Nuprl Lemma : last_wf
∀[T:Type]. ∀[L:T List]. last(L) ∈ T supposing ¬↑null(L)
Proof
Definitions occuring in Statement :
last: last(L),
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
last: last(L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
implies: P ⇒ Q,
true: True,
false: False,
cons: [a / b],
top: Top,
bfalse: ff,
guard: {T},
nat: ℕ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
prop: ℙ
Lemmas referenced :
select_wf,
subtract_wf,
length_wf,
subtract_nat_wf,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
istype-void,
null_cons_lemma,
length_wf_nat,
decidable__le,
istype-false,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
istype-int,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
decidable__lt,
not-lt-2,
add-mul-special,
zero-mul,
le-add-cancel-alt,
not_wf,
assert_wf,
null_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
independent_functionElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :isect_memberEquality_alt,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
setElimination,
rename,
addEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
Error :lambdaEquality_alt,
minusEquality,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. last(L) \mmember{} T supposing \mneg{}\muparrow{}null(L)
Date html generated:
2019_06_20-PM-00_40_42
Last ObjectModification:
2018_10_06-AM-11_20_39
Theory : list_0
Home
Index