{ 
[A:Type]. [P:A 
]. [x:A].
[f:x:A fp-> Top]. [eq:EqDecider(A)]. [z:Top].
(fpf-restrict(f;P)(x)?z ~ f(x)?z)
supposing 
(P x) }
{ Proof }
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
assert: b,
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
apply: f a,
function: x:A B[x],
universe: Type,
sqequal: s ~ t,
deq: EqDecider(T)
Definitions :
fpf-cap: f(x)?z,
member: t 
T,
so_lambda: 
x.t[x],
prop: 
,
and: P 
Q,
iff: P 
Q,
implies: P Q,
rev_implies: P Q,
uall: [x:A]. B[x],
so_apply: x[s],
sq_type: SQType(T),
uimplies: b supposing a,
all: x:A. B[x],
guard: {T}
Lemmas :
top_wf,
deq_wf,
fpf_wf,
assert_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
fpf-dom_wf,
fpf-restrict_wf2,
l_member_wf,
fpf-domain_wf,
iff_functionality_wrt_iff,
member-fpf-domain,
filter_wf,
member_filter
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A].
\mforall{}[f:x:A fp-> Top]. \mforall{}[eq:EqDecider(A)]. \mforall{}[z:Top]. (fpf-restrict(f;P)(x)?z \msim{} f(x)?z)
supposing \muparrow{}(P x)
Date html generated:
2011_08_10-AM-08_09_51
Last ObjectModification:
2011_06_18-AM-08_26_03
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