Nuprl Lemma : es-fset-loc-iff
∀es:EO. ∀s:fset(E). ∀i:Id. (i ∈ locs(s) ⇐⇒ ∃e:E. ((loc(e) = i ∈ Id) ∧ e ∈ s))
Proof
Definitions occuring in Statement :
es-fset-loc: i ∈ locs(s),
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
fset-member: a ∈ s,
fset: fset(T),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
es-fset-at-property,
es-fset-at_wf,
list_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
exists_wf,
es-loc_wf,
fset-member_wf,
es-eq_wf,
all_wf,
iff_wf,
l_member_wf,
no_repeats_wf,
sorted-by_wf,
es-le_wf,
Id_wf,
fset_wf,
es-E_wf,
event_ordering_wf,
list-cases,
product_subtype_list,
null_nil_lemma,
cons_member,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
null_cons_lemma,
false_wf
\mforall{}es:EO. \mforall{}s:fset(E). \mforall{}i:Id. (i \mmember{} locs(s) \mLeftarrow{}{}\mRightarrow{} \mexists{}e:E. ((loc(e) = i) \mwedge{} e \mmember{} s))
Date html generated:
2015_07_17-AM-09_01_05
Last ObjectModification:
2015_01_27-PM-00_55_38
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