Nuprl Lemma : es-interval-select
[es:EO]. [e',e:E]. [i:
].
firstn(i;[e, e']) = if (i =
0) then [] else [e, pred([e, e'][i])] fi supposing i < ||[e, e']||
Proof not projected
Definitions occuring in Statement :
es-interval: [e, e'],
es-pred: pred(e),
es-E: E,
event_ordering: EO,
select: l[i],
firstn: firstn(n;as),
length: ||as||,
eq_int: (i = j),
ifthenelse: if b then t else f fi ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
less_than: a < b,
nil: [],
list: type List,
natural_number: $n,
equal: s = t
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
member: t 
T,
guard: {T},
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
so_lambda: 
x.t[x],
all: x:A. B[x],
prop: 
,
implies: P 
Q,
not: 
A,
int_seg: {i..j
},
le: A 
B,
lelt: i j < k,
and: P 
Q,
false: False,
assert: 
b,
true: True,
squash: 
T,
nat: ,
uiff: uiff(P;Q),
unit: Unit,
bool: 
,
so_apply: x[s],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
iff: P 
Q,
cand: A c B,
sq_type: SQType(T),
decidable: Dec(P),
or: P 
Q,
it: 
Lemmas :
less_than_wf,
length_wf,
es-interval_wf,
nat_wf,
es-E_wf,
event_ordering_wf,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
uiff_transitivity,
all_wf,
es-locl-wellfnd,
equal_wf,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
es-pred_wf,
select_wf,
eq_int_wf,
l_before_select,
lelt_wf,
l_before-es-interval,
subtype_base_sq,
bool_subtype_base,
false_wf,
es-pred-locl,
decidable__lt,
es-locl-first,
true_wf,
squash_wf,
nat_properties,
es-first_wf,
member_wf,
bool_sq,
firstn_wf
\mforall{}[es:EO]. \mforall{}[e',e:E]. \mforall{}[i:\mBbbN{}].
firstn(i;[e, e']) = if (i =\msubz{} 0) then [] else [e, pred([e, e'][i])] fi supposing i < ||[e, e']||
Date html generated:
2012_01_23-PM-12_10_27
Last ObjectModification:
2011_12_13-AM-10_31_51
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