Nuprl Lemma : nullset_wf
∀[p:FinProbSpace]. ∀[S:(ℕ ⟶ Outcome) ⟶ ℙ]. (nullset(p;S) ∈ ℙ)
Proof
Definitions occuring in Statement :
nullset: nullset(p;S),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
nullset: nullset(p;S),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
all_wf,
rationals_wf,
qless_wf,
exists_wf,
p-open_wf,
nat_wf,
p-outcome_wf,
p-open-member_wf,
p-measure-le_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
natural_numberEquality,
applyEquality,
because_Cache,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
productEquality,
functionEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[S:(\mBbbN{} {}\mrightarrow{} Outcome) {}\mrightarrow{} \mBbbP{}]. (nullset(p;S) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-11_50_00
Last ObjectModification:
2015_12_28-PM-07_14_31
Theory : randomness
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