Nuprl Lemma : member-countable-p-union
∀p:FinProbSpace. ∀A:ℕ ─→ p-open(p). ∀s:ℕ ─→ Outcome. ((∃i:ℕ. s ∈ A[i]) ⇒ s ∈ countable-p-union(i.A[i]))
Proof
Definitions occuring in Statement :
countable-p-union: countable-p-union(i.A[i]),
p-open-member: s ∈ C,
p-open: p-open(p),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x]
Lemmas :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
less-iff-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,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
decidable__lt,
add-mul-special,
zero-mul,
equal-wf-T-base,
countable-p-union_wf,
nat_wf,
p-open_wf,
subtype_rel_dep_function,
p-outcome_wf,
int_seg_wf,
int_seg_subtype-nat,
subtype_rel_self,
eq_int_wf,
assert_wf,
bnot_wf,
not_wf,
uiff_transitivity,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
imax-list-ub,
map_wf,
upto_wf,
squash_wf,
true_wf,
map_length_nat,
iff_weakening_equal,
length_upto,
less_than_transitivity2,
l_exists_iff,
l_member_wf,
lelt_wf,
member_map,
equal-wf-base-T,
member_upto2,
imax-list-lb,
l_all_iff,
le-add-cancel2,
exists_wf,
all_wf,
imax-list_wf
\mforall{}p:FinProbSpace. \mforall{}A:\mBbbN{} {}\mrightarrow{} p-open(p). \mforall{}s:\mBbbN{} {}\mrightarrow{} Outcome.
((\mexists{}i:\mBbbN{}. s \mmember{} A[i]) {}\mRightarrow{} s \mmember{} countable-p-union(i.A[i]))
Date html generated:
2015_07_17-AM-08_00_48
Last ObjectModification:
2015_02_03-PM-09_45_28
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