Nuprl Lemma : collect_accm-wf2
∀[A:Type]. ∀[P:{L:A List| 0 < ||L||} ─→ 𝔹]. ∀[num:A ─→ ℕ].
(collect_accm(v.P[v];v.num[v]) ∈ {s:ℤ × {L:A List| 0 < ||L|| ⇒ (¬↑P[L])} × ({L:A List| 0 < ||L|| ∧ (↑P[L])} + Top)|\000C
(↑isl(snd(snd(s)))) ⇒ (1 ≤ (fst(s)))}
─→ A
─→ {s:ℤ × {L:A List| 0 < ||L|| ⇒ (¬↑P[L])} × ({L:A List| 0 < ||L|| ∧ (↑P[L])} + Top)|
(↑isl(snd(snd(s)))) ⇒ (1 ≤ (fst(s)))} )
Proof
Definitions occuring in Statement :
collect_accm: collect_accm(v.P[v];v.num[v]),
length: ||as||,
list: T List,
nat: ℕ,
assert: ↑b,
isl: isl(x),
bool: 𝔹,
less_than: a < b,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
le: A ≤ B,
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 :
assert_wf,
isl_wf,
less_than_wf,
length_wf,
top_wf,
le_wf,
not_wf,
value-type-has-value,
set-value-type,
int-value-type,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
assert_elim,
and_wf,
equal_wf,
bfalse_wf,
btrue_neq_bfalse,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
length_nil,
non_neg_length,
length_cons,
void_wf,
list_wf,
pi2_wf,
length_append,
subtype_rel_list,
nat_wf,
member_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{} \{s:\mBbbZ{}
\mtimes{} \{L:A List| 0 < ||L|| {}\mRightarrow{} (\mneg{}\muparrow{}P[L])\}
\mtimes{} (\{L:A List| 0 < ||L|| \mwedge{} (\muparrow{}P[L])\} + Top)|
(\muparrow{}isl(snd(snd(s)))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} A
{}\mrightarrow{} \{s:\mBbbZ{} \mtimes{} \{L:A List| 0 < ||L|| {}\mRightarrow{} (\mneg{}\muparrow{}P[L])\} \mtimes{} (\{L:A List| 0 < ||L|| \mwedge{} (\muparrow{}P[L])\} + Top)|
(\muparrow{}isl(snd(snd(s)))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\} )
Date html generated:
2015_07_17-AM-08_59_47
Last ObjectModification:
2015_01_27-PM-01_06_11
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