Nuprl Lemma : list_ind-wf-co-list-islist2
∀[A:Type]. ∀[B:co-list-islist(A) ⟶ Type]. ∀[L:co-list-islist(A)]. ∀[x:B[conil()]]. ∀[F:a:A
⟶ L:co-list-islist(A)
⟶ B[L]
⟶ B[cocons(a;L)]].
(rec-case(L) of
[] => x
h::t =>
r.F[h;t;r] ∈ B[L])
Proof
Definitions occuring in Statement :
cocons: cocons(a;L),
conil: conil(),
co-list-islist: co-list-islist(T),
list_ind: list_ind,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
nil: [],
it: ⋅,
conil: conil(),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
cons: [a / b],
cocons: cocons(a;L),
implies: P ⇒ Q,
so_apply: x[s1;s2;s3]
Lemmas referenced :
co-list-islist-ext-list,
list_ind-general-wf,
subtype_rel_dep_function,
co-list-islist_wf,
list_wf,
ext-eq_inversion,
subtype_rel_weakening,
cocons_wf,
conil_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
applyEquality,
instantiate,
cumulativity,
hypothesis,
sqequalRule,
lambdaEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
functionEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:co-list-islist(A) {}\mrightarrow{} Type]. \mforall{}[L:co-list-islist(A)]. \mforall{}[x:B[conil()]].
\mforall{}[F:a:A {}\mrightarrow{} L:co-list-islist(A) {}\mrightarrow{} B[L] {}\mrightarrow{} B[cocons(a;L)]].
(rec-case(L) of
[] => x
h::t =>
r.F[h;t;r] \mmember{} B[L])
Date html generated:
2016_05_15-PM-10_11_08
Last ObjectModification:
2015_12_27-PM-05_58_45
Theory : eval!all
Home
Index