Nuprl Lemma : expectation_wf
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[X:RandomVariable(p;n)]. (E(n;X) ∈ ℚ)
Proof
Definitions occuring in Statement :
expectation: E(n;F),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rationals: ℚ
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
random-variable_wf,
null-seq_wf,
int_seg_wf,
length_wf,
rationals_wf,
false_wf,
le_wf,
decidable__le,
subtract_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
nat_wf,
set_wf,
list_wf,
equal-wf-T-base,
Error :qsum_wf,
select_wf,
sq_stable__le,
l_all_wf2,
l_member_wf,
Error :qle_wf,
int-subtype-rationals,
eq_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_weakening,
bnot_wf,
not_wf,
weighted-sum_wf2,
rv-shift_wf,
p-outcome_wf,
le_weakening2,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:RandomVariable(p;n)]. (E(n;X) \mmember{} \mBbbQ{})
Date html generated:
2015_07_17-AM-07_58_52
Last ObjectModification:
2015_01_27-AM-11_24_41
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