Nuprl Lemma : prior-imax-class-lb
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[n:ℕ]. ∀[Z:EClass(ℕ)].
uiff(if e ∈b ((maximum x ≥ 0 with x from Z))' then ((maximum x ≥ 0 with x from Z))'(e) else -1 fi
≤ n;∀[e':E(Z)]. Z(e') ≤ n supposing e' ≤loc e )
supposing ¬↑e ∈b Z
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
imax-class: (maximum f[v] ≥ lb with v from X),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
nat: ℕ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
not: ¬A,
minus: -n,
natural_number: $n,
universe: Type
Lemmas :
prior-imax-class-lb2,
not_wf,
assert_wf,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
eclass_wf,
nat_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. \mforall{}[Z:EClass(\mBbbN{})].
uiff(if e \mmember{}\msubb{} ((maximum x \mgeq{} 0 with x from Z))'
then ((maximum x \mgeq{} 0 with x from Z))'(e)
else -1
fi \mleq{} n;\mforall{}[e':E(Z)]. Z(e') \mleq{} n supposing e' \mleq{}loc e )
supposing \mneg{}\muparrow{}e \mmember{}\msubb{} Z
Date html generated:
2015_07_21-PM-03_38_06
Last ObjectModification:
2015_01_27-PM-06_29_02
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