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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