Nuprl Lemma : bag-max-lb
∀[A:Type]. ∀[f:A ⟶ ℤ]. ∀[bs:bag(A)]. bag-max(f;bs) ↓∈ bag-map(f;bs) supposing 0 < #(bs)
Proof
Definitions occuring in Statement :
bag-max: bag-max(f;bs),
bag-member: x ↓∈ bs,
bag-size: #(bs),
bag-map: bag-map(f;bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-max: bag-max(f;bs),
implies: P ⇒ Q,
top: Top,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
bag_wf,
nat_wf,
bag-size_wf,
less_than_wf,
bag-size-map,
bag-map_wf,
imax-bag-lb
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
imageMemberEquality,
baseClosed,
natural_numberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \mforall{}[bs:bag(A)]. bag-max(f;bs) \mdownarrow{}\mmember{} bag-map(f;bs) supposing 0 < \#(bs)
Date html generated:
2016_05_15-PM-02_51_18
Last ObjectModification:
2016_01_16-AM-08_41_48
Theory : bags
Home
Index