Nuprl Lemma : last_singleton2
∀[x:Top]. (last([x]) ~ x)
Proof
Definitions occuring in Statement :
last: last(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,
last: last(L),
all: ∀x:A. B[x],
top: Top,
subtract: n - m,
select: L[n],
cons: [a / b]
Lemmas referenced :
length_of_cons_lemma,
length_of_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
Latex:
\mforall{}[x:Top]. (last([x]) \msim{} x)
Date html generated:
2016_05_14-PM-01_36_59
Last ObjectModification:
2015_12_26-PM-05_27_26
Theory : list_1
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