Nuprl Lemma : p-open-measure-one_wf
∀[p:FinProbSpace]. ∀[C:p-open(p)]. (measure(C) = 1 ∈ ℙ)
Proof
Definitions occuring in Statement :
p-open-measure-one: measure(C) = 1,
p-open: p-open(p),
finite-prob-space: FinProbSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
p-open-measure-one: measure(C) = 1,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
so_apply: x[s],
uimplies: b supposing a,
int_nzero: ℤ-o,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
random-variable: RandomVariable(p;n),
p-open: p-open(p),
p-outcome: Outcome,
int_seg: {i..j-},
finite-prob-space: FinProbSpace
Lemmas referenced :
finite-prob-space_wf,
p-open_wf,
length_wf,
lelt_wf,
p-outcome_wf,
int_seg_wf,
expectation_wf,
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
nat_plus_properties,
nequal_wf,
subtype_rel_sets,
int_nzero-rational,
int-subtype-rationals,
less_than_wf,
rationals_wf,
subtype_rel_set,
qdiv_wf,
qsub_wf,
qle_wf,
nat_wf,
exists_wf,
nat_plus_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
natural_numberEquality,
applyEquality,
because_Cache,
hypothesisEquality,
intEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
dependent_pairEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[C:p-open(p)]. (measure(C) = 1 \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-11_49_06
Last ObjectModification:
2016_01_17-AM-10_05_51
Theory : randomness
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