Nuprl Lemma : l_index_hd
[T:Type]. [dT:EqDecider(T)]. [L:T List]. index(L;hd(L)) ~ 0 supposing 
null(L)
Proof not projected
Definitions occuring in Statement :
l_index: index(L;x),
hd: hd(l),
null: null(as),
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
not: A,
list: type List,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
deq: EqDecider(T)
Definitions :
guard: {T},
implies: P 
Q,
subtype: S 
T,
top: Top,
all: x:A. B[x],
lt_int: i <z j,
bnot: 
b,
le_int: i 
z j,
ycomb: Y,
select: l[i],
eqof: eqof(d),
mu: mu(f),
member: t 
T,
true: True,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
hd: hd(l),
l_index: index(L;x),
and: P 
Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
unit: Unit,
bool: 
,
uall: [x:A]. B[x],
false: False,
null: null(as),
assert: b,
not: A,
deq: EqDecider(T),
it: 
Lemmas :
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert-deq,
eqtt_to_assert,
uiff_transitivity,
deq_wf,
top_wf,
null_wf3,
not_wf,
bnot_wf,
assert_wf,
equal_wf,
bool_wf
\mforall{}[T:Type]. \mforall{}[dT:EqDecider(T)]. \mforall{}[L:T List]. index(L;hd(L)) \msim{} 0 supposing \mneg{}\muparrow{}null(L)
Date html generated:
2012_01_23-AM-11_53_12
Last ObjectModification:
2011_12_09-PM-07_10_40
Home
Index