Nuprl Lemma : p-measure-le_wf
∀[p:FinProbSpace]. ∀[q:ℚ]. ∀[C:p-open(p)].  (measure(C) ≤ q ∈ ℙ)
Proof
Definitions occuring in Statement : 
p-measure-le: measure(C) ≤ q
, 
p-open: p-open(p)
, 
finite-prob-space: FinProbSpace
, 
rationals: ℚ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
p-measure-le: measure(C) ≤ q
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
random-variable: RandomVariable(p;n)
, 
p-open: p-open(p)
, 
p-outcome: Outcome
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
int_seg: {i..j-}
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
finite-prob-space: FinProbSpace
Lemmas referenced : 
all_wf, 
nat_wf, 
qless_wf, 
expectation_wf, 
int_seg_wf, 
p-outcome_wf, 
subtype_rel_set, 
rationals_wf, 
lelt_wf, 
int-subtype-rationals, 
length_wf, 
p-open_wf, 
finite-prob-space_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
lambdaEquality, 
hypothesisEquality, 
applyEquality, 
setElimination, 
rename, 
dependent_pairEquality, 
because_Cache, 
functionEquality, 
natural_numberEquality, 
intEquality, 
independent_isectElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality
Latex:
\mforall{}[p:FinProbSpace].  \mforall{}[q:\mBbbQ{}].  \mforall{}[C:p-open(p)].    (measure(C)  \mleq{}  q  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-11_48_52
Last ObjectModification:
2015_12_28-PM-07_14_40
Theory : randomness
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