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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