Nuprl Lemma : member-eclass-iff-size1
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ 1 ≤ #(X es e))
Proof
Definitions occuring in Statement :
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
le: A ≤ B,
iff: P ⇐⇒ Q,
apply: f a,
natural_number: $n,
universe: Type,
bag-size: #(bs)
Lemmas :
decidable__le,
bag-size_wf,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
less_than_wf,
decidable__lt,
le-add-cancel,
le_wf,
member-eclass-iff-size,
assert_wf,
member-eclass_wf,
iff_wf,
nat_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} 1 \mleq{} \#(X es e))
Date html generated:
2015_07_17-PM-00_16_49
Last ObjectModification:
2015_01_28-AM-00_03_03
Home
Index