{ 
[Info,T:Type]. [f:T 
]. [es:EO+(Info)]. [lb:]. [X:EClass(T)].
[e:E(X)].
((maximum f[v] 
lb with v from X)(e)
= imax-list([lb / map(
v.f[v];X(
(X)(e)))])) }
{ Proof }
Definitions occuring in Statement :
imax-class: (maximum f[v] lb with v from X),
es-interface-predecessors: (X)(e),
eclass-vals: X(L),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
map: map(f;as),
uall: [x:A]. B[x],
so_apply: x[s],
lambda: x.A[x],
function: x:A B[x],
cons: [car / cdr],
int: ,
universe: Type,
equal: s = t,
imax-list: imax-list(L)
Definitions :
uall: [x:A]. B[x],
imax-class: (maximum f[v] lb with v from X),
imax-list: imax-list(L),
eclass-vals: X(L),
member: t 
T,
top: Top,
assert: 
b,
btrue: tt,
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
true: True,
hd: hd(l),
tl: tl(l),
compose: f o g,
subtype: S 
T,
so_lambda: 
x y.t[x; y],
so_apply: x[s],
es-E-interface: E(X),
uimplies: b supposing a,
sq_type: SQType(T),
implies: P 
Q,
guard: {T},
so_apply: x[s1;s2]
Lemmas :
es-interface-accum-val,
is-interface-accum,
subtype_base_sq,
bool_wf,
bool_subtype_base,
map-map,
es-interface-predecessors_wf,
top_wf,
Id_wf,
es-loc_wf,
event-ordering+_inc,
es-E-interface_wf,
eclass_wf,
es-E_wf,
event-ordering+_wf,
assert_elim,
in-eclass_wf,
list_accum-map,
es-interface-top,
list_accum_wf,
imax_wf,
eclass-val_wf
\mforall{}[Info,T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[es:EO+(Info)]. \mforall{}[lb:\mBbbZ{}]. \mforall{}[X:EClass(T)]. \mforall{}[e:E(X)].
((maximum f[v] \mgeq{} lb with v from X)(e) = imax-list([lb / map(\mlambda{}v.f[v];X(\mleq{}(X)(e)))]))
Date html generated:
2011_08_16-PM-04_36_18
Last ObjectModification:
2011_06_20-AM-00_59_10
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