Nuprl Lemma : mem_nil_lemma
∀a,s:Top.  (a ∈b [] ~ ff)
Proof
Definitions occuring in Statement : 
mem: a ∈b as
, 
nil: []
, 
bfalse: ff
, 
top: Top
, 
all: ∀x:A. B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
mem: a ∈b as
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
top: Top
, 
so_apply: x[s]
, 
bor_mon: <𝔹,∨b>
, 
grp_id: e
, 
pi2: snd(t)
, 
pi1: fst(t)
Lemmas referenced : 
mon_for_nil_lemma, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis
Latex:
\mforall{}a,s:Top.    (a  \mmember{}\msubb{}  []  \msim{}  ff)
Date html generated:
2016_05_16-AM-07_36_54
Last ObjectModification:
2015_12_28-PM-05_45_06
Theory : list_2
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