Nuprl Lemma : empty_intersect_lemma
∀b,eq:Top. ({} ⋂ b ~ {})
Proof
Definitions occuring in Statement :
empty-fset: {},
fset-intersection: a ⋂ b,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
empty-fset: {},
fset-intersection: a ⋂ b,
fset-filter: {x ∈ s | 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{}b,eq:Top. (\{\} \mcap{} b \msim{} \{\})
Date html generated:
2016_05_14-PM-03_45_53
Last ObjectModification:
2015_12_26-PM-06_37_28
Theory : finite!sets
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