Nuprl Lemma : fpf-normalize-dom
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [g:x:A fp-> B[x]]. [x:A]. (x 
dom(fpf-normalize(eq;g)) ~ x dom(g))
Proof not projected
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
sqequal: s ~ t,
deq: EqDecider(T)
Definitions :
so_apply: x[s],
fpf-dom: x dom(f),
fpf-normalize: fpf-normalize(eq;g),
deq-member: deq-member(eq;x;L),
pi1: fst(t),
reduce: reduce(f;k;as),
fpf-join: f 
g,
fpf-single: x : v,
pi2: snd(t),
fpf-empty: 
,
append: as @ bs,
member: t T,
top: Top,
all: x:A. B[x],
implies: P 
Q,
so_lambda: 
x.t[x],
bor: p 
q,
eqof: eqof(d),
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
and: P 
Q,
bnot: 
b,
assert: 
b,
false: False,
true: True,
not: A,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
deq: EqDecider(T),
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
iff: P 
Q,
sq_type: SQType(T),
rev_implies: P Q,
it: 
,
prop: 
Lemmas :
top_wf,
fpf_wf,
deq_wf,
eqof_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
eqtt_to_assert,
assert-deq,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
reduce_wf,
filter_wf,
bor_wf,
bfalse_wf,
member_filter,
and_wf,
not_functionality_wrt_iff,
btrue_wf,
bnot_thru_bor,
filter_functionality,
band_wf,
assert-deq-member,
iff_weakening_uiff,
l_member_wf,
iff_transitivity,
deq-member_wf,
bool_subtype_base,
subtype_base_sq,
and_functionality_wrt_uiff2,
assert_of_band,
true_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]]. \mforall{}[x:A].
(x \mmember{} dom(fpf-normalize(eq;g)) \msim{} x \mmember{} dom(g))
Date html generated:
2012_01_23-AM-11_56_16
Last ObjectModification:
2011_12_10-PM-12_59_32
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