Nuprl Lemma : count_nil_lemma
∀a,s:Top. (a #∈ [] ~ 0)
Proof
Definitions occuring in Statement :
count: a #∈ as,
nil: [],
top: Top,
all: ∀x:A. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
count: a #∈ as,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
int_add_grp: <ℤ+>,
grp_id: e,
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
top_wf,
mon_for_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,s:Top. (a \#\mmember{} [] \msim{} 0)
Date html generated:
2016_05_16-AM-07_39_26
Last ObjectModification:
2015_12_28-PM-05_43_31
Theory : list_2
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