Nuprl Lemma : non_neg_length
∀[A:Type]. ∀[l:A List].  (||l|| ≥ 0 )
Proof
Definitions occuring in Statement : 
length: ||as||
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
ge: i ≥ j 
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
ge: i ≥ j 
, 
le: A ≤ B
, 
and: P ∧ Q
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
top: Top
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
subtract: n - m
, 
subtype_rel: A ⊆r B
, 
true: True
Lemmas referenced : 
list_induction, 
ge_wf, 
length_wf, 
list_wf, 
length_of_nil_lemma, 
false_wf, 
length_of_cons_lemma, 
decidable__le, 
not-ge-2, 
condition-implies-le, 
minus-add, 
minus-one-mul, 
zero-add, 
minus-one-mul-top, 
add-associates, 
add-swap, 
add-commutes, 
add_functionality_wrt_le, 
add-zero, 
le-add-cancel, 
less_than'_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
hypothesis, 
natural_numberEquality, 
independent_functionElimination, 
independent_pairFormation, 
lambdaFormation, 
rename, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
addEquality, 
unionElimination, 
productElimination, 
independent_isectElimination, 
applyEquality, 
intEquality, 
because_Cache, 
minusEquality, 
independent_pairEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}[l:A  List].    (||l||  \mgeq{}  0  )
Date html generated:
2016_05_14-AM-06_33_01
Last ObjectModification:
2015_12_26-PM-00_37_49
Theory : list_0
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