Nuprl Lemma : bag-combine-append-empty
∀[f,bs:Top]. (⋃x∈bs.f[x] @ [] ~ ⋃x∈bs.f[x])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
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-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
bag-union: bag-union(bbs),
concat: concat(ll),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
reduce_nil_lemma,
concat_append,
map-append-empty,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
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_49
Last ObjectModification:
2015_12_27-AM-09_26_13
Theory : bags
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