Nuprl Lemma : ws_single_lemma
∀F,p:Top. (weighted-sum([p];F) ~ 0 + ((F 0) * p))
Proof
Definitions occuring in Statement :
weighted-sum: weighted-sum(p;F),
qmul: r * s,
qadd: r + s,
cons: [a / b],
nil: [],
top: Top,
all: ∀x:A. B[x],
apply: f a,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
weighted-sum: weighted-sum(p;F),
qsum: Σa ≤ j < b. E[j],
rng_sum: rng_sum,
mon_itop: Π lb ≤ i < ub. E[i],
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
top: Top,
add_grp_of_rng: r↓+gp,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
grp_id: e,
qrng: <ℚ+*>,
rng_plus: +r,
rng_zero: 0,
lt_int: i <z j,
infix_ap: x f y,
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
select: L[n],
cons: [a / b],
bfalse: ff
Lemmas referenced :
top_wf,
length_of_cons_lemma,
length_of_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}F,p:Top. (weighted-sum([p];F) \msim{} 0 + ((F 0) * p))
Date html generated:
2016_05_15-PM-11_45_12
Last ObjectModification:
2015_12_28-PM-07_16_42
Theory : randomness
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