Nuprl Lemma : ws-constant
∀[a:ℚ]. ∀[p:FinProbSpace]. ∀[F:Outcome ─→ ℚ]. weighted-sum(p;F) = a ∈ ℚ supposing ∀x:Outcome. ((F x) = a ∈ ℚ)
Proof
Definitions occuring in Statement :
weighted-sum: weighted-sum(p;F),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
equal: s = t ∈ T,
rationals: ℚ
Lemmas :
all_wf,
int_seg_wf,
length_wf,
rationals_wf,
equal_wf,
set_wf,
list_wf,
equal-wf-T-base,
Error :qsum_wf,
select_wf,
sq_stable__le,
l_all_wf2,
l_member_wf,
Error :qle_wf,
int-subtype-rationals,
squash_wf,
true_wf,
qmul_wf,
iff_weakening_equal,
Error :prod_sum_l_q,
non_neg_length,
length_wf_nat,
Error :qmul_one_qrng
\mforall{}[a:\mBbbQ{}]. \mforall{}[p:FinProbSpace]. \mforall{}[F:Outcome {}\mrightarrow{} \mBbbQ{}].
weighted-sum(p;F) = a supposing \mforall{}x:Outcome. ((F x) = a)
Date html generated:
2015_07_17-AM-07_58_28
Last ObjectModification:
2015_02_03-PM-09_44_12
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