Nuprl Lemma : rv-disjoint-monotone-in-first
∀p:FinProbSpace. ∀n:ℕ. ∀X,Y:RandomVariable(p;n). (rv-disjoint(p;n;X;Y) ⇒ (∀m:ℕ. rv-disjoint(p;m;X;Y) supposing n ≤ m))
Proof
Definitions occuring in Statement :
rv-disjoint: rv-disjoint(p;n;X;Y),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas :
less_than_wf,
decidable__lt,
int_seg_wf,
le_wf,
nat_wf,
rv-disjoint_wf,
random-variable_wf,
finite-prob-space_wf,
equal-wf-T-base,
all_wf,
equal_wf,
not_wf,
iff_weakening_equal,
less_than_transitivity1,
int-subtype-rationals,
subtype_rel_self,
false_wf,
subtype_rel-int_seg,
l_member_wf,
Error :qle_wf,
l_all_wf2,
sq_stable__le,
select_wf,
length_wf,
Error :qsum_wf,
rationals_wf,
p-outcome_wf,
subtype_rel_dep_function,
lelt_wf,
or_wf,
le-add-cancel2,
add_functionality_wrt_le,
less-iff-le,
zero-add,
add-commutes,
add-swap,
minus-one-mul,
minus-add,
add-associates,
condition-implies-le,
not-le-2,
decidable__le,
not-equal-2
\mforall{}p:FinProbSpace. \mforall{}n:\mBbbN{}. \mforall{}X,Y:RandomVariable(p;n).
(rv-disjoint(p;n;X;Y) {}\mRightarrow{} (\mforall{}m:\mBbbN{}. rv-disjoint(p;m;X;Y) supposing n \mleq{} m))
Date html generated:
2015_07_17-AM-07_59_16
Last ObjectModification:
2015_07_16-AM-09_52_15
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