Nuprl Lemma : is-first-class
∀[Info,A:Type]. ∀L:EClass(A) List. ∀es:EO+(Info). ∀e:E. (↑e ∈b first-class(L) ⇐⇒ (∃X∈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,
l_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
top: Top,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
first-class: first-class(L),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
false: False,
rev_implies: P ⇐ Q,
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
select: L[n],
nil: [],
it: ⋅,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[Info,A:Type]. \mforall{}L:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-class(L) \mLeftarrow{}{}\mRightarrow{} (\mexists{}X\mmember{}L. \muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_16-PM-02_38_55
Last ObjectModification:
2016_01_17-PM-07_32_27
Theory : event-ordering
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