Nuprl Lemma : l-last_wf
∀[T:Type]. ∀[L:T List]. l-last(L) ∈ T supposing ¬↑null(L)
Proof
Definitions occuring in Statement :
l-last: l-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 :
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,
l-last: l-last(l),
l-last-default: l-last-default(l;d),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
prop: ℙ
Lemmas referenced :
list-cases,
null_nil_lemma,
product_subtype_list,
null_cons_lemma,
list_ind_cons_lemma,
list_ind_wf,
list_wf,
not_wf,
assert_wf,
null_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
independent_functionElimination,
natural_numberEquality,
voidElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidEquality,
applyEquality,
functionEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. l-last(L) \mmember{} T supposing \mneg{}\muparrow{}null(L)
Date html generated:
2016_05_14-AM-07_41_45
Last ObjectModification:
2015_12_26-PM-02_51_25
Theory : list_1
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