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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