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