Nuprl Lemma : nullset-union
∀p:FinProbSpace. ∀[S:ℕ ─→ (ℕ ─→ Outcome) ─→ ℙ]. ((∀i:ℕ. nullset(p;S[i])) ⇒ nullset(p;λs.∃i:ℕ. (S[i] s)))
Proof
Definitions occuring in Statement :
nullset: nullset(p;S),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x]
Lemmas :
countable-p-union_wf,
nat_wf,
all_wf,
p-outcome_wf,
exists_wf,
p-open-member_wf,
p-measure-le_wf,
Error :qmul-positive,
Error :qexp_wf,
qdiv_wf,
Error :int_nzero-rational,
not-equal-2,
decidable__le,
le_wf,
false_wf,
not-le-2,
condition-implies-le,
add-commutes,
add-associates,
minus-add,
zero-add,
add-swap,
or_wf,
nequal_wf,
sq_stable__le,
minus-one-mul,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
sq_stable_from_decidable,
Error :qless_wf,
Error :decidable__qless,
Error :qexp-positive-iff,
Error :qinv-positive,
Error :assert-q_less-eq,
iff_weakening_equal,
int-equal-in-rationals,
rationals_wf,
not_wf,
equal_wf,
assert_wf,
isEven_wf,
equal-wf-T-base,
qmul_wf,
member-countable-p-union,
Error :qless_witness,
expectation_wf,
p-open_wf,
int_seg_wf,
subtype_rel_set,
lelt_wf,
int-subtype-rationals,
length_wf,
set_wf,
finite-prob-space_wf,
eq_int_wf,
bool_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
expectation-constant,
top_wf,
subtype_rel_dep_function,
expectation-imax-list,
decidable__lt,
minus-zero,
less_than_wf,
int_seg_subtype-nat,
Error :qsum-qle,
Error :qle_weakening_lt_qorder,
squash_wf,
true_wf,
Error :prod_sum_l_q,
Error :qsum_wf,
qmul_com,
Error :qexp_step,
Error :q-geometric-series,
qsub_wf,
assert-qeq,
equal-wf-base,
qadd_wf,
Error :qmul_ac_1_qrng,
Error :qmul_comm_qrng,
Error :qmul-qdiv-cancel3,
Error :qmul_over_plus_qrng,
Error :qmul_over_minus_qrng,
Error :qmul_one_qrng,
Error :qadd_preserves_qless,
Error :qadd_ac_1_q,
Error :qadd_comm_q,
Error :qadd_inv_assoc_q,
Error :qinverse_q,
Error :mon_ident_q,
Error :qless_transitivity_1_qorder,
imax-list_wf,
map_wf,
upto_wf,
map_length_nat,
length_upto
\mforall{}p:FinProbSpace
\mforall{}[S:\mBbbN{} {}\mrightarrow{} (\mBbbN{} {}\mrightarrow{} Outcome) {}\mrightarrow{} \mBbbP{}]. ((\mforall{}i:\mBbbN{}. nullset(p;S[i])) {}\mRightarrow{} nullset(p;\mlambda{}s.\mexists{}i:\mBbbN{}. (S[i] s)))
Date html generated:
2015_07_17-AM-08_01_16
Last ObjectModification:
2015_02_03-PM-09_50_24
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