Nuprl Lemma : sv-class-iff
∀[Info:Type]. ∀[A:es:EO+(Info) ⟶ E ⟶ Type]. ∀[X:EClass(A[es;e])].
(Singlevalued(X) ⇐⇒ ∀es:EO+(Info). ∀e:E. ((X es e) = if (#(X es e) =z 1) then X es e else {} fi ∈ bag(A[es;e])))
Proof
Definitions occuring in Statement :
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s],
sv-class: Singlevalued(X),
le: A ≤ B,
not: ¬A,
nat: ℕ,
nequal: a ≠ b ∈ T ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
true: True,
less_than': less_than'(a;b),
squash: ↓T
Latex:
\mforall{}[Info:Type]. \mforall{}[A:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} Type]. \mforall{}[X:EClass(A[es;e])].
(Singlevalued(X)
\mLeftarrow{}{}\mRightarrow{} \mforall{}es:EO+(Info). \mforall{}e:E. ((X es e) = if (\#(X es e) =\msubz{} 1) then X es e else \{\} fi ))
Date html generated:
2016_05_16-PM-02_20_10
Last ObjectModification:
2016_01_17-PM-07_37_15
Theory : event-ordering
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