Nuprl Lemma : split-maximal-consecutive_wf
∀[T:Type]. ∀[g:T ─→ ℤ]. ∀[L:T List+].
(split-maximal-consecutive(g;L) ∈ {p:T List+ × (T List)| L = ((fst(p)) @ (snd(p))) ∈ (T List)} )
Proof
Definitions occuring in Statement :
split-maximal-consecutive: split-maximal-consecutive(g;L),
listp: A List+,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
product: x:A × B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
find-maximal-consecutive_wf,
int_seg_wf,
length_wf,
value-type-has-value,
set-value-type,
lelt_wf,
int-value-type,
eval_list_sq,
firstn_wf,
subtype_rel_list,
top_wf,
nth_tl_wf,
list_wf,
list-value-type,
assert_of_lt_int,
non_neg_length,
length_firstn_eq,
subtype_rel_sets,
le_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
less-iff-le,
add-swap,
le-add-cancel2,
length_wf_nat,
assert_wf,
lt_int_wf,
append_firstn_lastn,
iff_weakening_equal,
append_wf,
listp_wf
Latex:
\mforall{}[T:Type]. \mforall{}[g:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List\msupplus{}].
(split-maximal-consecutive(g;L) \mmember{} \{p:T List\msupplus{} \mtimes{} (T List)| L = ((fst(p)) @ (snd(p)))\} )
Date html generated:
2015_07_23-PM-00_27_57
Last ObjectModification:
2015_02_04-PM-03_09_47
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