Nuprl Lemma : first-class-val
∀[Info,A:Type]. ∀[L:EClass(A) List]. ∀[es:EO+(Info)]. ∀[e:E].
(↑e ∈b L[index-of-first X in L.e ∈b X - 1]) ∧ (first-class(L)(e) = L[index-of-first X in L.e ∈b X - 1](e) ∈ A)
supposing ↑e ∈b first-class(L)
Proof
Definitions occuring in Statement :
first-class: first-class(L),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
select: L[n],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
first_index: index-of-first x in L.P[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
first-class: first-class(L),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
ge: i ≥ j ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
sq_type: SQType(T),
bnot: ¬bb,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
select: L[n],
cons: [a / b],
cand: A c∧ B,
true: True
Latex:
\mforall{}[Info,A:Type]. \mforall{}[L:EClass(A) List]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(\muparrow{}e \mmember{}\msubb{} L[index-of-first X in L.e \mmember{}\msubb{} X - 1])
\mwedge{} (first-class(L)(e) = L[index-of-first X in L.e \mmember{}\msubb{} X - 1](e))
supposing \muparrow{}e \mmember{}\msubb{} first-class(L)
Date html generated:
2016_05_16-PM-02_39_29
Last ObjectModification:
2016_01_17-PM-07_43_55
Theory : event-ordering
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