Nuprl Lemma : nth_tl_wf
∀[A:Type]. ∀[as:A List]. ∀[i:ℤ]. (nth_tl(i;as) ∈ A List)
Proof
Definitions occuring in Statement :
nth_tl: nth_tl(n;as),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
implies: P ⇒ Q,
false: False,
guard: {T},
uimplies: b supposing a,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
exists: ∃x:A. B[x],
sq_type: SQType(T),
assert: ↑b
Lemmas referenced :
list_wf,
decidable__le,
nat_wf,
le_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_int_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert_of_le_int,
tl_wf,
not-le-2,
minus-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
cumulativity,
universeEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
hypothesis_subsumption,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
intWeakElimination,
lambdaFormation,
independent_isectElimination,
independent_functionElimination,
voidElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
voidEquality,
minusEquality,
equalityElimination,
dependent_pairFormation,
promote_hyp,
instantiate
Latex:
\mforall{}[A:Type]. \mforall{}[as:A List]. \mforall{}[i:\mBbbZ{}]. (nth\_tl(i;as) \mmember{} A List)
Date html generated:
2017_04_14-AM-08_34_25
Last ObjectModification:
2017_02_27-PM-03_22_08
Theory : list_0
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