Nuprl Lemma : bag-no-repeats_wf
∀[T:Type]. ∀[bs:bag(T)].  (bag-no-repeats(T;bs) ∈ ℙ)
Proof
Definitions occuring in Statement : 
bag-no-repeats: bag-no-repeats(T;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
, 
bag-no-repeats: bag-no-repeats(T;bs)
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
so_apply: x[s]
Lemmas referenced : 
squash_wf, 
exists_wf, 
list_wf, 
and_wf, 
equal_wf, 
bag_wf, 
list-subtype-bag, 
no_repeats_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaEquality, 
applyEquality, 
because_Cache, 
independent_isectElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[bs:bag(T)].    (bag-no-repeats(T;bs)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-02_33_34
Last ObjectModification:
2015_12_27-AM-09_47_00
Theory : bags
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