Nuprl 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))
Proof
Definitions occuring in Statement :
rv-compose: (x.F[x]) o X,
rv-disjoint: rv-disjoint(p;n;X;Y),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
rationals: ℚ
Lemmas :
all_wf,
not_wf,
equal_wf,
p-outcome_wf,
rv-compose_wf,
random-variable_wf,
int_seg_wf,
rv-disjoint_wf,
nat_wf,
finite-prob-space_wf,
rationals_wf
\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))
Date html generated:
2015_07_17-AM-07_59_18
Last ObjectModification:
2015_01_27-AM-11_24_44
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