Nuprl Lemma : bag-combine-unit-left-top
∀[f,a:Top]. (⋃x∈[a].f[x] ~ f[a] + {})
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
bag-append: as + bs,
empty-bag: {},
cons: [a / b],
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,
empty-bag: {},
bag-append: as + bs,
bag-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
bag-union: bag-union(bbs),
all: ∀x:A. B[x],
top: Top,
concat: concat(ll)
Lemmas referenced :
map_cons_lemma,
map_nil_lemma,
reduce_cons_lemma,
reduce_nil_lemma,
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,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[f,a:Top]. (\mcup{}x\mmember{}[a].f[x] \msim{} f[a] + \{\})
Date html generated:
2016_05_15-PM-02_28_15
Last ObjectModification:
2015_12_27-AM-09_50_44
Theory : bags
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