Nuprl Lemma : is-list_wf
∀[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,
colist: colist(T),
is-list: is-list(t),
uimplies: b supposing a,
bool: 𝔹,
so_lambda: λ2x.t[x],
so_apply: x[s],
has-value: (a)↓,
unit: Unit,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
pi2: snd(t),
subtype_rel: A ⊆r B
Lemmas referenced :
fix_wf_corec-partial1,
bool_wf,
union-value-type,
unit_wf2,
bool-mono,
b-union_wf,
list-functor,
value-type-has-value,
bunion-value-type,
equal-value-type,
product-value-type,
btrue_wf,
inclusion-partial,
partial_wf,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
lambdaEquality,
productEquality,
hypothesisEquality,
universeEquality,
isect_memberEquality,
callbyvalueReduce,
intEquality,
natural_numberEquality,
imageElimination,
productElimination,
unionElimination,
equalityElimination,
applyEquality,
cumulativity,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. (is-list(t) \mmember{} partial(\mBbbB{}))
Date html generated:
2016_05_15-PM-10_07_29
Last ObjectModification:
2015_12_27-PM-06_00_56
Theory : eval!all
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