Nuprl Lemma : fpf-as-apply-alist
[A,B:Type]. [f:a:A fp-> B]. [eq:EqDecider(A)].
(f = <fpf-domain(f), 
x.outl(apply-alist(eq;map(x.<x, f(x)>;fpf-domain(f));x))>)
Proof not projected
Definitions occuring in Statement :
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
map: map(f;as),
outl: outl(x),
uall: [x:A]. B[x],
lambda: x.A[x],
pair: <a, b>,
universe: Type,
equal: s = t,
apply-alist: apply-alist(eq;L;x),
deq: EqDecider(T)
Definitions :
so_lambda: 
x.t[x],
pi2: snd(t),
pi1: fst(t),
member: t 
T,
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
top: Top,
prop: 
,
suptype: suptype(S; T),
subtype: S 
T,
all: x:A. B[x],
lelt: i 
j < k,
outl: outl(x),
and: P 
Q,
int_seg: {i..j
},
false: False,
implies: P 
Q,
le: A B,
not: 
A,
so_apply: x[s],
nat: 
,
exists: 
x:A. B[x],
uimplies: b supposing a
Lemmas :
fpf_wf,
deq_wf,
list-subtype,
l_member_wf,
map_wf,
top_wf,
apply-alist-cases,
alist-domain-first,
less_than_wf,
nat_wf,
equal_wf,
and_wf,
length_wf_nat,
length-map,
length_wf,
lelt_wf,
pi2_wf,
pi1_wf_top,
select_wf,
map_select
\mforall{}[A,B:Type]. \mforall{}[f:a:A fp-> B]. \mforall{}[eq:EqDecider(A)].
(f = <fpf-domain(f), \mlambda{}x.outl(apply-alist(eq;map(\mlambda{}x.<x, f(x)>fpf-domain(f));x))>)
Date html generated:
2012_01_23-AM-11_53_23
Last ObjectModification:
2011_12_10-AM-11_52_54
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