Nuprl Lemma : select-tagged-indices-aux_wf
∀[A,B:Type]. ∀[tg:A ─→ B]. ∀[P:A ─→ 𝔹]. ∀[L:A List]. (select-tagged-indices-aux(P;tg;L) ∈ ℕ ─→ ((ℕ × B) List))
Proof
Definitions occuring in Statement :
select-tagged-indices-aux: select-tagged-indices-aux(P;tg;L),
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
product_subtype_list,
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_wf,
bool_wf,
list_ind_nil_lemma,
nil_wf,
list_ind_cons_lemma,
eqtt_to_assert,
cons_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot
Latex:
\mforall{}[A,B:Type]. \mforall{}[tg:A {}\mrightarrow{} B]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[L:A List].
(select-tagged-indices-aux(P;tg;L) \mmember{} \mBbbN{} {}\mrightarrow{} ((\mBbbN{} \mtimes{} B) List))
Date html generated:
2015_07_23-AM-11_57_41
Last ObjectModification:
2015_01_29-AM-07_40_37
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