmax_desc_implies
∀Cmd:ValueAllType. ∀ldrs_uid:Id ⟶ ℤ. ∀pvals:(pv11_p1_Ballot_Num() × ℤ × Cmd) List. ∀b:pv11_p1_Ballot_Num(). ∀s:ℤ.
∀c:Cmd.
((<b, s, c> ∈ pvals) ⇒ (∃c':Cmd. (<s, c'> ∈ pv11_p1_pmax(Cmd;ldrs_uid) pvals)))
Proof
Definitions occuring in Statement :
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
spreadn: spread3,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
let: let,
band: p ∧b q,
cand: A c∧ B,
pi2: snd(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_member: (x ∈ l),
bl-exists: (∃x∈L.P[x])_b,
reduce: reduce(f;k;as),
list_ind: list_ind,
nil: [],
true: True,
top: Top,
bor: p ∨bq,
not: ¬A,
rev_uimplies: rev_uimplies(P;Q),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b,
squash: ↓T,
nequal: a ≠ b ∈ T ,
pi1: fst(t),
subtype_rel: A ⊆r B
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}pvals:(pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd\000C) List.
\mforall{}b:pv11\_p1\_Ballot\_Num(). \mforall{}s:\mBbbZ{}. \mforall{}c:Cmd.
((<b, s, c> \mmember{} pvals) {}\mRightarrow{} (\mexists{}c':Cmd. (<s, c'> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) pv\000Cals)))
Date html generated:
2016_05_17-PM-03_17_09
Last ObjectModification:
2016_01_18-AM-11_19_13
Theory : paxos!synod
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