{ 
[A:Type]. [eq:EqDecider(A)]. [df:x:A fp-> Type]. [f:x:A fp-> df(x)?Top].
[dg:x:A fp-> Type]. [g:x:A fp-> dg(x)?Top].
(f 
g 
x:A fp-> df dg(x)?Top) supposing
((x:A. ((
x dom(g)) 
(x dom(dg)))) and
(x:A. ((x dom(f)) (x dom(df)))) and
df || dg) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
implies: P Q,
member: t T,
universe: Type,
deq: EqDecider(T)
Definitions :
all: x:A. B[x],
implies: P Q,
member: t T,
prop: 
,
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
fpf-join: f g,
fpf-dom: x dom(f),
pi1: fst(t),
fpf-cap: f(x)?z,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
rev_implies: P 
Q,
iff: P Q,
and: P 
Q,
assert: b,
or: P 
Q,
true: True,
top: Top,
uall: [x:A]. B[x],
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
not: 
A,
false: False,
sq_type: SQType(T),
guard: {T},
fpf-compatible: f || g,
it: 
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-trivial-subtype-top,
fpf-cap_wf,
top_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf,
append_wf,
filter_wf,
bnot_wf,
deq-member_wf,
bool_wf,
not_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-ap_wf,
fpf-join_wf,
fpf-join-ap,
subtype_rel_self,
fpf-join-dom,
subtype_base_sq,
bool_subtype_base,
assert_elim,
member_append,
not_functionality_wrt_iff,
l_member_wf,
assert-deq-member,
member_filter
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[df:x:A fp-> Type]. \mforall{}[f:x:A fp-> df(x)?Top]. \mforall{}[dg:x:A fp-> Type].
\mforall{}[g:x:A fp-> dg(x)?Top].
(f \moplus{} g \mmember{} x:A fp-> df \moplus{} dg(x)?Top) supposing
((\mforall{}x:A. ((\muparrow{}x \mmember{} dom(g)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(dg)))) and
(\mforall{}x:A. ((\muparrow{}x \mmember{} dom(f)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(df)))) and
df || dg)
Date html generated:
2011_08_10-AM-08_00_08
Last ObjectModification:
2011_06_18-AM-08_19_20
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