Nuprl Lemma : has-value-is-list-of-co-list
∀[T:Type]. ∀[t:colist(T)]. ((is-list(t))↓ ∈ ℙ)
Proof
Definitions occuring in Statement :
is-list: is-list(t),
colist: colist(T),
has-value: (a)↓,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bool: 𝔹
Lemmas referenced :
has-value_wf-partial,
bool_wf,
union-value-type,
unit_wf2,
is-list_wf,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
cumulativity,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. ((is-list(t))\mdownarrow{} \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_10_05
Last ObjectModification:
2015_12_27-PM-05_58_58
Theory : eval!all
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