{ 
[A:Type]
eq:EqDecider(A)
[B:A 
Type]
L:a:A fp-> B[a] List. x:A.
(
f
L. (
x dom(f)) 
(
(L)(x) = f(x))) supposing x dom((L)) }
{ Proof }
Definitions occuring in Statement :
fpf-join-list: (L),
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
and: P Q,
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t,
l_exists: (xL. P[x]),
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
so_apply: x[s],
uimplies: b supposing a,
assert: b,
fpf-dom: x dom(f),
fpf-join-list: (L),
reduce: reduce(f;k;as),
fpf-empty: 
,
deq-member: deq-member(eq;x;L),
pi1: fst(t),
bfalse: ff,
ifthenelse: if b then t else f fi ,
false: False,
member: t T,
so_lambda: 
x.t[x],
subtype: S 
T,
and: P Q,
prop: 
,
cand: A c B,
or: P 
Q,
rev_implies: P 
Q,
iff: P 
Q,
implies: P Q,
btrue: tt,
guard: {T},
l_exists: (xL. P[x]),
exists: x:A. B[x],
true: True,
decidable: Dec(P),
not: 
A,
bool: 
,
unit: Unit,
sq_type: SQType(T),
it: 
Lemmas :
false_wf,
assert_witness,
fpf-dom_wf,
fpf-join_wf,
top_wf,
fpf-trivial-subtype-top,
fpf-join-list_wf,
fpf_wf,
assert_wf,
deq_wf,
l_exists_cons,
fpf-ap_wf,
fpf-join-dom,
decidable__assert,
l_exists_wf,
l_member_wf,
fpf-join-ap,
bool_wf,
not_wf,
bnot_wf,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
not_assert_elim,
subtype_base_sq,
bool_subtype_base,
assert_elim
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]
\mforall{}L:a:A fp-> B[a] List. \mforall{}x:A.
(\mexists{}f\mmember{}L. (\muparrow{}x \mmember{} dom(f)) \mwedge{} (\moplus{}(L)(x) = f(x))) supposing \muparrow{}x \mmember{} dom(\moplus{}(L))
Date html generated:
2011_08_10-AM-08_01_13
Last ObjectModification:
2011_06_18-AM-08_19_53
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