Nuprl Lemma : countable-p-union_wf
∀[p:FinProbSpace]. ∀[A:ℕ ─→ p-open(p)]. (countable-p-union(i.A[i]) ∈ p-open(p))
Proof
Definitions occuring in Statement :
countable-p-union: countable-p-union(i.A[i]),
p-open: p-open(p),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x]
Lemmas :
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
iff_transitivity,
assert_of_eq_int,
eqtt_to_assert,
uiff_transitivity,
not_wf,
bnot_wf,
assert_wf,
equal-wf-T-base,
bool_wf,
eq_int_wf,
p-outcome_wf,
int_seg_wf,
nat_wf,
lelt_wf,
false_wf,
minus-zero,
minus-add,
add-commutes,
condition-implies-le,
le-add-cancel,
zero-add,
add-zero,
add-associates,
add_functionality_wrt_le,
not-equal-2,
decidable__lt,
length_upto,
iff_weakening_equal,
map_length_nat,
true_wf,
squash_wf,
less_than_wf,
upto_wf,
subtype_rel_self,
subtype_rel_dep_function,
le_wf,
all_wf,
int_seg_subtype-nat,
map_wf,
imax-list_wf,
imax-list-ub,
l_member_wf,
l_exists_iff,
member_upto,
subtype_rel_list,
member_map,
le-add-cancel2,
imax-list-lb,
less-iff-le,
sq_stable__le,
add-swap,
not-le-2,
decidable__le,
l_all_iff,
length_wf,
less_than_transitivity2,
decidable__equal_int,
int_subtype_base,
subtype_base_sq,
le_weakening,
le_weakening2,
member_upto2,
set_subtype_base,
equal_wf,
set_wf
\mforall{}[p:FinProbSpace]. \mforall{}[A:\mBbbN{} {}\mrightarrow{} p-open(p)]. (countable-p-union(i.A[i]) \mmember{} p-open(p))
Date html generated:
2015_07_17-AM-08_00_43
Last ObjectModification:
2015_07_16-AM-09_51_59
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