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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