Nuprl Lemma : conil_wf
∀[A:Type]. (conil() ∈ co-list-islist(A))
Proof
Definitions occuring in Statement :
conil: conil(),
co-list-islist: co-list-islist(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
conil: conil(),
co-list-islist: co-list-islist(T),
prop: ℙ,
it: ⋅,
subtype_rel: A ⊆r B,
has-value: (a)↓,
is-list: is-list(t),
btrue: tt
Lemmas referenced :
has-value-is-list-of-co-list,
istype-universe,
it_wf,
unit_subtype_colist,
has-value_wf_base,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
dependent_set_memberEquality_alt,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
applyEquality,
divergentSqle,
sqleReflexivity,
baseClosed
Latex:
\mforall{}[A:Type]. (conil() \mmember{} co-list-islist(A))
Date html generated:
2019_10_16-AM-11_38_48
Last ObjectModification:
2018_12_08-PM-00_22_51
Theory : eval!all
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