Nuprl Lemma : open-expectation-monotone
∀[p:FinProbSpace]. ∀[n,m:ℕ]. ∀[C:p-open(p)]. (E(n;λs.(C <n, s>)) ≤ E(m;λs.(C <m, s>))) supposing n ≤ m
Proof
Definitions occuring in Statement :
p-open: p-open(p),
expectation: E(n;F),
finite-prob-space: FinProbSpace,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
apply: f a,
lambda: λx.A[x],
pair: <a, b>
Lemmas :
expectation-constant,
false_wf,
le_wf,
null-seq_wf,
p-outcome_wf,
int_seg_wf,
length_wf,
rationals_wf,
expectation-monotone,
Error :qle_wf,
expectation_wf,
subtype_rel_set,
lelt_wf,
int-subtype-rationals,
Error :qle-int,
subtype_base_sq,
int_subtype_base,
sq_stable__le,
subtype_rel_dep_function,
subtype_rel-int_seg,
less_than_transitivity1,
less_than_irreflexivity,
le_weakening,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
less_than_wf,
decidable__equal_int,
natural_number_wf_p-outcome,
int_upper_subtype_nat,
nat_properties,
nequal-le-implies,
zero-add,
nat_wf,
decidable__lt,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
eq_int_wf,
equal-wf-base,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
uiff_transitivity,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
ws-monotone,
subtract_wf,
decidable__le,
not-le-2,
less-iff-le,
minus-one-mul,
minus-minus,
add-swap,
rv-shift_wf,
le_weakening2,
sq_stable_from_decidable,
Error :decidable__qle,
l_all_iff,
l_member_wf,
le-add-cancel-alt,
zero-le-nat,
non_neg_length,
length_wf_nat,
cons-seq_wf,
int_seg_properties,
int_seg_subtype-nat,
subtype_rel_self,
neg_assert_of_eq_int,
le-add-cancel2,
all_wf,
trivial-int-eq1
\mforall{}[p:FinProbSpace]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[C:p-open(p)]. (E(n;\mlambda{}s.(C <n, s>)) \mleq{} E(m;\mlambda{}s.(C <m, s>))) supposing n \000C\mleq{} m
Date html generated:
2015_07_17-AM-08_00_07
Last ObjectModification:
2015_01_27-AM-11_24_09
Home
Index