Nuprl Lemma : listp_properties
∀[A:Type]. ∀[l:A List+]. (||l|| ≥ 1 )
Proof
Definitions occuring in Statement :
listp: A List+,
length: ||as||,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
listp: A List+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
and: P ∧ Q,
cons: [a / b],
top: Top,
implies: P ⇒ Q,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
prop: ℙ,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_stable: SqStable(P),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__le,
false_wf,
not-ge-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
equal_wf,
less_than'_wf,
length_wf,
set_wf,
list_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
lambdaFormation,
natural_numberEquality,
addEquality,
independent_pairFormation,
independent_functionElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
applyEquality,
lambdaEquality,
intEquality,
because_Cache,
minusEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairEquality,
cumulativity,
axiomEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List\msupplus{}]. (||l|| \mgeq{} 1 )
Date html generated:
2017_04_17-AM-07_30_48
Last ObjectModification:
2017_02_27-PM-04_08_11
Theory : list_1
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