Nuprl Lemma : collect_accm_wf
∀[A:Type]. ∀[P:{L:A List| 0 < ||L||} ─→ 𝔹]. ∀[num:A ─→ ℕ].
(collect_accm(v.P[v];v.num[v]) ∈ (ℤ × {L:A List| 0 < ||L|| ⇒ (¬↑P[L])} × ({L:A List| 0 < ||L|| ∧ (↑P[L])} + Top))
─→ A
─→ (ℤ × {L:A List| 0 < ||L|| ⇒ (¬↑P[L])} × ({L:A List| 0 < ||L|| ∧ (↑P[L])} + Top)))
Proof
Definitions occuring in Statement :
collect_accm: collect_accm(v.P[v];v.num[v]),
length: ||as||,
list: T List,
nat: ℕ,
assert: ↑b,
bool: 𝔹,
less_than: a < b,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
natural_number: $n,
int: ℤ,
universe: Type
Lemmas :
cons_wf_listp,
nil_wf,
subtype_rel_sets,
assert_wf,
lt_int_wf,
length_wf,
less_than_wf,
assert_of_lt_int,
bool_wf,
eqtt_to_assert,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
length_append,
subtype_rel_set,
list_wf,
subtype_rel_list,
top_wf
\mforall{}[A:Type]. \mforall{}[P:\{L:A List| 0 < ||L||\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}].
(collect\_accm(v.P[v];v.num[v]) \mmember{} (\mBbbZ{}
\mtimes{} \{L:A List| 0 < ||L|| {}\mRightarrow{} (\mneg{}\muparrow{}P[L])\}
\mtimes{} (\{L:A List| 0 < ||L|| \mwedge{} (\muparrow{}P[L])\} + Top))
{}\mrightarrow{} A
{}\mrightarrow{} (\mBbbZ{} \mtimes{} \{L:A List| 0 < ||L|| {}\mRightarrow{} (\mneg{}\muparrow{}P[L])\} \mtimes{} (\{L:A List| 0 < ||L|| \mwedge{} (\muparrow{}P[L])\} + Top)))
Date html generated:
2015_07_17-AM-08_59_43
Last ObjectModification:
2015_01_27-PM-01_05_50
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