Nuprl Lemma : hd-reverse
∀[T:Type]. ∀[L:T List]. (hd(rev(L)) ~ last(L))
Proof
Definitions occuring in Statement :
last: last(L),
hd: hd(l),
reverse: rev(as),
list: T List,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top
Lemmas referenced :
list_wf,
reverse-reverse,
subtype_rel_list,
top_wf,
last-reverse,
reverse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
because_Cache,
universeEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. (hd(rev(L)) \msim{} last(L))
Date html generated:
2016_05_14-PM-03_11_33
Last ObjectModification:
2015_12_26-PM-01_47_44
Theory : list_1
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