Nuprl Lemma : ml-maprevappend_wf
∀[T,A:Type]. ∀[f:A ⟶ T].
  ∀[as:A List]. ∀[bs:T List].  (ml-maprevappend(f;as;bs) ∈ T List) supposing valueall-type(T) ∧ valueall-type(A) ∧ A
Proof
Definitions occuring in Statement : 
ml-maprevappend: ml-maprevappend(f;as;bs)
, 
list: T List
, 
valueall-type: valueall-type(T)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
prop: ℙ
Lemmas referenced : 
ml-maprevappend-sq, 
append_wf, 
map_wf, 
reverse_wf, 
list_wf, 
valueall-type_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
independent_pairFormation, 
cumulativity, 
functionExtensionality, 
applyEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
productEquality, 
functionEquality, 
universeEquality
Latex:
\mforall{}[T,A:Type].  \mforall{}[f:A  {}\mrightarrow{}  T].
    \mforall{}[as:A  List].  \mforall{}[bs:T  List].    (ml-maprevappend(f;as;bs)  \mmember{}  T  List) 
    supposing  valueall-type(T)  \mwedge{}  valueall-type(A)  \mwedge{}  A
Date html generated:
2017_09_29-PM-05_51_14
Last ObjectModification:
2017_05_19-PM-03_24_00
Theory : ML
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