Step
*
of Lemma
rv-disjoint-compose
∀F,G:ℚ ─→ ℚ. ∀p:FinProbSpace. ∀n:ℕ. ∀X,Y:RandomVariable(p;n).
(rv-disjoint(p;n;X;Y)
⇒ rv-disjoint(p;n;(X.F[X]) o X;(Y.G[Y]) o Y))
BY
{ (Auto
THEN RepeatFor 3 (ParallelLast)
THEN Try ((Fold `random-variable` 0 THEN Auto))
THEN (Try ((Fold `p-outcome` 0 THEN Auto)) THEN RepeatFor 3 (ParallelLast))
THEN Try ((RepUR ``rv-compose`` 0 THEN EqCD THEN Auto))) }
Latex:
\mforall{}F,G:\mBbbQ{} {}\mrightarrow{} \mBbbQ{}. \mforall{}p:FinProbSpace. \mforall{}n:\mBbbN{}. \mforall{}X,Y:RandomVariable(p;n).
(rv-disjoint(p;n;X;Y) {}\mRightarrow{} rv-disjoint(p;n;(X.F[X]) o X;(Y.G[Y]) o Y))
By
(Auto
THEN RepeatFor 3 (ParallelLast)
THEN Try ((Fold `random-variable` 0 THEN Auto))
THEN (Try ((Fold `p-outcome` 0 THEN Auto)) THEN RepeatFor 3 (ParallelLast))
THEN Try ((RepUR ``rv-compose`` 0 THEN EqCD THEN Auto)))
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