{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [P:A 
].
[f:x:A fp-> B[x]]. [a:A].
(fpf-vals(eq;P;f) = [<a, f(a)>]) supposing
((b:A. (
(P b) 
b = a)) and
(a 
dom(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],
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
apply: f a,
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
cons: [car / cdr],
nil: [],
list: type List,
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
so_apply: x[s],
all: x:A. B[x],
fpf-vals: fpf-vals(eq;P;f),
let: let,
pi1: fst(t),
pi2: snd(t),
member: t T,
prop: 
,
so_lambda: 
x.t[x],
and: P 
Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
implies: P Q,
bfalse: ff,
filter: filter(P;l),
reduce: reduce(f;k;as),
or: P 
Q,
guard: {T},
hd: hd(l),
top: Top,
subtype: S 
T,
squash: 
T,
ge: i 
j ,
true: True,
false: False,
tl: tl(l),
zip: zip(as;bs),
map: map(f;as),
ycomb: Y,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
iff: P Q,
rev_implies: P Q,
fpf-dom: x dom(f),
bool: ,
unit: Unit,
uimplies: b supposing a,
not: 
A,
sq_type: SQType(T),
it: 
Lemmas :
iff_wf,
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf_wf,
bool_wf,
deq_wf,
remove-repeats_property,
assert-deq-member,
deq-member_wf,
l_member_wf,
bnot_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_iff,
nil_member,
false_wf,
no_repeats_wf,
cons_member,
no_repeats_cons,
uiff_transitivity,
remove-repeats_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
length_wf1,
non_neg_length,
length_wf_nat,
top_wf,
length_cons,
hd_wf,
squash_wf,
ge_wf,
tl_wf
\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{}[a:A].
(fpf-vals(eq;P;f) = [<a, f(a)>]) supposing ((\mforall{}b:A. (\muparrow{}(P b) \mLeftarrow{}{}\mRightarrow{} b = a)) and (\muparrow{}a \mmember{} dom(f)))
Date html generated:
2011_08_10-AM-08_03_48
Last ObjectModification:
2011_06_18-AM-08_22_16
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