Nuprl Lemma : bag-combine-bag-append-empty
∀[f,bs:Top].  (⋃x∈bs.f[x] + [] ~ ⋃x∈bs.f[x])
Proof
Definitions occuring in Statement : 
bag-combine: ⋃x∈bs.f[x]
, 
bag-append: as + bs
, 
nil: []
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag-append: as + bs
, 
so_lambda: λ2x.t[x]
, 
top: Top
, 
so_apply: x[s]
Lemmas referenced : 
bag-combine-append-empty, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
sqequalRule, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesisEquality, 
hypothesis, 
sqequalAxiom, 
because_Cache
Latex:
\mforall{}[f,bs:Top].    (\mcup{}x\mmember{}bs.f[x]  +  []  \msim{}  \mcup{}x\mmember{}bs.f[x])
Date html generated:
2016_05_15-PM-03_08_56
Last ObjectModification:
2015_12_27-AM-09_26_00
Theory : bags
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