Nuprl Lemma : collect_accum_wf
∀[A,B:Type]. ∀[P:B ─→ 𝔹]. ∀[num:A ─→ ℕ]. ∀[init:B]. ∀[f:B ─→ A ─→ B].
(collect_accum(x.num[x];init;a,v.f[a;v];a.P[a]) ∈ (ℤ × B × (B + Top)) ─→ A ─→ (ℤ × B × (B + Top)))
Proof
Definitions occuring in Statement :
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type
Lemmas :
bool_wf,
eqtt_to_assert,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
lt_int_wf,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
top_wf
\mforall{}[A,B:Type]. \mforall{}[P:B {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[init:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(collect\_accum(x.num[x];init;a,v.f[a;v];a.P[a]) \mmember{} (\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)) {}\mrightarrow{} A {}\mrightarrow{} (\mBbbZ{} \mtimes{} B \mtimes{} (B + Top)))
Date html generated:
2015_07_17-AM-08_59_54
Last ObjectModification:
2015_01_27-PM-01_02_53
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