Nuprl Lemma : member-co-list-islist
∀[T:Type]. ∀[L:colist(T)]. L ∈ co-list-islist(T) supposing (is-list(L))↓
Proof
Definitions occuring in Statement :
co-list-islist: co-list-islist(T),
is-list: is-list(t),
colist: colist(T),
has-value: (a)↓,
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,
bool: 𝔹,
prop: ℙ,
co-list-islist: co-list-islist(T)
Lemmas referenced :
is-list-wf-co-list,
has-value_wf-partial,
bool_wf,
union-value-type,
unit_wf2,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:colist(T)]. L \mmember{} co-list-islist(T) supposing (is-list(L))\mdownarrow{}
Date html generated:
2019_10_16-AM-11_38_26
Last ObjectModification:
2018_09_26-PM-09_35_02
Theory : eval!all
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