Nuprl Lemma : test-bag-filter-empty
∀[p:Top]. ([b∈{}|p[b]] ~ {})
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
empty-bag: {},
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s],
uall: ∀[x:A]. B[x]
Lemmas referenced :
bag_filter_empty_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[p:Top]. ([b\mmember{}\{\}|p[b]] \msim{} \{\})
Date html generated:
2016_05_15-PM-02_23_39
Last ObjectModification:
2015_12_27-AM-09_54_04
Theory : bags
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