Nuprl Lemma : member-fpf-vals
[A:Type]
eq:EqDecider(A)
[B:A 
Type]
P:A 
. f:x:A fp-> B[x]. x:A. v:B[x].
((<x, v> 
fpf-vals(eq;P;f)) 
{((
x dom(f)) 
((P x))) (v = f(x))})
Proof not projected
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: ,
uall: [x:A]. B[x],
guard: {T},
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
and: P Q,
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 :
uall: [x:A]. B[x],
all: x:A. B[x],
so_apply: x[s],
fpf-vals: fpf-vals(eq;P;f),
fpf-dom: x dom(f),
fpf-ap: f(x),
let: let,
pi1: fst(t),
pi2: snd(t),
member: t T,
implies: P Q,
so_lambda: 
x.t[x],
zip: zip(as;bs),
filter: filter(P;l),
assert: b,
deq-member: deq-member(eq;x;L),
reduce: reduce(f;k;as),
ifthenelse: if b then t else f fi ,
bfalse: ff,
ycomb: Y,
prop: 
,
or: P 
Q,
guard: {T},
btrue: tt,
map: map(f;as),
subtype: S 
T,
eqof: eqof(d),
rev_implies: P Q,
cand: A c B,
and: P Q,
iff: P Q,
true: True,
squash: 
T,
top: Top,
bor: p 
q,
bool: ,
fpf: a:A fp-> B[a],
sq_type: SQType(T),
uimplies: b supposing a,
unit: Unit,
not: 
A,
false: False,
uiff: uiff(P;Q),
deq: EqDecider(T),
it: 
Lemmas :
subtype_base_sq,
bool_wf,
bool_subtype_base,
deq-member_wf,
remove-repeats_wf,
iff_transitivity,
equal_wf,
assert_wf,
l_member_wf,
iff_weakening_uiff,
eqtt_to_assert,
assert-deq-member,
member-remove-repeats,
btrue_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_iff,
bfalse_wf,
fpf_wf,
deq_wf,
cons_member,
subtype_rel_list,
list-subtype,
uiff_transitivity,
guard_wf,
assert_witness,
bor_wf,
pair_wf,
and_wf,
pi1_wf_top,
pi2_wf,
assert-deq,
or_functionality_wrt_iff,
assert_of_bor,
or_wf,
not_assert_elim,
assert_elim,
not_functionality_wrt_uiff,
btrue_neq_bfalse
\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. \mforall{}v:B[x].
((<x, v> \mmember{} fpf-vals(eq;P;f)) \mLeftarrow{}{}\mRightarrow{} \{((\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}(P x))) \mwedge{} (v = f(x))\})
Date html generated:
2012_01_23-AM-11_55_07
Last ObjectModification:
2011_12_10-PM-12_03_40
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