Nuprl Lemma : is-first-class2
∀[Info,A:Type]. ∀[L:EClass(A) List]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(↑e ∈b first-class(L);0 < index-of-first X in L.e ∈b X)
Proof
Definitions occuring in Statement :
first-class: first-class(L),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
list: T List,
assert: ↑b,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
first_index: index-of-first x in L.P[x]
Lemmas :
is-first-class,
member-less_than,
first_index_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
assert_wf,
first-class_wf,
subtype_rel_list,
assert_witness,
less_than_wf,
nat_wf,
l_exists_wf,
l_member_wf,
first_index-positive,
uiff_wf
\mforall{}[Info,A:Type]. \mforall{}[L:EClass(A) List]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} first-class(L);0 < index-of-first X in L.e \mmember{}\msubb{} X)
Date html generated:
2015_07_17-PM-00_50_45
Last ObjectModification:
2015_01_27-PM-11_05_58
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