Nuprl Lemma : fpf-decompose
[A:Type]
eq:EqDecider(A)
[B:A 
Type]
f:a:A fp-> B[a]
g:a:A fp-> B[a]
a:A
b:B[a]
((f 
g 
a : b 
g a : b f)
(a':A. 
(a' = a) supposing 
a' 
dom(g))
(||fpf-domain(g)|| < ||fpf-domain(f)||))
supposing 0 < ||fpf-domain(f)||
Proof not projected
Definitions occuring in Statement :
fpf-single: x : v,
fpf-join: f g,
fpf-sub: f g,
fpf-domain: fpf-domain(f),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
length: ||as||,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
and: P Q,
less_than: a < b,
function: x:A B[x],
natural_number: $n,
universe: Type,
equal: s = t,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
so_apply: x[s],
uimplies: b supposing a,
fpf-domain: fpf-domain(f),
exists: x:A. B[x],
and: P Q,
assert: b,
fpf-dom: x dom(f),
not: A,
member: t T,
prop: 
,
implies: P 
Q,
so_lambda: 
x.t[x],
eqof: eqof(d),
hd: hd(l),
ge: i 
j ,
le: A 
B,
false: False,
pi1: fst(t),
deq-member: deq-member(eq;x;L),
reduce: reduce(f;k;as),
bfalse: ff,
ifthenelse: if b then t else f fi ,
or: P 
Q,
guard: {T},
fpf-compatible: f || g,
pi2: snd(t),
cand: A c B,
fpf-ap: f(x),
fpf-single: x : v,
fpf-sub: f g,
top: Top,
true: True,
squash: 
T,
btrue: tt,
uiff: uiff(P;Q),
deq: EqDecider(T),
fpf: a:A fp-> B[a],
length: ||as||,
ycomb: Y,
rev_implies: P 
Q,
iff: P Q,
decidable: Dec(P),
rev_uimplies: rev_uimplies(P;Q),
sq_type: SQType(T)
Lemmas :
fpf-split,
assert_wf,
bnot_wf,
eqof_wf,
hd_wf,
fpf-domain_wf,
length_wf,
decidable__assert,
fpf-trivial-subtype-top,
less_than_wf,
fpf-ap_wf,
fpf-sub_wf,
fpf-join_wf,
fpf-single_wf,
all_wf,
fpf-dom_wf,
not_wf,
equal_wf,
exists_wf,
fpf_wf,
deq_wf,
bor_wf,
deq-member_wf,
or_wf,
l_member_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
or_functionality_wrt_iff,
assert-deq,
assert-deq-member,
fpf-join-sub,
fpf-sub_transitivity,
and_wf,
assert_of_bnot,
uiff_transitivity,
not_functionality_wrt_uiff,
decidable-equal-deq,
fpf-single-dom-sq,
eqff_to_assert,
eqtt_to_assert,
bool_subtype_base,
subtype_base_sq,
bool_cases,
fpf-join-ap-sq,
top_wf,
true_wf,
squash_wf,
bool_wf,
assert_elim,
member_wf,
fpf-compatible-symmetry,
fpf-compatible_wf,
isect_wf,
fpf-compatible-single-iff,
fpf-sub_weakening,
deq_property,
fpf-join-dom,
length_sublist,
decidable__equal_int,
proper_sublist_length,
member-fpf-domain
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]
\mforall{}f:a:A fp-> B[a]
\mexists{}g:a:A fp-> B[a]
\mexists{}a:A
\mexists{}b:B[a]
((f \msubseteq{} g \moplus{} a : b \mwedge{} g \moplus{} a : b \msubseteq{} f)
\mwedge{} (\mforall{}a':A. \mneg{}(a' = a) supposing \muparrow{}a' \mmember{} dom(g))
\mwedge{} (||fpf-domain(g)|| < ||fpf-domain(f)||))
supposing 0 < ||fpf-domain(f)||
Date html generated:
2012_01_23-AM-11_55_39
Last ObjectModification:
2011_12_27-PM-11_20_19
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