Nuprl Lemma : list_ind-wf-co-list-islist
∀[A,B:Type]. ∀[L:co-list-islist(A)]. ∀[x:B]. ∀[F:A ⟶ co-list-islist(A) ⟶ B ⟶ B].
(rec-case(L) of
[] => x
h::t =>
r.F[h;t;r] ∈ B)
Proof
Definitions occuring in Statement :
co-list-islist: co-list-islist(T),
list_ind: list_ind,
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: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
co-list-islist-ext-list,
list_ind_wf,
ext-eq_inversion,
co-list-islist_wf,
list_wf,
subtype_rel_weakening
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
independent_isectElimination,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:co-list-islist(A)]. \mforall{}[x:B]. \mforall{}[F:A {}\mrightarrow{} co-list-islist(A) {}\mrightarrow{} B {}\mrightarrow{} B].
(rec-case(L) of
[] => x
h::t =>
r.F[h;t;r] \mmember{} B)
Date html generated:
2016_05_15-PM-10_10_53
Last ObjectModification:
2015_12_27-PM-05_58_32
Theory : eval!all
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