Nuprl Lemma : pv11_p1_add_if_new_iff
∀Cmd:ValueAllType. ∀p,x:ℤ × Cmd. ∀proposals:(ℤ × Cmd) List.
((p ∈ pv11_p1_add_if_new() pv11_p1_same_proposal(Cmd) x proposals)
⇐⇒ (p ∈ proposals) ∨ if (∃z∈proposals.pv11_p1_same_proposal(Cmd) x z)_b then False else p = x ∈ (ℤ × Cmd) fi )
Proof
Definitions occuring in Statement :
pv11_p1_add_if_new: pv11_p1_add_if_new(),
pv11_p1_same_proposal: pv11_p1_same_proposal(Cmd),
bl-exists: (∃x∈L.P[x])_b,
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
false: False,
apply: f a,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
pv11_p1_add_if_new: pv11_p1_add_if_new(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
bfalse: ff,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}p,x:\mBbbZ{} \mtimes{} Cmd. \mforall{}proposals:(\mBbbZ{} \mtimes{} Cmd) List.
((p \mmember{} pv11\_p1\_add\_if\_new() pv11\_p1\_same\_proposal(Cmd) x proposals)
\mLeftarrow{}{}\mRightarrow{} (p \mmember{} proposals)
\mvee{} if (\mexists{}z\mmember{}proposals.pv11\_p1\_same\_proposal(Cmd) x z)\_b then False else p = x fi )
Date html generated:
2016_05_17-PM-03_16_22
Last ObjectModification:
2015_12_29-PM-11_21_06
Theory : paxos!synod
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