{ 
[A,C:Type]. [B:A 
Type]. [x:a:A fp-> B[a]]. [f:a:{a:A|
(a 
fpf-domain(x))}
B[a]
C].
(fpf-map(a,v.f[a;v];x) C List) }
{ Proof }
Definitions occuring in Statement :
fpf-map: fpf-map(a,v.f[a; v];x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
list: type List,
universe: Type,
l_member: (x l)
Definitions :
axiom: Ax,
so_apply: x[s1;s2],
fpf-map: fpf-map(a,v.f[a; v];x),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
list: type List,
product: x:A 
B[x],
subtype_rel: A 
r B,
top: Top,
fpf-domain: fpf-domain(f),
prop: 
,
l_member: (x l),
set: {x:A| B[x]} ,
lambda: 
x.A[x],
so_apply: x[s],
apply: f a,
universe: Type,
fpf: a:A fp-> B[a],
all: x:A. B[x],
function: x:A B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
so_lambda: 
x.t[x],
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
pi2: snd(t),
pi1: fst(t),
Complete: Error :Complete,
Try: Error :Try,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
pi1_wf_top,
map-wf2,
l_member_wf,
fpf-domain_wf,
member_wf,
top_wf,
fpf_wf,
subtype_rel_wf,
fpf-trivial-subtype-top
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:a:A fp-> B[a]]. \mforall{}[f:a:\{a:A| (a \mmember{} fpf-domain(x))\} {}\mrightarrow{} B[a] {}\mrightarrow{} C].
(fpf-map(a,v.f[a;v];x) \mmember{} C List)
Date html generated:
2011_08_10-AM-08_04_04
Last ObjectModification:
2011_06_18-AM-08_22_24
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