Nuprl Lemma : collect_filter_accum_fun_wf
∀[A,B:Type]. ∀[base:B]. ∀[f:B ─→ A ─→ B]. ∀[size:ℕ+]. ∀[num:A ─→ ℕ]. ∀[P:A ─→ 𝔹].
(collect_filter_accum_fun(b,v.f[b;v];base;size;v.num[v];v.P[v]) ∈ {s:ℤ × ℕ × B × (𝔹 + Top)|
(↑isl(snd(snd(snd(s))))) ⇒ (1 ≤ (fst(s)))}
─→ A
─→ {s:ℤ × ℕ × B × (𝔹 + Top)| (↑isl(snd(snd(snd(s))))) ⇒ (1 ≤ (fst(s)))} )
Proof
Definitions occuring in Statement :
collect_filter_accum_fun: collect_filter_accum_fun(b,v.f[b; v];base;size;v.num[v];v.P[v]),
nat_plus: ℕ+,
nat: ℕ,
assert: ↑b,
isl: isl(x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
le: A ≤ B,
implies: 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 :
value-type-has-value,
set-value-type,
le_wf,
int-value-type,
union-value-type,
unit_wf2,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
nat_wf,
assert_elim,
isl_wf,
and_wf,
equal_wf,
pi2_wf,
bfalse_wf,
btrue_neq_bfalse,
assert_wf,
eqff_to_assert,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
eq_int_wf,
assert_of_eq_int,
false_wf,
btrue_wf,
neg_assert_of_eq_int,
true_wf,
decidable__le,
not-le-2,
not-equal-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
top_wf,
nat_plus_wf
\mforall{}[A,B:Type]. \mforall{}[base:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
(collect\_filter\_accum\_fun(b,v.f[b;v];base;size;v.num[v];v.P[v]) \mmember{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)|
(\muparrow{}isl(snd(snd(snd(s)))))
{}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} A
{}\mrightarrow{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)| (\muparrow{}isl(snd(snd(snd(s))))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\} )
Date html generated:
2015_07_17-AM-09_00_21
Last ObjectModification:
2015_01_27-PM-01_06_07
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