Nuprl Lemma : bag-merge_wf
∀A,B:Type. ∀as:bag(A). ∀bs:bag(B).  (bag-merge(as;bs) ∈ bag(A + B))
Proof
Definitions occuring in Statement : 
bag-merge: bag-merge(as;bs)
, 
bag: bag(T)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
union: left + right
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
bag-merge: bag-merge(as;bs)
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
bag-append_wf, 
bag-map_wf, 
bag_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
unionEquality, 
hypothesisEquality, 
lambdaEquality, 
inlEquality, 
hypothesis, 
inrEquality, 
universeEquality
Latex:
\mforall{}A,B:Type.  \mforall{}as:bag(A).  \mforall{}bs:bag(B).    (bag-merge(as;bs)  \mmember{}  bag(A  +  B))
Date html generated:
2016_05_15-PM-02_35_24
Last ObjectModification:
2015_12_27-AM-09_45_57
Theory : bags
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