Nuprl Lemma : rv-compose_wf
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[X:RandomVariable(p;n)]. ∀[F:ℚ ─→ ℚ]. ((X.F[X]) o X ∈ RandomVariable(p;n))
Proof
Definitions occuring in Statement :
rv-compose: (x.F[x]) o X,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
rationals: ℚ
Lemmas :
int_seg_wf,
p-outcome_wf,
rationals_wf,
nat_wf,
finite-prob-space_wf
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:RandomVariable(p;n)]. \mforall{}[F:\mBbbQ{} {}\mrightarrow{} \mBbbQ{}].
((X.F[X]) o X \mmember{} RandomVariable(p;n))
Date html generated:
2015_07_17-AM-07_59_17
Last ObjectModification:
2015_01_27-AM-11_22_29
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