Nuprl Lemma : list_ind_wf

[A,B:Type]. ∀[x:B]. ∀[F:A ⟶ (A List) ⟶ B ⟶ B]. ∀[L:A List].  (rec-case(L) of [] => h::t => r.F[h;t;r] ∈ B)


Definitions occuring in Statement :  list_ind: list_ind list: List uall: [x:A]. B[x] so_apply: x[s1;s2;s3] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] prop: so_apply: x[s] implies:  Q all: x:A. B[x]
Lemmas referenced :  list_ind-general-wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality hypothesis equalityTransitivity equalitySymmetry axiomEquality isect_memberEquality because_Cache functionEquality universeEquality

\mforall{}[A,B:Type].  \mforall{}[x:B].  \mforall{}[F:A  {}\mrightarrow{}  (A  List)  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[L:A  List].
    (rec-case(L)  of
      []  =>  x
      h::t  =>
        r.F[h;t;r]  \mmember{}  B)

Date html generated: 2016_05_14-AM-06_26_46
Last ObjectModification: 2015_12_26-PM-00_41_46

Theory : list_0

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