Nuprl Lemma : reverse-cons
∀[as,a:Top]. (rev([a / as]) ~ rev(as) @ [a])
Proof
Definitions occuring in Statement :
reverse: rev(as),
append: as @ bs,
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,
reverse: rev(as),
all: ∀x:A. B[x],
top: Top,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
rev_app_cons_lemma,
rev-append-property-top,
list_ind_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,
isectElimination,
hypothesisEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[as,a:Top]. (rev([a / as]) \msim{} rev(as) @ [a])
Date html generated:
2016_05_14-AM-06_54_24
Last ObjectModification:
2015_12_26-PM-00_19_24
Theory : list_0
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