Nuprl Lemma : rv-shift-linear
∀[k:FinProbSpace]. ∀[x:Outcome]. ∀[n:ℕ+]. ∀[X,Y:RandomVariable(k;n)]. ∀[a,b:ℚ].
(rv-shift(x;a*X + b*Y) = a*rv-shift(x;X) + b*rv-shift(x;Y) ∈ RandomVariable(k;n - 1))
Proof
Definitions occuring in Statement :
rv-shift: rv-shift(x;X),
rv-scale: q*X,
rv-add: X + Y,
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T,
rationals: ℚ
Lemmas :
qadd_wf,
qmul_wf,
cons-seq_wf,
int_seg_wf,
length_wf,
rationals_wf,
decidable__le,
subtract_wf,
false_wf,
not-le-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,
le_wf,
trivial-int-eq1,
subtype_rel_self,
nat_plus_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
\mforall{}[k:FinProbSpace]. \mforall{}[x:Outcome]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[X,Y:RandomVariable(k;n)]. \mforall{}[a,b:\mBbbQ{}].
(rv-shift(x;a*X + b*Y) = a*rv-shift(x;X) + b*rv-shift(x;Y))
Date html generated:
2015_07_17-AM-07_58_45
Last ObjectModification:
2015_01_27-AM-11_23_19
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