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,
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
rv-compose: (x.F[x]) o X,
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
nat: ℕ
Lemmas referenced :
int_seg_wf,
p-outcome_wf,
rationals_wf,
nat_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
applyEquality,
hypothesisEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\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:
2016_05_15-PM-11_47_33
Last ObjectModification:
2015_12_28-PM-07_15_50
Theory : randomness
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