Nuprl Lemma : mem_empty_lemma
∀a,eq:Top. (a ∈ {} ~ False)
Proof
Definitions occuring in Statement :
empty-fset: {},
fset-member: a ∈ s,
top: Top,
all: ∀x:A. B[x],
false: False,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
empty-fset: {},
fset-member: a ∈ s,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff
Lemmas referenced :
top_wf,
deq_member_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{}a,eq:Top. (a \mmember{} \{\} \msim{} False)
Date html generated:
2016_05_14-PM-03_40_32
Last ObjectModification:
2015_12_26-PM-06_40_57
Theory : finite!sets
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