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)
Lemmas :
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
sv-class_wf,
all_wf,
equal_wf,
bag_wf,
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
empty-bag_wf,
less_than_wf,
eclass_wf,
nequal-le-implies,
equal-wf-base-T,
bag-size-zero,
decidable__le,
nat_wf,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-associates,
zero-add,
add-commutes,
minus-zero,
add_functionality_wrt_le,
le-add-cancel2,
le_weakening,
bag_size_empty_lemma,
le_wf,
squash_wf,
true_wf,
iff_weakening_equal
\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:
2015_07_17-PM-00_41_15
Last ObjectModification:
2015_02_04-PM-05_31_58
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