Nuprl Lemma : similar-bags_wf
∀[A:Type]. ∀[as,bs:bag(A)]. (similar-bags(A;as;bs) ∈ ℙ)
Proof
Definitions occuring in Statement :
similar-bags: similar-bags(A;as;bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
similar-bags: similar-bags(A;as;bs),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
all_wf,
iff_wf,
and_wf,
bag-member_wf,
less_than_wf,
bag-size_wf,
nat_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,
natural_numberEquality,
applyEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as,bs:bag(A)]. (similar-bags(A;as;bs) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-02_42_12
Last ObjectModification:
2015_12_27-AM-09_39_51
Theory : bags
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