Nuprl Lemma : expectation-rv-const
∀[p:FinProbSpace]. ∀[a:ℚ]. ∀[n:ℕ]. (E(n;a) = a ∈ ℚ)
Proof
Definitions occuring in Statement :
expectation: E(n;F),
rv-const: a,
finite-prob-space: FinProbSpace,
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
rv-const: a,
nat: ℕ
Lemmas referenced :
expectation-constant,
rv-const_wf,
int_seg_wf,
p-outcome_wf,
nat_wf,
rationals_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
lambdaFormation,
sqequalRule,
functionEquality,
natural_numberEquality,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[a:\mBbbQ{}]. \mforall{}[n:\mBbbN{}]. (E(n;a) = a)
Date html generated:
2016_05_15-PM-11_46_47
Last ObjectModification:
2015_12_28-PM-07_15_59
Theory : randomness
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