Nuprl Lemma : rv-disjoint_wf
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[X,Y:RandomVariable(p;n)]. (rv-disjoint(p;n;X;Y) ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-disjoint: rv-disjoint(p;n;X;Y),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
rv-disjoint: rv-disjoint(p;n;X;Y),
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
int_seg_wf,
or_wf,
p-outcome_wf,
not_wf,
equal_wf,
rationals_wf,
nat_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
intEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[X,Y:RandomVariable(p;n)]. (rv-disjoint(p;n;X;Y) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-AM-00_35_02
Last ObjectModification:
2017_07_26-PM-07_00_00
Theory : randomness
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