Nuprl Lemma : is-list-wf-co-list
∀[T:Type]. ∀[t:colist(T)]. (is-list(t) ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
is-list: is-list(t),
colist: colist(T),
partial: partial(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-list: is-list(t),
uimplies: b supposing a,
bool: 𝔹,
top: Top,
so_lambda: λ2x.t[x],
is-list-fun: is-list-fun()
Lemmas referenced :
fixpoint-induction-bottom,
bool_wf,
colist_wf,
partial_wf,
union-value-type,
unit_wf2,
bool-mono,
strictness-apply,
bottom_wf-partial,
is-list-fun_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
functionEquality,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
because_Cache,
functionExtensionality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. (is-list(t) \mmember{} partial(\mBbbB{}))
Date html generated:
2016_05_15-PM-10_09_57
Last ObjectModification:
2015_12_27-PM-05_59_06
Theory : eval!all
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