Nuprl Lemma : weighted-sum_wf2
∀[p:FinProbSpace]. ∀[F:Outcome ⟶ ℚ]. (weighted-sum(p;F) ∈ ℚ)
Proof
Definitions occuring in Statement :
weighted-sum: weighted-sum(p;F),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
int-subtype-rationals,
qle_wf,
l_member_wf,
l_all_wf2,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
select_wf,
qsum_wf,
equal-wf-T-base,
list_wf,
set_wf,
rationals_wf,
length_wf,
int_seg_wf,
weighted-sum_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
natural_numberEquality,
isect_memberEquality,
because_Cache,
lambdaEquality,
productEquality,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
baseClosed,
lambdaFormation,
applyEquality,
setEquality
Latex:
\mforall{}[p:FinProbSpace]. \mforall{}[F:Outcome {}\mrightarrow{} \mBbbQ{}]. (weighted-sum(p;F) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_45_41
Last ObjectModification:
2016_01_17-AM-10_07_20
Theory : randomness
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