Nuprl Lemma : pv11_p1_add_if_new_iff2
∀A:Type. ∀p,x:A. ∀L:A List. ∀test:A ⟶ A ⟶ 𝔹.
((p ∈ pv11_p1_add_if_new() test x L) ⇐⇒ (p ∈ L) ∨ if (∃z∈L.test x z)_b then False else p = x ∈ A fi )
Proof
Definitions occuring in Statement :
pv11_p1_add_if_new: pv11_p1_add_if_new(),
bl-exists: (∃x∈L.P[x])_b,
l_member: (x ∈ l),
list: T List,
ifthenelse: if b then t else f fi ,
bool: 𝔹,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
false: False,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
pv11_p1_add_if_new: pv11_p1_add_if_new(),
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,
not: ¬A,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
false: False,
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}A:Type. \mforall{}p,x:A. \mforall{}L:A List. \mforall{}test:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}.
((p \mmember{} pv11\_p1\_add\_if\_new() test x L) \mLeftarrow{}{}\mRightarrow{} (p \mmember{} L) \mvee{} if (\mexists{}z\mmember{}L.test x z)\_b then False else p = x fi )
Date html generated:
2016_05_17-PM-03_16_28
Last ObjectModification:
2015_12_29-PM-11_20_54
Theory : paxos!synod
Home
Index