Nuprl Lemma : expectation-non-neg
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[Y:RandomVariable(p;n)]. 0 ≤ E(n;Y) supposing 0 ≤ Y
Proof
Definitions occuring in Statement :
rv-le: X ≤ Y,
expectation: E(n;F),
rv-const: a,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Lemmas :
expectation-monotone,
rv-const_wf,
int-subtype-rationals,
Error :qle_wf,
squash_wf,
true_wf,
rationals_wf,
expectation-rv-const,
expectation_wf,
iff_weakening_equal,
Error :qle_witness,
rv-le_wf,
random-variable_wf,
nat_wf,
finite-prob-space_wf
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[Y:RandomVariable(p;n)]. 0 \mleq{} E(n;Y) supposing 0 \mleq{} Y
Date html generated:
2015_07_17-AM-07_59_52
Last ObjectModification:
2015_02_03-PM-09_44_41
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