Nuprl Lemma : es-interval-select
∀[es:EO]. ∀[e',e:E]. ∀[i:ℕ].
firstn(i;[e, e']) = if (i =z 0) then [] else [e, pred([e, e'][i])] fi ∈ (E List) supposing i < ||[e, e']||
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-pred: pred(e),
es-E: E,
event_ordering: EO,
select: L[n],
firstn: firstn(n;as),
length: ||as||,
nil: [],
list: T List,
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Lemmas :
less_than_wf,
length_wf,
es-interval_wf,
nat_wf,
es-E_wf,
event_ordering_wf,
equal_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
nil_wf,
bnot_wf,
not_wf,
es-pred_wf,
select_wf,
sq_stable__le,
es-locl_wf,
es-locl-wellfnd,
all_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
l_before_select,
lelt_wf,
l_before-es-interval,
false_wf,
less_than_transitivity2,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-first_wf2,
subtype_base_sq,
int_subtype_base,
first0,
subtype_rel_list,
top_wf,
es-le-trans,
es-locl_transitivity2,
es-le_weakening,
squash_wf,
true_wf,
select-as-hd,
hd-es-interval,
iff_weakening_equal,
es-le-trans3,
es-interval-less,
es-pred-locl,
decidable__lt,
eq_int_wf,
bool_cases,
bool_subtype_base,
length-append,
length-singleton,
list_wf,
firstn_append,
cons_wf,
less_than_transitivity1,
le_weakening,
firstn_wf,
select_append_front,
select_append_back,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
select-cons-hd,
subtract_wf,
and_wf,
member_wf,
firstn_all
\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:
2015_07_17-AM-08_42_46
Last ObjectModification:
2015_02_04-AM-07_09_05
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