Nuprl Lemma : imax-class-val
∀[Info,T:Type]. ∀[f:T ─→ ℤ]. ∀[es:EO+(Info)]. ∀[lb:ℤ]. ∀[X:EClass(T)]. ∀[e:E(X)].
((maximum f[v] ≥ lb with v from X)(e) = imax-list([lb / map(λv.f[v];X(≤(X)(e)))]) ∈ ℤ)
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),
imax-list: imax-list(L),
map: map(f;as),
cons: [a / b],
uall: ∀[x:A]. B[x],
so_apply: x[s],
lambda: λx.A[x],
function: x:A ─→ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
list_accum-map,
list_accum_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
Id_wf,
es-loc_wf,
es-interface-predecessors_wf,
imax_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base
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)].
((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:
2015_07_20-PM-03_47_48
Last ObjectModification:
2015_01_27-PM-10_09_59
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