Nuprl Lemma : imax-class-lb
∀[Info,T:Type]. ∀[f:T ─→ ℤ]. ∀[es:EO+(Info)]. ∀[lb:ℤ]. ∀[X:EClass(T)]. ∀[e:E(X)]. ∀[n:ℤ].
uiff((maximum f[v] ≥ lb with v from X)(e) ≤ n;(∀[e':E(X)]. f[X(e')] ≤ n supposing e' ≤loc e ) ∧ (lb ≤ n))
Proof
Definitions occuring in Statement :
imax-class: (maximum f[v] ≥ lb with v from X),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
and: P ∧ Q,
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
iff_weakening_uiff,
le_wf,
imax-list_wf,
cons_wf,
map_wf,
eclass-vals_wf,
es-interface-predecessors_wf,
subtype_rel_list,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
Id_wf,
es-loc_wf,
length_wf,
non_neg_length,
length_wf_nat,
map_length,
length_cons,
l_all_wf2,
l_member_wf,
imax-list-lb,
less_than_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-le_wf,
uall_wf,
isect_wf,
imax-class-val,
iff_weakening_equal,
imax-class_wf,
es-E-interface-property,
es-E-interface_functionality,
is-imax-class,
assert_wf,
uiff_wf,
subtype_top,
eclass_wf,
map-map,
l_all_cons,
l_all_map,
select_wf,
sq_stable__le,
int_seg_wf,
set_wf,
sq_stable__assert,
l_all_iff,
es-le-loc,
member-interface-predecessors,
l_member-settype,
equal_wf,
l_all-interface-predecessors
Latex:
\mforall{}[Info,T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[es:EO+(Info)]. \mforall{}[lb:\mBbbZ{}]. \mforall{}[X:EClass(T)]. \mforall{}[e:E(X)]. \mforall{}[n:\mBbbZ{}].
uiff((maximum f[v] \mgeq{} lb with v from X)(e) \mleq{} n;(\mforall{}[e':E(X)]. f[X(e')] \mleq{} n supposing e' \mleq{}loc e )
\mwedge{} (lb \mleq{} n))
Date html generated:
2015_07_21-PM-03_37_42
Last ObjectModification:
2015_02_04-PM-06_14_53
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