Nuprl Lemma : rv-disjoint-rv-scale
∀p:FinProbSpace. ∀n:ℕ. ∀X,Y:RandomVariable(p;n). ∀a:ℚ. (rv-disjoint(p;n;X;Y) ⇒ rv-disjoint(p;n;X;a*Y))
Proof
Definitions occuring in Statement :
rv-disjoint: rv-disjoint(p;n;X;Y),
rv-scale: q*X,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
rationals: ℚ,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
rv-compose: (x.F[x]) o X,
random-variable: RandomVariable(p;n),
nat: ℕ,
finite-prob-space: FinProbSpace,
rv-scale: q*X,
true: True
Lemmas referenced :
rv-disjoint_wf,
rationals_wf,
random-variable_wf,
nat_wf,
finite-prob-space_wf,
rv-disjoint-compose,
qmul_wf,
squash_wf,
true_wf,
int_seg_wf,
length_wf,
rv-compose_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
independent_functionElimination,
hyp_replacement,
equalitySymmetry,
applyEquality,
imageElimination,
equalityTransitivity,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
functionEquality,
because_Cache,
imageMemberEquality,
baseClosed
Latex:
\mforall{}p:FinProbSpace. \mforall{}n:\mBbbN{}. \mforall{}X,Y:RandomVariable(p;n). \mforall{}a:\mBbbQ{}.
(rv-disjoint(p;n;X;Y) {}\mRightarrow{} rv-disjoint(p;n;X;a*Y))
Date html generated:
2016_10_26-AM-06_49_53
Last ObjectModification:
2016_07_12-AM-08_04_09
Theory : randomness
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