Nuprl Lemma : has-value-last-list
∀[l:Base]. l ∈ Top List supposing (last(l))↓
Proof
Definitions occuring in Statement :
last: last(L),
list: T List,
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
last: last(L),
select: L[n],
implies: P ⇒ Q,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
prop: ℙ,
subtract: n - m,
not: ¬A,
false: False
Lemmas referenced :
bottom_diverge,
int-value-type,
has-value_wf_base,
base_wf,
subtype_rel_list,
stuck-spread,
top_wf,
product-value-type,
value-type-has-value,
has-value-implies-dec-ispair-2,
list-if-has-value-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
independent_functionElimination,
callbyvalueSpread,
hypothesis,
isectElimination,
because_Cache,
lambdaEquality,
unionElimination,
callbyvalueLess,
baseApply,
closedConclusion,
baseClosed,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
callbyvalueCallbyvalue,
callbyvalueReduce,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
callbyvalueAdd
Latex:
\mforall{}[l:Base]. l \mmember{} Top List supposing (last(l))\mdownarrow{}
Date html generated:
2016_05_14-AM-07_42_06
Last ObjectModification:
2016_01_15-AM-08_41_53
Theory : list_1
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