Nuprl Lemma : rv-shift_wf
∀[p:FinProbSpace]. ∀[n:ℕ+]. ∀[X:RandomVariable(p;n)]. ∀[x:Outcome]. (rv-shift(x;X) ∈ RandomVariable(p;n - 1))
Proof
Definitions occuring in Statement :
rv-shift: rv-shift(x;X),
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtract: n - m,
natural_number: $n
Lemmas :
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{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[X:RandomVariable(p;n)]. \mforall{}[x:Outcome].
(rv-shift(x;X) \mmember{} RandomVariable(p;n - 1))
Date html generated:
2015_07_17-AM-07_58_44
Last ObjectModification:
2015_01_27-AM-11_23_21
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