{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [P:A 
].
[f:x:A fp-> B[x]]. [x:{a:A| 
(P a)} ]. [v:B[x]].
{(x 
dom(f)) 
(v = f(x))} supposing (<x, v> fpf-vals(eq;P;f)) }
{ Proof }
Definitions occuring in Statement :
fpf-vals: fpf-vals(eq;P;f),
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
so_apply: x[s],
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
universe: Type,
equal: s = t,
l_member: (x l),
deq: EqDecider(T)
Definitions :
bnot: 
b,
bfalse: ff,
btrue: tt,
l_all: (xL.P[x]),
filter: filter(P;l),
natural_number: $n,
select: l[i],
length: ||as||,
real: 
,
grp_car: |g|,
int: 
,
intensional-universe: IType,
nil: [],
sq_type: SQType(T),
fpf-sub: f 
g,
nat: 
,
tag-by: zT,
or: P 
Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
union: left + right,
fpf-domain: fpf-domain(f),
cand: A c B,
fpf-cap: f(x)?z,
list: type List,
top: Top,
subtype: S T,
suptype: suptype(S; T),
rev_implies: P 
Q,
iff: P 
Q,
fpf-dom: x dom(f),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: A,
less_than: a < b,
uiff: uiff(P;Q),
exists: 
x:A. B[x],
subtype_rel: A r B,
axiom: Ax,
fpf-ap: f(x),
implies: P Q,
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 ,
and: P Q,
guard: {T},
fpf-vals: fpf-vals(eq;P;f),
pair: <a, b>,
l_member: (x l),
uimplies: b supposing a,
prop: 
,
product: x:A B[x],
lambda: 
x.A[x],
apply: f a,
so_apply: x[s],
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
bool: ,
set: {x:A| B[x]} ,
assert: b,
all: x:A. B[x],
isect: x:A. B[x],
uall: [x:A]. B[x],
function: x:A B[x],
universe: Type,
member: t T,
deq: EqDecider(T),
equal: s = t,
tactic: Error :tactic
Lemmas :
l_member_subtype,
member-fpf-vals,
bool_wf,
member_wf,
assert_wf,
iff_wf,
fpf-dom_wf,
guard_wf,
assert_witness,
fpf-vals_wf,
l_member_wf,
fpf_wf,
deq_wf,
subtype_rel_wf,
top_wf,
fpf-trivial-subtype-top,
strong-subtype-deq-subtype,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
fpf-type,
subtype-fpf3,
subtype_rel_product,
subtype_rel_list,
subtype_base_sq,
false_wf,
ifthenelse_wf,
true_wf,
list-subtype,
subtype_rel_dep_function,
intensional-universe_wf,
nat_wf,
length_wf1,
select_wf,
list-set-type2,
l_all_wf,
length_wf_nat
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[x:\{a:A| \muparrow{}(P a)\} ].
\mforall{}[v:B[x]].
\{(\muparrow{}x \mmember{} dom(f)) \mwedge{} (v = f(x))\} supposing (<x, v> \mmember{} fpf-vals(eq;P;f))
Date html generated:
2011_08_10-AM-08_03_35
Last ObjectModification:
2011_06_18-AM-08_22_12
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