Nuprl Lemma : bag-maximals_wf
∀[T:Type]. ∀[b:bag(T)]. ∀[R:T ⟶ T ⟶ 𝔹].  (bag-maximals(b;R) ∈ bag(T))
Proof
Definitions occuring in Statement : 
bag-maximals: bag-maximals(bg;R)
, 
bag: bag(T)
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag-maximals: bag-maximals(bg;R)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
uimplies: b supposing a
Lemmas referenced : 
bag-filter_wf, 
bag-maximal?_wf, 
subtype_rel_bag, 
assert_wf, 
bool_wf, 
bag_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
hypothesis, 
applyEquality, 
setEquality, 
independent_isectElimination, 
setElimination, 
rename, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[b:bag(T)].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbB{}].    (bag-maximals(b;R)  \mmember{}  bag(T))
Date html generated:
2016_05_15-PM-02_30_41
Last ObjectModification:
2015_12_27-AM-09_48_37
Theory : bags
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