Nuprl Lemma : map-index_wf
∀[A,B:Type]. ∀[L:A List]. ∀[f:ℕ||L|| ⟶ {a:A| (a ∈ L)} ⟶ B]. (map-index(f;L) ∈ B List)
Proof
Definitions occuring in Statement :
map-index: map-index(f;L),
l_member: (x ∈ l),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
map-index: map-index(f;L),
prop: ℙ,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
map-index_aux_wf,
l_member_wf,
list-subtype,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
zero-add,
length_wf,
length_wf_nat,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesisEquality,
hypothesis,
cumulativity,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
instantiate,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:A List]. \mforall{}[f:\mBbbN{}||L|| {}\mrightarrow{} \{a:A| (a \mmember{} L)\} {}\mrightarrow{} B]. (map-index(f;L) \mmember{} B List)
Date html generated:
2016_05_14-PM-03_12_48
Last ObjectModification:
2015_12_26-PM-01_46_48
Theory : list_1
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