Nuprl Lemma : rv-partial-sum_wf
∀[p:FinProbSpace]. ∀[f:ℕ ─→ ℕ]. ∀[X:n:ℕ ─→ RandomVariable(p;f[n])]. ∀[n:ℕ].
rv-partial-sum(n;i.X[i]) ∈ RandomVariable(p;f[n]) supposing ∀n:ℕ. ∀i:ℕn. f[i] < f[n]
Proof
Definitions occuring in Statement :
rv-partial-sum: rv-partial-sum(n;i.X[i]),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
natural_number: $n
Lemmas :
Error :qsum_wf,
int_seg_subtype-nat,
false_wf,
subtype_rel_dep_function,
int_seg_wf,
p-outcome_wf,
subtype_rel-int_seg,
le_weakening2,
subtype_rel_self,
all_wf,
nat_wf,
less_than_wf,
random-variable_wf,
finite-prob-space_wf
\mforall{}[p:FinProbSpace]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[X:n:\mBbbN{} {}\mrightarrow{} RandomVariable(p;f[n])]. \mforall{}[n:\mBbbN{}].
rv-partial-sum(n;i.X[i]) \mmember{} RandomVariable(p;f[n]) supposing \mforall{}n:\mBbbN{}. \mforall{}i:\mBbbN{}n. f[i] < f[n]
Date html generated:
2015_07_17-AM-08_02_22
Last ObjectModification:
2015_01_27-AM-11_21_57
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