Nuprl Lemma : ws_nil_lemma
∀F:Top. (weighted-sum([];F) ~ 0)
Proof
Definitions occuring in Statement : 
weighted-sum: weighted-sum(p;F)
, 
nil: []
, 
top: Top
, 
all: ∀x:A. B[x]
, 
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
, 
add_grp_of_rng: r↓+gp
, 
grp_op: *
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
grp_id: e
, 
select: L[n]
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
nil: []
, 
it: ⋅
, 
so_lambda: λ2x y.t[x; y]
, 
top: Top
, 
so_apply: x[s1;s2]
, 
lt_int: i <z j
, 
qrng: <ℚ+*>
, 
rng_plus: +r
, 
rng_zero: 0
, 
subtract: n - m
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
Lemmas referenced : 
base_wf, 
stuck-spread, 
length_of_nil_lemma, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
hypothesis, 
lemma_by_obid, 
sqequalRule, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
baseClosed, 
independent_isectElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality
Latex:
\mforall{}F:Top.  (weighted-sum([];F)  \msim{}  0)
Date html generated:
2016_05_15-PM-11_45_10
Last ObjectModification:
2016_01_17-AM-10_07_22
Theory : randomness
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