{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [f:x:A fp-> B[x]].
[P:A 
]. [x:A].
uiff(
x 
dom(fpf-restrict(f;P));{(x dom(f)) 
((P x))}) }
{ Proof }
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
bool: ,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
guard: {T},
so_apply: x[s],
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
cand: A c B,
fpf-join: f 
g,
eqof: eqof(d),
subtype: S 
T,
union: left + right,
or: P 
Q,
eq_knd: a = b,
l_member: (x l),
fpf-single: x : v,
rev_implies: P 
Q,
fpf-restrict: fpf-restrict(f;P),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
set: {x:A| B[x]} ,
list: type List,
subtype_rel: A r B,
top: Top,
fpf-dom: x dom(f),
iff: P 
Q,
implies: P Q,
prop: 
,
pair: <a, b>,
void: Void,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: b,
guard: {T},
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
bool: ,
lambda: 
x.A[x],
all: x:A. B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
so_lambda: 
x.t[x],
so_apply: x[s],
apply: f a,
member: t T,
equal: s = t,
universe: Type,
function: x:A B[x],
deq: EqDecider(T),
Repeat: Error :Repeat,
MaAuto: Error :MaAuto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
fpf-domain: fpf-domain(f),
filter: filter(P;l),
domain_fpf_restrict: domain_fpf_restrict{domain_fpf_restrict_compseq_tag_def:o}(P; f),
Auto: Error :Auto,
CollapseTHENM: Error :CollapseTHENM,
Unfold: Error :Unfold,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
fpf-domain_wf,
member_filter,
iff_functionality_wrt_iff,
member-fpf-domain,
and_functionality_wrt_iff,
filter_wf,
fpf-dom_wf,
assert_witness,
guard_wf,
assert_wf,
fpf-trivial-subtype-top,
subtype_rel_wf,
fpf_wf,
top_wf,
member_wf,
fpf-restrict_wf2,
uiff_wf,
bool_wf,
deq_wf,
false_wf,
ifthenelse_wf,
true_wf,
rev_implies_wf,
iff_wf,
uiff_inversion,
l_member_wf,
member-fpf-dom
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A].
uiff(\muparrow{}x \mmember{} dom(fpf-restrict(f;P));\{(\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}(P x))\})
Date html generated:
2011_08_10-AM-08_09_45
Last ObjectModification:
2011_06_18-AM-08_25_57
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