### Nuprl Lemma : list_ind_wf

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

Proof

Definitions occuring in Statement :  list_ind: list_ind list: `T 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: `ℙ` so_apply: `x[s]` implies: `P `` 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

Latex:
\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

Home Index