{ 
[A:Type]. [B:A 
Type]. [f:a:A fp-> B[a]]. [eq:EqDecider(A)]. [x:A].
[z:B[x]].
(f(x)?z 
B[x]) }
{ Proof }
Definitions occuring in Statement :
fpf-cap: f(x)?z,
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],
so_apply: x[s],
member: t T,
fpf-cap: f(x)?z,
so_lambda: 
x.t[x],
prop: 
,
ifthenelse: if b then t else f fi ,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
bfalse: ff,
uimplies: b supposing a,
bool: 
,
unit: Unit,
iff: P 
Q,
and: P 
Q,
it: 
Lemmas :
deq_wf,
fpf_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
bool_wf,
assert_wf,
fpf-ap_wf,
not_wf,
bnot_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x:A]. \mforall{}[z:B[x]].
(f(x)?z \mmember{} B[x])
Date html generated:
2011_08_10-AM-07_55_39
Last ObjectModification:
2011_06_18-AM-08_16_48
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