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]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ
Latex:
\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:
2016_05_16-PM-02_39_09
Last ObjectModification:
2015_12_29-AM-11_32_17
Theory : event-ordering
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