Nuprl Lemma : bag_filter_empty_lemma
∀p:Top. ([x∈{}|p[x]] ~ {})
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
empty-bag: {},
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
empty-bag: {},
bag-filter: [x∈b|p[x]],
top: Top
Lemmas referenced :
top_wf,
filter_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}p:Top. ([x\mmember{}\{\}|p[x]] \msim{} \{\})
Date html generated:
2016_05_15-PM-02_23_25
Last ObjectModification:
2015_12_27-AM-09_54_09
Theory : bags
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