{ 
[A:Type]. [d1,d2:EqDecider(A)]. [B:A 
Type]. [f:a:A fp-> B[a]]. [x:A].
[z:B[x]].
(f(x)?z = f(x)?z) }
{ Proof }
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf: a:A fp-> B[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],
member: t 
T,
so_lambda: 
x.t[x],
prop: 
,
uall: [x:A]. B[x],
fpf-cap: f(x)?z,
ifthenelse: if b then t else f fi ,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
bfalse: ff,
fpf: a:A fp-> B[a],
fpf-dom: x dom(f),
pi1: fst(t),
iff: P 
Q,
and: P 
Q,
not: 
A,
uimplies: b supposing a,
false: False,
bool: 
,
unit: Unit,
it: 
Lemmas :
fpf-dom_wf,
fpf-trivial-subtype-top,
bool_wf,
assert_wf,
assert-deq-member,
l_member_wf,
not_wf,
bnot_wf,
not_functionality_wrt_iff,
deq-member_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[d1,d2:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[z:B[x]].
(f(x)?z = f(x)?z)
Date html generated:
2011_08_10-AM-07_57_53
Last ObjectModification:
2011_06_18-AM-08_17_59
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