Nuprl Lemma : longest-prefix-singleton
∀[x,P:Top]. (longest-prefix(P;[x]) ~ [])
Proof
Definitions occuring in Statement :
longest-prefix: longest-prefix(P;L),
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
longest-prefix: longest-prefix(P;L),
let: let,
all: ∀x:A. B[x],
top: Top,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
null_cons_lemma,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
null_nil_lemma,
reduce_tl_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[x,P:Top]. (longest-prefix(P;[x]) \msim{} [])
Date html generated:
2016_05_15-PM-03_43_37
Last ObjectModification:
2015_12_27-PM-01_18_54
Theory : general
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