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
Lemmas :
rv-disjoint_wf,
random-variable_wf,
nat_wf,
finite-prob-space_wf,
rv-add_wf,
rv-disjoint-symmetry,
rv-disjoint-rv-add
\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:
2015_07_17-AM-07_59_09
Last ObjectModification:
2015_01_27-AM-11_22_38
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