Nuprl Lemma : rv-disjoint-rv-add2
∀p:FinProbSpace. ∀n:ℕ. ∀X,Y,Z:RandomVariable(p;n).
(rv-disjoint(p;n;Y;X) ⇒ rv-disjoint(p;n;Z;X) ⇒ rv-disjoint(p;n;Y + Z;X))
Proof
Definitions occuring in Statement :
rv-disjoint: rv-disjoint(p;n;X;Y),
rv-add: X + Y,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
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]
Lemmas referenced :
rv-disjoint_wf,
random-variable_wf,
nat_wf,
finite-prob-space_wf,
rv-add_wf,
rv-disjoint-symmetry,
rv-disjoint-rv-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}p:FinProbSpace. \mforall{}n:\mBbbN{}. \mforall{}X,Y,Z:RandomVariable(p;n).
(rv-disjoint(p;n;Y;X) {}\mRightarrow{} rv-disjoint(p;n;Z;X) {}\mRightarrow{} rv-disjoint(p;n;Y + Z;X))
Date html generated:
2016_05_15-PM-11_47_18
Last ObjectModification:
2015_12_28-PM-07_15_56
Theory : randomness
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