{ 
[A:Type]. [B:A 
Type]. [f,g:a:A fp-> B[a]]. [eq:EqDecider(A)].
(f 
g 
a:A fp-> B[a]) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s],
member: t T,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
so_apply: x[s],
member: t T,
fpf-join: f g,
top: Top,
all: x:A. B[x],
subtype: S 
T,
so_lambda: 
x.t[x],
prop: 
,
fpf-cap: f(x)?z,
ifthenelse: if b then t else f fi ,
implies: P 
Q,
btrue: tt,
bfalse: ff,
fpf-dom: x dom(f),
bool: 
,
unit: Unit,
iff: P 
Q,
and: P 
Q,
uimplies: b supposing a,
or: P 
Q,
not: 
A,
false: False,
rev_implies: P Q,
it: 
Lemmas :
append_wf,
pi1_wf_top,
l_member_wf,
filter_wf,
bnot_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
deq_wf,
bool_wf,
assert_wf,
not_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-ap_wf,
member_append,
deq-member_wf,
not_functionality_wrt_iff,
assert-deq-member,
member_filter
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. (f \moplus{} g \mmember{} a:A fp-> B[a])
Date html generated:
2011_08_10-AM-07_58_50
Last ObjectModification:
2011_06_18-AM-08_18_38
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