Nuprl Lemma : ml-length_wf
∀[T:Type]. ∀[l:T List]. (ml-length(l) ∈ ℕ) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
ml-length: ml-length(l),
list: T List,
nat: ℕ,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
ml-length-sq,
length_wf_nat,
list_wf,
valueall-type_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
cumulativity,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. (ml-length(l) \mmember{} \mBbbN{}) supposing valueall-type(T)
Date html generated:
2017_09_29-PM-05_50_54
Last ObjectModification:
2017_05_10-PM-05_13_20
Theory : ML
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