Nuprl Lemma : fpf-normalize-ap
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [g:x:A fp-> B[x]]. [x:A].
fpf-normalize(eq;g)(x) = g(x) supposing 
x 
dom(g)
Proof not projected
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
so_apply: x[s],
fpf-dom: x dom(f),
fpf-ap: f(x),
fpf-normalize: fpf-normalize(eq;g),
pi2: snd(t),
reduce: reduce(f;k;as),
fpf-join: f 
g,
fpf-single: x : v,
fpf-empty: 
,
pi1: fst(t),
append: as @ bs,
fpf-cap: f(x)?z,
deq-member: deq-member(eq;x;L),
member: t T,
so_lambda: 
x.t[x],
implies: P 
Q,
all: x:A. B[x],
top: Top,
prop: 
,
bfalse: ff,
ifthenelse: if b then t else f fi ,
assert: b,
bor: p 
q,
eqof: eqof(d),
btrue: tt,
guard: {T},
subtype: S 
T,
and: P 
Q,
true: True,
squash: 
T,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
false: False,
deq: EqDecider(T),
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
not: 
A,
iff: P 
Q,
rev_implies: P Q,
or: P Q,
it: 
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf_wf,
deq_wf,
top_wf,
list-subtype,
l_member_wf,
equal_wf,
false_wf,
eqof_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert-deq,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
deq-member_wf,
and_wf,
member_wf,
assert-deq-member,
cons_member
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]]. \mforall{}[x:A].
fpf-normalize(eq;g)(x) = g(x) supposing \muparrow{}x \mmember{} dom(g)
Date html generated:
2012_01_23-AM-11_56_24
Last ObjectModification:
2011_12_10-PM-12_57_40
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