Nuprl Lemma : prior-imax-class-lb2
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[n:ℕ]. ∀[A:Type]. ∀[f:A ─→ ℕ]. ∀[Z:EClass(A)].
uiff(if e ∈b ((maximum f[x] ≥ 0 with x from Z))' then ((maximum f[x] ≥ 0 with x from Z))'(e) else -1 fi
≤ n;∀[e':E(Z)]. f[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],
so_apply: x[s],
le: A ≤ B,
not: ¬A,
function: x:A ─→ B[x],
minus: -n,
natural_number: $n,
universe: Type
Lemmas :
prior-val-val,
imax-class_wf,
nat_wf,
subtype_base_sq,
int_subtype_base,
is-imax-class,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
less_than_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
bool_wf,
bool_subtype_base,
es-le_wf,
es-E-interface_wf,
uall_wf,
isect_wf,
le_wf,
es-locl_transitivity1,
es-le_weakening,
sq_stable__le,
iff_weakening_uiff,
imax-class-lb,
assert_wf,
uiff_wf,
decidable__es-le,
decidable__es-locl,
es-le-not-locl,
es-le-loc,
not_assert_elim,
and_wf,
equal_wf,
btrue_neq_bfalse,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
is-prior-val,
es-E-interface-property,
subtype_top,
es-E-interface_functionality,
es-locl_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[Z:EClass(A)].
uiff(if e \mmember{}\msubb{} ((maximum f[x] \mgeq{} 0 with x from Z))'
then ((maximum f[x] \mgeq{} 0 with x from Z))'(e)
else -1
fi \mleq{} n;\mforall{}[e':E(Z)]. f[Z(e')] \mleq{} n supposing e' \mleq{}loc e )
supposing \mneg{}\muparrow{}e \mmember{}\msubb{} Z
Date html generated:
2015_07_21-PM-03_37_54
Last ObjectModification:
2015_01_27-PM-06_35_59
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