Nuprl Lemma : member-empty-fset
∀[eq,x:Top]. (x ∈ {} ~ False)
Proof
Definitions occuring in Statement :
empty-fset: {},
fset-member: a ∈ s,
uall: ∀[x:A]. B[x],
top: Top,
false: False,
sqequal: s ~ t
Definitions unfolded in proof :
empty-fset: {},
fset-member: a ∈ s,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uall: ∀[x:A]. B[x]
Lemmas referenced :
deq_member_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[eq,x:Top]. (x \mmember{} \{\} \msim{} False)
Date html generated:
2017_02_20-AM-10_49_12
Last ObjectModification:
2017_02_03-AM-11_02_01
Theory : finite!sets
Home
Index