Nuprl Lemma : bag-null_wf
∀T:Type. ∀bs:bag(T). (bag-null(bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag-null: bag-null(bs),
bag: bag(T),
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
bag-null: bag-null(bs)
Lemmas referenced :
bag-subtype-list,
list_wf,
top_wf,
equal_wf,
bag_wf,
null_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
cumulativity,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}bs:bag(T). (bag-null(bs) \mmember{} \mBbbB{})
Date html generated:
2017_10_01-AM-08_45_31
Last ObjectModification:
2017_07_26-PM-04_30_48
Theory : bags
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