Nuprl Lemma : bag-max_wf
∀[A:Type]. ∀[f:A ⟶ ℤ]. ∀[bs:bag(A)]. bag-max(f;bs) ∈ ℤ supposing 0 < #(bs)
Proof
Definitions occuring in Statement :
bag-max: bag-max(f;bs),
bag-size: #(bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
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),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
imax-bag_wf,
bag-map_wf,
bag-size-map,
istype-less_than,
bag-size_wf,
bag_wf,
istype-int,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
intEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
Error :memTop,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \mforall{}[bs:bag(A)]. bag-max(f;bs) \mmember{} \mBbbZ{} supposing 0 < \#(bs)
Date html generated:
2020_05_20-AM-08_02_09
Last ObjectModification:
2019_12_31-PM-06_32_14
Theory : bags
Home
Index