Nuprl Lemma : rv-le_witness
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[X,Y:RandomVariable(p;n)]. (X ≤ Y ⇒ (λs.Ax ∈ X ≤ Y))
Proof
Definitions occuring in Statement :
rv-le: X ≤ Y,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
lambda: λx.A[x],
axiom: Ax
Definitions unfolded in proof :
rv-le: X ≤ Y,
random-variable: RandomVariable(p;n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
finite-prob-space: FinProbSpace,
and: P ∧ Q,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
p-outcome: Outcome,
so_apply: x[s]
Lemmas referenced :
int_seg_wf,
p-outcome_wf,
all_wf,
qle_wf,
length_wf,
rationals_wf,
nat_wf,
finite-prob-space_wf,
qle_witness
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
hypothesis,
functionEquality,
lemma_by_obid,
isectElimination,
natural_numberEquality,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
independent_functionElimination
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[X,Y:RandomVariable(p;n)]. (X \mleq{} Y {}\mRightarrow{} (\mlambda{}s.Ax \mmember{} X \mleq{} Y))
Date html generated:
2016_05_15-PM-11_48_21
Last ObjectModification:
2015_12_28-PM-07_15_06
Theory : randomness
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