{ 
[A:Type]. [eq:EqDecider(A)]. [f,g:a:A fp-> Top]. [x:A]. [z:Top].
(f 
g(x)?z ~ f(x)?g(x)?z) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
uall: [x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t,
deq: EqDecider(T)
Definitions :
top: Top,
fpf-cap: f(x)?z,
member: t 
T,
so_lambda: 
x.t[x],
prop: 
,
or: P 
Q,
guard: {T},
ifthenelse: if b then t else f fi ,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
bfalse: ff,
uall: [x:A]. B[x],
so_apply: x[s],
not: 
A,
iff: P 
Q,
and: P 
Q,
false: False,
uimplies: b supposing a,
bool: 
,
unit: Unit,
it: 
Lemmas :
fpf-join-ap-sq,
fpf-dom_wf,
fpf-join_wf,
bool_wf,
assert_wf,
not_wf,
bnot_wf,
fpf-join-dom,
not_functionality_wrt_iff,
top_wf,
fpf_wf,
deq_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Top]. \mforall{}[x:A]. \mforall{}[z:Top]. (f \moplus{} g(x)?z \msim{} f(x)?g(x)?z)
Date html generated:
2011_08_10-AM-08_00_02
Last ObjectModification:
2011_06_18-AM-08_19_18
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