Nuprl Lemma : reverse_append
∀[T:Type]. ∀[as,bs:T List]. (rev(as @ bs) = (rev(bs) @ rev(as)) ∈ (T List))
Proof
Definitions occuring in Statement :
reverse: rev(as),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
reverse: rev(as),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
rev-append-append,
subtype_rel_list,
top_wf,
list_wf,
append_assoc,
append-nil,
rev-append_wf,
nil_wf,
list_ind_nil_lemma,
append_wf,
rev-append-property
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
axiomEquality,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (rev(as @ bs) = (rev(bs) @ rev(as)))
Date html generated:
2016_05_14-AM-07_35_23
Last ObjectModification:
2015_12_26-PM-02_11_23
Theory : list_1
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