{ 
[A:Type]. [B:A 
Type]. [f:a:A fp-> B[a]]. [eq:EqDecider(A)].
(
f ~ <fst(f), 
a.((snd(f)) a)>) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-empty: ,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
apply: f a,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
universe: Type,
sqequal: s ~ t,
deq: EqDecider(T)
Definitions :
so_apply: x[s],
fpf-join: f g,
fpf-empty: ,
pi1: fst(t),
pi2: snd(t),
append: as @ bs,
bnot: 
b,
fpf-dom: x 
dom(f),
fpf-cap: f(x)?z,
deq-member: deq-member(eq;x;L),
ifthenelse: if b then t else f fi ,
reduce: reduce(f;k;as),
bfalse: ff,
top: Top,
member: t T,
all: x:A. B[x],
subtype: S 
T,
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
uall: [x:A]. B[x]
Lemmas :
filter_tt,
top_wf,
deq_wf,
fpf_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)].
(\motimes{} \moplus{} f \msim{} <fst(f), \mlambda{}a.((snd(f)) a)>)
Date html generated:
2011_08_10-AM-07_59_06
Last ObjectModification:
2011_06_18-AM-08_18_47
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