Nuprl Lemma : find-maximal-consecutive_wf
∀[T:Type]. ∀[g:T ─→ ℤ]. ∀[L:T List+]. (find-maximal-consecutive(g;L) ∈ {1..||L|| + 1-})
Proof
Definitions occuring in Statement :
find-maximal-consecutive: find-maximal-consecutive(g;L),
listp: A List+,
length: ||as||,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type
Lemmas :
listp_properties,
listp_wf,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
reduce_tl_cons_lemma,
hd_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list_wf,
list_accum_nil_lemma,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
list_accum_cons_lemma,
le_weakening,
decidable__lt,
lelt_wf,
value-type-has-value,
int-value-type,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_rel-int_seg,
length_wf,
add-mul-special,
zero-mul,
le-add-cancel2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Latex:
\mforall{}[T:Type]. \mforall{}[g:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List\msupplus{}]. (find-maximal-consecutive(g;L) \mmember{} \{1..||L|| + 1\msupminus{}\})
Date html generated:
2015_07_23-PM-00_27_51
Last ObjectModification:
2015_01_29-AM-01_31_34
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