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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