Nuprl Lemma : ws-lower-bound
∀[p:FinProbSpace]. ∀[F:Outcome ─→ ℚ]. ∀[q:ℚ]. q ≤ weighted-sum(p;F) supposing ∀x:Outcome. (q ≤ (F x))
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],
rationals: ℚ
Lemmas :
ws-monotone,
sq_stable_from_decidable,
Error :qle_wf,
Error :decidable__qle,
l_all_iff,
l_member_wf,
Error :qle_witness,
weighted-sum_wf2,
all_wf,
int_seg_wf,
length_wf,
rationals_wf,
set_wf,
list_wf,
equal-wf-T-base,
Error :qsum_wf,
select_wf,
sq_stable__le,
l_all_wf2,
int-subtype-rationals,
squash_wf,
true_wf,
ws-constant,
p-outcome_wf
\mforall{}[p:FinProbSpace]. \mforall{}[F:Outcome {}\mrightarrow{} \mBbbQ{}]. \mforall{}[q:\mBbbQ{}].
q \mleq{} weighted-sum(p;F) supposing \mforall{}x:Outcome. (q \mleq{} (F x))
Date html generated:
2015_07_17-AM-07_58_29
Last ObjectModification:
2015_01_27-AM-11_24_13
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